Optical Communications

Telecommunications and Information Technology

Alberto Paradisi Rafael Carvalho Figueiredo Andrea Chiuchiarelli Eduardo de Souza Rosa Editors

Optical Communications Advanced Systems and Devices for Next Generation Networks

Telecommunications and Information Technology Series editor Alberto Paradisi, Vice President Research and Development, Campinas, São Paulo, Brazil

Telecommunications and Information Technology is an official book series of the Brazilian Center for Research and Development (CPqD). It publishes scientific monographs on a varied array of topics or themes in telecommunications and information technology, mainly on topics under research and development at CPqD: optical and wireless communications, sensors, cognitive and advanced computing, information security, embedded systems, smart grid, energy storage, and operation support systems. The topics are in line with current modern-day trends: broadband, smart grid, future banking, smart cities, defense and security.

More information about this series at http://www.springer.com/series/14176

Alberto Paradisi Rafael Carvalho Figueiredo Andrea Chiuchiarelli Eduardo de Souza Rosa •

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Editors

Optical Communications Advanced Systems and Devices for Next Generation Networks

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Editors Alberto Paradisi Centro de Pesquisa e Desenvolvimento em Telecomunicações (CPqD) Campinas, São Paulo, Brazil Rafael Carvalho Figueiredo Optical Technologies Division Centro de Pesquisa e Desenvolvimento em Telecomunicações (CPqD) Campinas, São Paulo, Brazil

Andrea Chiuchiarelli Department of Electronic Engineering Universidade Federal de Minas Gerais (UFMG) Belo Horizonte, Minas Gerais, Brazil Eduardo de Souza Rosa Optical Technologies Division Centro de Pesquisa e Desenvolvimento em Telecomunicações (CPqD) Campinas, São Paulo, Brazil

ISSN 2365-564X ISSN 2365-5658 (electronic) Telecommunications and Information Technology ISBN 978-3-319-97186-5 ISBN 978-3-319-97187-2 (eBook) https://doi.org/10.1007/978-3-319-97187-2 Library of Congress Control Number: 2018950212 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Foreword

Telecommunication systems are unique in the range of distances over which their relevant processes take place. This was already true in the middle of last century, when centimetric devices such as vacuum tubes would process signals to be transmitted over a few kilometers over metallic cables, thus integrating processes occurring over a range of five orders of magnitude in reach. Nowadays, this range has increased by at least ten orders of magnitude, as some processes occur over nanometric structures such as quantum dots; and signals may reach thousands of kilometers on Earth and even millions of kilometers in interplanetary communications. The evolution of telecom systems is then closely associated with scientific advances on two of the most challenging frontiers of human knowledge: the realms of the very small and the very large. Optical communication has played a crucial role to make this feasible, integrating electrons and photons into the same networking architectures to reach the end of achieving ever-increasing information rates over longer and longer reaches to an ever-increasing number of hubs and nodes. The concurrent evolution of wireless systems has taken these high volumes of information to mobile users, upgrading the Internet from a primitive “best effort” network interconnecting academic users into a de facto,—if not yet de jure,—evolving public utility. Public utilities are typically devoted to the universal delivery of some products considered essential to a modern, productive life style, such as water and electricity. While certainly open to innovations, traditional utilities are evaluated by their ability to provide a reliable supply of their deliverable, so as to sustain a sound living standard. While the Internet has become as indispensable to modern living as other public utilities, its deliverable is innovation itself, so its role is the transformation of the living and working standards, rather than their static support. For this reason, the Internet is a new entity in itself, challenging our perception of the benefits and pitfalls of its everlasting ubiquity. The emerging Internet of Things (IoT) opens up the opportunity of connecting devices in a networking environment that will potentialize their interaction with humans, embedding us into superstructures such as smart cities, smart transportation systems, etc., which will in turn change the scope and capabilities of the v

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devices themselves and the way we move, work, and live. In addition, new communication standards, such as the emerging 5G technology, will enhance the naturalness of the communication environments delivered by the Internet. If successful, these developments will certainly reinforce the current trends of working and living online. The amount of traffic generated by such new applications as they are adopted by an increasing number of users is bound to intensify the compound annual growth rate (CAGR) of traffic in the communication networks, which has been around 40% per year since the turn of the century, when Internet traffic became dominant in the communication networks. This rate doubles the traffic every 2 years, thus multiplying it by a factor of one thousand in 20 years. Fortunately, the advent of WDM technology in the 1990s meant that fibers that were then supporting one wavelength could now support a hundred wavelengths in the 4–5 THz gain bandwidth of the erbium-doped fiber amplifiers (EDFAs), or a few hundreds if other amplifiers are added in neighboring spectral windows. This has started a two-decade period of fierce “bandwidth mining”, characterized by growing occupation of the erbium bandwidth by an increasing number of more and more closely spaced wavelengths. Together with the fast developments in lasers and electronics that allowed for a 10-fold increase in the modulation rate, the fiber plant of the year 2000 was ready to absorb the 1000-fold increase in traffic predicted for the first two decades of the new century. As we approach the third decade, though, we are now facing the prospect of a capacity crunch. Its implications are expected to be profound, as resource over-provisioning will not be taken for granted anymore under the impending crunch. Since over-provisioning has been central to the quality delivery of best effort services up to now, its cessation is bound to hinder the quality of such services in the presence of other ones with more stringent, contractually agreed availability and other QoS requirements. This prospect has intensified the debate about network neutrality, one of the founding principles of the Internet, as it seems to be under threat. Even though this discussion is currently taken by business and government stakeholders that seem to be unaware of the complexities of a multiservice infrastructure, mitigating the societal and economic threats posed by the capacity crunch will actually be an engineering challenge that needs to be faced in due time with proper network management tools. As of today, though, the main engineering challenge is the postponement of the capacity crunch. The bandwidth mining effort launched two decades ago has been successful in occupying the multi-THz bandwidth of the erbium amplifiers, albeit not necessarily in a spectrally efficient way, as spectral bandwidth was not regarded as a scarce resource in the optical fiber. Hence, the timely challenge of upgrading the spectral efficiency of the network, in order to extract more bits per second from each Hz of the fiber spectral bandwidth. In metropolitan areas, where most of the traffic growth is concentrated and many links are much shorter than the maximal network reach, there is more room for such upgrade. This drives the emerging need for distance adaptiveness in the node equipment in order to exploit this opportunity.

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These new challenges cannot be met without the deployment of new technologies. Among them, optical coherent detection and advanced digital signal processing stand as decisive to support phase and polarization state detection, respectively, thus adding two new dimensions to be exploited to convey more information within the same bandwidth, when compared with plain old, spectrally inefficient direct detection on intensity modulated signals that has been used for “bandwidth mining” purposes since the birth of optical communications. When noise immunity is a limiting factor in the presence of nonlinearities as in optical fibers, adding new dimensions to the signal space is the foremost strategy to increase the spectral efficiency, before resorting to multilevel formats that would come with higher noise penalties. This book provides a representative collection of chapters that discuss these emerging technologies and their application in optical communication networks to transport current and emerging IP traffic. They approach the state of the art of several critical applications for next-generation communication networks to support the increasing rates of increasingly heterogeneous traffic. It addresses the challenging need to promote the understanding of the state of the art as it evolves, thus filling a critical gap between the classical textbook that normally discusses mature, steady technologies and the short paper that discusses a specific contribution to the state of the art, which is assumed to be known by the reader. I therefore congratulate the editors and authors for this worthy editorial endeavor. Campinas, Brazil April 2018

Helio Waldman Professor Colaborador DECOM/FEEC/UNICAMP

Preface

Optical communications are essential to meet the current and future demands of global data traffic. Efforts to achieve higher data rates, higher transmission distance, more robust digital signal processing, and more efficient devices have boosted the research in different fields of fiber-optic communications. This book aims to present state-of-the-art techniques and results from research activities conducted at CPqD and in partner institutions, namely University of Sao Paulo (USP) and University of Campinas (Unicamp). The book is structured in eleven chapters, focusing on coherent and noncoherent transmission, digital signal processing techniques, and photonic devices. The first two Chapters “Multilevel Pulse Amplitude Modulation Transmissions for Data Center Applications” and “Ultrafast Electro-Optical Switches Based on Semiconductor Optical Amplifiers”, address intensity modulation–direct detection (IM-DD) transmission and switching techniques for data center applications. Chapters “Coherent Optical Access Networks” and “High-Capacity Unrepeatered Optical Transmission”, focus on coherent modulation formats and their applications in different system scenarios, from optical access networks to longer distances, featuring transmission records achieved in unrepeatered transmissions. The following chapters are devoted to digital processing techniques for mitigation of nonlinear effects in coherent optical systems (Chapter “Impact of Nonlinear Effects and Mitigation on Coherent Optical Systems”), for power consumption reduction and performance enhancement in higher order modulation transmission (Chapter “High-Order Modulation Formats for Future Optical Communication Systems”), error correcting codes (Chapter “Soft-Decision Forward Error Correction in Optical Communications”), and details on the implementation of all-optical orthogonal frequency-division multiplexing (Chapter “Challenges Towards a CostEffective Implementation of Optical OFDM”). Finally, the last three chapters highlight the advances in the field of photonic devices, showing details on the development of fundamental components of an optical system, such as lasers (Chapter “Narrow Linewidth and Compact External-Cavity Lasers for Coherent Optical Communications”), optical amplifiers for submarine applications (Chapter “Photonic Devices for Submarine Optical ix

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Amplifiers”), and passive and active components for silicon photonic integrated circuits (Chapter “Optical Devices in Silicon Photonics”). We, the editors, would like to thank the authors and reviewers of this book. We also would like to specially thank Prof. Helio Waldman for honoring us with a delightful Foreword. Finally, we would like to thank you readers. We really hope you enjoy reading this book as much as we appreciate editing it. Campinas, Brazil

Alberto Paradisi Andrea Chiuchiarelli Eduardo de Souza Rosa Rafael Carvalho Figueiredo

Contents

Multilevel Pulse Amplitude Modulation Transmissions for Data Center Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rafael Carvalho Figueiredo, André L. N. Souza, Stenio M. Ranzini and Andrea Chiuchiarelli Ultrafast Electro-Optical Switches Based on Semiconductor Optical Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tiago Sutili, Rafael Carvalho Figueiredo, Bruno Taglietti, Cristiano M. Gallep and Evandro Conforti

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Coherent Optical Access Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Andrea Chiuchiarelli and Sandro M. Rossi

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High-Capacity Unrepeatered Optical Transmission . . . . . . . . . . . . . . . . Sandro M. Rossi, João C. S. S. Januário, José Hélio da C. Júnior, Andrea Chiuchiarelli and André L. N. Souza

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Impact of Nonlinear Effects and Mitigation on Coherent Optical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stenio M. Ranzini, Victor E. Parahyba, José Hélio da C. Júnior, Fernando Guiomar and Andrea Carena

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High-Order Modulation Formats for Future Optical Communication Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 André L. N. Souza and José Hélio da C. Júnior Soft-Decision Forward Error Correction in Optical Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Alexandre Felipe and André L. N. Souza

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Challenges Toward a Cost-Effective Implementation of Optical OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Mônica L. Rocha, Rafael J. L. Ferreira, Diego M. Dourado, Matheus M. Rodrigues, Stenio M. Ranzini, Sandro M. Rossi, Fabio D. Simões and Daniel M. Pataca Narrow Linewidth and Compact External-Cavity Lasers for Coherent Optical Communications . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Giovanni B. de Farias, Leandro T. Zanvettor, Hening A. de Andrade, João C. S. S. Januário, Mayara E. Bonani, Maria Chiara Ubaldi, Aldo Righetti, Fausto Meli, Giorgio Grasso and Luis H. H. de Carvalho Photonic Devices for Submarine Optical Amplifiers . . . . . . . . . . . . . . . . 211 Uiara Moura, Giovanni B. de Farias, João C. S. S. Januário, Márcio C. Argentato and Sandro M. Rossi Optical Devices in Silicon Photonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Yesica R. R. Bustamante, Uiara Moura, Henrique F. Santana and Giovanni B. de Farias

About the Editors

Alberto Paradisi holds bachelor’s degree in Electronic Engineering from the Di Genova University (1990), Ph.D. in Electronic Engineering—Di Torin Politecnico (1993), and MBA in Corporate Management by Fundação Getúlio Vargas (2004). He has vast R&D experience, coordination and management in Electrical Engineering, Innovation Management with special focus on Telecom Systems. His main activities include the following areas: modeling and simulation of optical devices and subsystems, data networks and traffic engineering, wavelength division multiplexed (WDM) optical transmission systems, erbium-doped fiber amplification and Raman-type amplification, optical routing technology, performance monitoring of WDM optical networks, ASON/GMPLS control plans, digital processing of optical systems, passive optical networking, OTN networks and advanced Ethernet networks, protection and restoration of optical networks. He has participated in dozens of R&D projects in the area of photonic technology and coordination, as head of the same CPqD group, of all major R&D projects since 2001. He has filed several patent applications with INPI and written over 60 articles in periodicals and national/ international conference proceedings. As the leader of the R&D groups, he has coordinated the transfer of more than 10 technological products to national industries over the last 10 years. He has also participated actively in the conception and creation of Brazilian industries with Já! and BrPhotonics technological foundations. Rafael Carvalho Figueiredo was born in Vinhedo-SP, Brazil, in 1982. He received the Technologist degree in Telecommunications and the M.Sc. and Ph.D. in Electrical Engineering from University of Campinas (Unicamp), Campinas/SP— Brazil, in 2007, 2010, and 2015, respectively. From August 2010 to December 2013, he was Teaching Assistant at School of Technology (Unicamp) and from June 2015 to July 2016, he was a Postdoc Fellow at Department of Communications—School of Electrical and Computer Engineering (Unicamp). Since August 2016, he is a researcher at CPqD, in the Optical Technologies Division. His current areas of interest include optical amplification, high-speed optical communications, optical switching, and semiconductor optical amplifiers.

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Andrea Chiuchiarelli was born in Rome, Italy, on March 4, 1979. He received his BSc degree in Electronic Engineering from the University of L’Aquila, Italy, in 2005, and his PhD in Innovative Technologies from Scuola Superiore S.Anna, Italy, in 2010. From January 2013 to November 2014 he was a visiting post-doc researcher at Unicamp, Campinas, Brazil. From November 2014 to April 2018 he was a senior researcher at CPqD, in the Division of Optical Technologies. He is currently a lecturer at the Department of Electronic Engineering in UFMG (Federal University of Minas Gerais). His main areas of interest are Optical Communication Systems, Coherent Optical Technologies and High-Capacity Optical Data Center Interconnect. Eduardo de Souza Rosa holds a bachelor’s degree (2008) and a master’s degree (2010) in Electrical Engineering from University of Campinas (Unicamp). He is currently a Ph.D. candidate in Electrical Engineering at Unicamp and the head and leader of the Optical Technologies Division at CPqD, the Telecommunications Research and Development Center Foundation. He has experience in Electrical Engineering with emphasis on optical communications systems and signal processing for communications.

Multilevel Pulse Amplitude Modulation Transmissions for Data Center Applications Rafael Carvalho Figueiredo, André L. N. Souza, Stenio M. Ranzini and Andrea Chiuchiarelli

Abstract Four-level pulse amplitude modulation (PAM4) is appearing as an important option for many applications that require optical communications at high data rate for short distances and/or with low complexity, such as Data Center interconnects. In this sense, this chapter aims to evaluate key features requirements for PAM4 transmissions focusing on short-reach DC applications. Therefore, we present a software to emulate PAM4 transmission at a high baud rate (56 GBd) in order to evaluate different configurations and impairments that could affect data transmission in the C-band, namely the digital signal processing (DSP) complexity, bandwidth limitation, chromatic dispersion tolerance, differential group delay (DGD) tolerance, and analog-to-digital converter (ADC) sampling requirements.

1 Introduction Emerging applications on cloud computing, streaming, and Internet of Things (IoT) have a significant impact on data traffic in Data Center (DC) interconnects. According to Cisco’s Global Cloud Index, the “global data center IP traffic will grow threefold over the next 5 years” [1], evidencing the need for immediate solutions to meet the demand while keeping cost and complexity at acceptable levels. In this regard, four-level pulse amplitude modulation (PAM4) appears like a viable solution for intra- and inter-DC scenarios at high data rates [2]. Some recent devices have been focusing on O-band applications [3–5], where chromatic dispersion (CD) is not a critical issue. On the other hand, there are also demonstrations that exploit C-band applications [6–8], where CD—among other impairments—could severely affect transmission, emphasizing the importance of carefully evaluating the behavior and limitations of PAM4 modulation format in the 1550-nm window. With that in mind, in [9], we presented simulated results of bandwidth (BW) and chromatic dispersion (CD) requirement analysis for 56-GBd PAM4 at 1550 nm. Here, an extension of this previous work [9] with a slight different approach will be R. C. Figueiredo (B) · A. L. N. Souza · S. M. Ranzini · A. Chiuchiarelli CPqD, Optical Technologies Division, Campinas, SP 13086-902, Brazil e-mail: [email protected] © Springer Nature Switzerland AG 2019 A. Paradisi et al. (eds.), Optical Communications, Telecommunications and Information Technology, https://doi.org/10.1007/978-3-319-97187-2_1

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presented. CD tolerance and BW limitations are analyzed by considering the total electro-optical filtering imposed at transmitter and receiver sides. Additional parameters are also evaluated, namely the complexity of digital signal processing (DSP), the differential group delay (DGD) tolerance, and the receiver sampling requirements by reducing analog-to-digital (ADC) samples per symbol (SpS), providing an insightful analysis of different parameters involved in PAM4 transmissions. Before presenting the obtained results, Sect. 2 brings some basics on PAM4 transmissions; Sect. 3 describes the optical simulator and the simulations’ details; Sect. 4 shows the simulated results for each analyzed parameter: DSP, BW, CD, DGD, and SpS; Sect. 5 summarizes our main findings and concludes the chapter.

2 A Bit of Background Before entering into the simulated results, this section will address basics of PAM4 signaling, presenting the main characteristics of this kind of modulation, its advantages, and drawbacks. Taking a two-level pulse amplitude modulation as a starting point (PAM2), the information is encoded using lower voltage level to represent binary “0” and higher voltage level to represent binary “1”, as shown in Fig. 1a. In this scenario, also known as nonreturn-to-zero (NRZ) on-off keying (OOK), we have one bit corresponding to each symbol, i.e., the baud rate is equal to the bit rate. The quality of the the transmitted signal can be analyzed at a glance through an eye diagram, as shown in Fig. 1b, which is generated by superimposing repetitive samples of the PAM2 signal. The vertical eye opening is related to the signal amplitude and signal-to-noise ratio (SNR)—higher the opening, better the SNR. Meanwhile, the bit time is related to signal frequency and required bandwidth—shorter the bit time, higher the frequency and higher the required bandwidth. If one wants to increase the capacity of a system, there are some options available: 1. 2. 3. 4.

increasing the signal’s frequency; increasing the number of fibers; increasing the number of channels; increasing the modulation complexity.

Fig. 1 a Amplitude levels (bit pattern) and b eye diagram for PAM2 signaling

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Fig. 2 a Amplitude levels (bit pattern) and b eye diagram for PAM4 signaling

The first option would require a proportional increase in bandwidth, while the other options would require the inclusion or replacement of equipment, resulting in higher cost, complexity, and power consumption. PAM4 is a viable alternative to attend option 4 without a considerable increase in complexity while keeping a direct detection receiver. PAM4 signaling represents each symbol with two bits, using four voltage levels, as presented in Fig. 2a. Therefore, PAM4 doubles the throughput at a same baud rate. Then, comparing it to PAM2, PAM4 offers the advantage of doubling the bit rate at the same bandwidth, but it degrades the SNR, once PAM4 stacks three eye diagrams at a bit time, reducing the vertical eye opening by at least a third, as shown in Fig. 2b [10–12]. Characteristics of PAM4 signaling are suitable for applications that require highcapacity over short distances, making it the option for intra-data center applications, as adopted by the IEEE Ethernet Task Force [13], for different distances (500 m, 2 km, 10 km) and baud rates (26 and 53 GBd). Then, considering the current importance of this modulation format and its application prospects, we simulated PAM4 transmissions at a high data rate (56 GBd = 112 Gb/s) and evaluate the requirements of some key parameters for a proper signal transmission, as will be presented in the next sections.

3 Simulation Environment This section brings details on the optical simulator employed during the analysis for high-rate PAM4 transmissions. First, the optical simulator blocks will be presented followed by a description of the methods applied to carry out the simulations.

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Fig. 3 Block diagram of the transmitter side of the optical simulator. The sinc pulse is represented in time domain and the Bessel/Gaussian filters are in the frequency domain. PRBS: pseudo-random bit sequence. NRZ: nonreturn-to-zero. RC: raised cosine. DAC: digital-to-analog converter. MZM: Mach–Zehnder modulator

3.1 Optical Simulator The optical simulator was built on Octave [14] (a free software under the GNU General Public License) to numerically model the signal behavior of the optical communication system: transmitter, channel (optical fiber), and receiver. Figure 3 shows the block diagram of the transmitter side. Two pseudo-random bit sequences (PRBS) with 218 transmitted bits are generated and mapped onto the four-level symbols of the PAM4 signal. The signal is upsampled to two samples per symbol and shaped using a NRZ or a raised cosine (RC) pulse format. A digital-toanalog (DAC) block converts the signal from an 8-bit resolution to analog domain by upsampling it to 32 samples per symbol. A fifth-order low-pass Bessel filter emulates the DAC’s bandwidth limitation. The signal modulates a continuous-wave (CW) laser with power of 12 dBm and linewidth of 100 kHz using an ideal (zero-chirp) Mach– Zehnder modulator (MZM) [15]. Figure 4 illustrates the optical channel and the receiver side of the optical simulator. The output of the transmitter is amplified by a booster, in which the noise figure can be controlled in order to sweep the optical signal-to-noise ratio (OSNR) of the simulation. The model for optical fiber propagation takes into account only the chromatic dispersion effect, according to [16]:

Fig. 4 Representation of the optical channel and block diagram of the receiver side of the optical simulator. The Gaussian/Bessel filter are represented in the frequency domain. ADC: analog-todigital converter. CMA: constant modulus algorithm. RDE: radius directed equalization. LMS: least mean square. DSP: digital signal processing

Multilevel Pulse Amplitude Modulation Transmissions for Data Center Applications

E(z, ω) = E(0, ω)exp(iβ2 ω 2 z/2)

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where E(z, ω) is the Fourier transform of the signal propagating along the fiber at a position z, ω is the angular frequency of the signal, and β2 is the group velocity dispersion (GVD) parameter. At the receiver side, a photodetector (PD) converts the optical signal to the electrical domain. A Gaussian filter emulates the devices’s bandwidth limitation. The ADC converts the analog electrical signal to an 8-bit resolution digital signal by downsampling it to two samples per symbol, i.e., the reverse operation of the DAC. A fifth-order low-pass Bessel filter emulates the ADC’s bandwidth limitation. In the digital domain, the digital signal processing (DSP) is composed by three adaptive filter: constant modulus algorithm (CMA) [17], radius directed equalization (RDE) [16], and least mean square (LMS) [18]. CMA is a blind non-data-aided (NDA) algorithm. It is based on the constant modulus criteria proposed to equalize modulated signals with constant modulus. This algorithm works with a closed eye diagram which is the initial condition of the received signal. Nevertheless, the PAM4 signal does not have a constant modulus, so the equalization is penalized. The RDE is employed to work around this problem. The RDE algorithm is similar to CMA, but each set of symbols is decided by the closest radius, ideal for a multilevel constellation. The RDE algorithm does not work with a closed eye. In this case, the CMA is used as the initialization processes of the RDE in order to achieve a better equalization. Next, the LMS uses the Wiener criteria to minimize the mean square error between the output of the equalization filter and a reference. The reference is obtained by deciding the output of the equalization filter and using it as a reference. In this way, the algorithm is NDA, but is necessary to have an input signal with high signal-to-noise ratio (SNR) in order to make the decision of the symbol as correct as possible. To satisfy the high SNR requirement, the LMS is initialized using the coefficients achieved by the RDE. It is worth to highlight that all the algorithms presented here use the same finite impulse response (FIR) filter structure. They only determine what is the value of the coefficients that will be used in the equalization. After the equalization stage, the signal is decided and the bit error ratio (BER) is calculated.

3.2 Method By employing the optical simulator described in the subsection above (Sect. 3.1), we analyzed some key parameters in transmissions using PAM4 at a baud rate of 56 GBd (112 Gbps). In a previous work [9], we investigate bandwidth limitations and chromatic dispersion tolerance by imposing BW constraints at transmitter and receiver side components individually, namely DAC, MZM, ADC, and PD. In this chapter, we took a slightly different approach, replacing the filtering imposed by those components by a unique electro-optical filter at each side (Tx and Rx). Figure 5 shows the signal spectrum and the filtering imposed by components at transmitter side: DAC (dashed green line), represented by a fifth-order low-pass Bessel filter, and

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Fig. 5 Optical signal spectrum and bandwidth filtering imposed by components at transmitter side: DAC (dashed green line), MZM (dotted light blue line), and EO filter (solid red line)

MZM (dotted light blue line), represented by a fourth-order low-pass Gaussian filter. By combining these two components, we have an electro-optical (EO) filter (solid red line), whose behavior could be approximated by a second-order Gaussian filter. Therefore, in order to evaluate the total bandwidth limitation imposed at transmitter side, we replaced the DAC and MZM filter by the EO filter. At the receiver side, ADC and PD filtering were also replaced by a second-order low-pass Gaussian filter, representing the total BW limitation imposed by these components. The optical simulator was previously calibrated [9] based on experimental results obtained earlier [19]. As shown in Fig. 6, we reached a good match between experimental (dashed blue line with empty squares) and simulated results (dashed blue line with empty circles). Now, we included the results obtained when the transmitter and receiver side components are replaced by the EO filters (solid red line with filled circles). The latter results, with the combined filters, reach a floor before a BER of 10−4 , but still presenting a good agreement between experimental and simulated results. The results presented in Fig. 6 were obtained setting the optical simulator with the parameters listed in Table 1. Then, we employed this new simulation environment—with EO filter at Tx and Rx—to investigate the requirements of PAM4 transmissions focusing on DC applications, by evaluating the following parameters: 1. Digital Signal Processing Complexity: varying the number of taps of the adaptive equalizers. 2. Bandwidth Limitation: narrowing the EO filters at transmitter and receiver sides.

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Fig. 6 Experimental results [19] (empty squares) compared to earlier calibration [9] (empty circles) and to new results using combined filters (filled circles) Table 1 Simulation parameters Parameter Modulation format Symbol rate (Rs ) Pulse format Laser power Laser linewidth MZM Vπ MZM extinction ratio MZM insertion loss Transmitter side bandwidth Fiber length Fiber dispersion Receiver side bandwidth DSP filters’ taps (baseline)

Value PAM4 56 Gbaud NRZ 12 dBm 100 kHz 3.75 V 20 dB 11 dB Variable (baseline at 56 GHz) Variable (baseline at B2B) 16.5 ps nm km Variable (baseline at 56 GHz) 14 (CMA), 14 (RDE), 26 (LMS)

3. Chromatic Dispersion Tolerance: extending the distance of propagation (fiber length) with and without BW restrictions. 4. Differential Group Delay Tolerance: increasing the delay time between the two different polarizations at the receiver. 5. Receiver Sampling Requirements: reducing the samples per symbol (SpS) at ADC to values below two samples per symbol.

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4 Requirements Analysis This section presents simulated results for each analyzed parameter, preceded by a brief overview of the importance and impact of the parameter on the system. All results are presented as a relation between optical signal-to-noise ratio (OSNR) and bit error rate (BER). The penalties imposed by each parameter are analyzed considering the baseline value at Hard-FEC (forward error correction) BER reference of 3.8 × 10−3 , considering overhead of 7%.

4.1 Digital Signal Processing Complexity Due to signal deterioration, DSP is essential for signal recovery in current optical networks. DSP complexity is related to the number of taps of the equalizers—the greater the number of taps, the greater the footprint size and the power consumption. Besides, there is a compromise between DSP complexity and performance, and a greater number of taps will not always result in better performance. As described before, the DSP used in our simulator is composed by three adaptive equalizers at the receiver: CMA, RDE, and LMS. Signal evolution through these equalizers is illustrated in Fig. 7a–d. CMA initializes the equalization of a closed eye received signal. Next, the RDE coefficients initialize the LMS, which minimizes the mean square error to equalize the PAM4 signal levels. Here, the initial number of taps was defined according to the calibration procedure detailed before in Sect. 3.2. Then, our first set of simulations consisted of evaluating DSP complexity according to the number of taps of the algorithms. To do that, we took the calibrated values as our baseline DSP and investigated the results when decreasing and increasing the DSP complexity, according to the following scenarios: • Lower complexity: CMA = RDE = 6 taps, LMS = 10 taps; • Medium complexity (baseline): CMA = RDE = 14 taps, LMS = 26 taps; • Higher complexity: CMA = RDE = 22 taps, LMS = 42 taps. The obtained results are presented in Fig. 8, in which it is possible to observe that there is a small penalty (around 0.5 dB) between “Scenario 1” and “Scenario 2”, but there is no penalty between “Scenario 2” and “Scenario 3”, i.e., an increase in complexity has no additional effect on performance. During the next simulations, the medium complexity DSP will be employed, since this scenario proved to be enough to recover the transmitted signal without significantly increasing in complexity.

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4.2 Bandwidth Limitation Band-limited channels could induce intersymbol interference (ISI) in the transmitted signal and, above a certain threshold, ISI could compromise the integrity of the received signal. Effects from ISI can be minimized by employing pulse shaping and/or adaptive equalizers [20]. Here, we emulate a system with the adaptive equalizers described in Sect. 3.1 (CMA, RDE, and LMS) but without pulse shaping. The bandwidth (BW) limitations from the transmitter and receiver components are analyzed considering one electrooptical (EO) filter at Tx and another at Rx. Starting from 56 GHz (scenario without BW limitation), the EO filters’ BW are narrowed according to the three following scenarios: • Tx side: narrowing EO filter at transmitter side while keeping the receiver side fixed at 56 GHz (matched filter);

Fig. 7 Received signal a before digital signal processing and its evolution through the equalizers: b constant modulus algorithm (CMA), c radius directed equalization (RDE), and d least mean square (LMS) algorithm

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Fig. 8 Simulated results of DSP complexity ranging the taps of the equalizers at three different scenarios

Fig. 9 Simulated results narrowing BW of EO filters at a transmitter and b receiver sides

• Rx side: narrowing EO filter at receiver side while keeping the transmitter side fixed at 56 GHz; • Both Tx and Rx: narrowing both EO filters (at transmitter and receiver sides). The results obtained when ranging Tx side and Rx side are presented in Fig. 9a and b, respectively. The results indicate that Tx side is more sensible to BW limitations, since at 24 GHz, it is not possible to reach BER values below the HD-FEC threshold (BER = 3.8 × 10−3 ), while at the Rx side, it is possible to work with narrower bandwidth values (18 GHz). The penalties for each scenario, considering 56 GHz as baseline reference at HDFEC limit, are presented in Fig. 10. It is possible to confirm that BW impairments are more severe at the transmitter side, limiting the transmission when the Tx and Rx BW are narrowed together. At the transmitter side, it is possible to narrow the BW down to 28 GHz (half the baud rate) but with a penalty of almost 4.5 dB. Meanwhile, the limit BW value at the receiver side is 18 GHz, with a penalty below 2 dB.

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Fig. 10 Penalties for each bandwidth scenario at BER = 3.8 × 10−3 : ranging Tx-BW (empty squares), Rx-BW (empty circles), both Tx and Rx (filled triangles)

4.3 Chromatic Dispersion Tolerance Chromatic dispersion (CD) arises from the fact that different wavelengths travel at different speed inside the optical fiber, resulting in a pulse spreading that can induce errors at the receiver. Effects from CD become more serious with the distance, since dispersion accumulates during propagation. CD is particularly critical for intensity modulation–direct detection (IM-DD) systems operating in the C-band, limiting the propagation after few kilometers. Therefore, it is extremely important to evaluate the restrictions imposed by CD on PAM4 transmissions at high data rate in 1550 nm and to employ CD compensation techniques whenever necessary. As detailed in Sect. 3.1, the optical simulator considers only the linear effects from chromatic dispersion, allowing us to isolate limitations imposed by this parameter and evaluate the CD tolerance when propagating the signal into the fiber. At first, we evaluated a scenario without bandwidth limitation (Tx and Rx at 56 GHz), ranging the fiber length from 0 km (back-to-back, B2B) up to 4 km, getting the results presented in Fig. 11a. Next, we imposed a bandwidth restriction both at transmitter and receiver sides by reducing the filters by a half (28 GHz), resulting in more severe limitations, as shown in Fig. 11b. Without bandwidth limitation, it is possible to propagate the signal at a maximum distance of 3 km, considering the HD-FEC threshold (BER = 3.8 × 10−3 ). With bandwidth limitation, the maximum distance is reduced to 2 km and with considerable higher penalties in BER. The penalties for the two scenarios (without and with BW limitations) are presented in Fig. 12, with respect to the B2B scenario without BW restriction at a BER of 3.8 × 10−3 as baseline reference. As the required OSNR values are higher for half-BW scenario (around 35 dB for B2B), it already starts with

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Fig. 11 Simulated results of chromatic dispersion tolerance ranging fiber length from 0 km (B2B scenario) up to 4 km at a 56 GHz and b 28 GHz Fig. 12 Penalties for CD tolerance at BER = 3.8 × 10−3 with (filled circles) and without (filled squares) bandwidth restrictions

a penalty of almost 5 dB, since the B2B required OSNR for the scenario without BW limitation is 30 dB. Such results indicate that intra-DC applications distances (100 m–2 km) can be attained with uncompensated PAM4 transmissions at 112 Gbps. However, the obtained results highlight the importance of a proper CD compensation even at distances of a few kilometers (above 3 km).

4.4 Differential Group Delay Tolerance Due to the fiber birefringence, light can travel at different speeds when the propagating signal is polarized into the X-axis and the Y -axis, resulting in a delay between the two polarized states, called differential group delay (DGD). Pulse spreading due

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Fig. 13 a Simulated results for DGD tolerance ranging delay time between the X-pol and Y -pol axes and b the penalties imposed at the receptor at HD-FEC limit

to DGD should be taken into account to avoid degradation on system performance. Therefore, we investigated the impairments from DGD when splitting the signal into the two axes and inserting a delay (in ps) before combining them at the receiver. Our simulations were carried out at B2B scenario by emulating the delay between axes by ranging the DGD from 0 ps up to 17 ps. The obtained results ranging DGD are presented in Fig. 13a, where it is possible to observe that penalties became significant (greater than 1 dB) after 9 ps of delay between the polarizations. The penalty behavior considering the HD-FEC limit is illustrated in Fig. 13b. DGD is related to the polarization mode dispersion coefficient (PMDcoef ) and distance of propagation (L), according to the following relation [21]: √ DGD = PMDcoef L.

(2)

Therefore, considering our results and a optical fiber with high PMD coefficient, √ 0.5 ps/ km for example, a DGD of 12 ps (penalty of approximately 2 dB) will occur only after 576 km of propagation. Therefore, even with chromatic dispersion compensation, DGD will not be of serious concern in PAM4 transmissions for DC applications.

4.5 Receiver Sampling Requirements When working with NRZ pulse format, DAC sampling rate is not a problem, since it could work at 1 sample per symbol (SpS) using a zero-order-hold approach. On the other hand, at receiver side, the Nyquist sampling theorem states that the signal must be sampled at a rate that is at least two times larger than the signal’s highest frequency,

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Fig. 14 Simulated results of downsampling tolerance ranging sample rate per symbol (SpS) at ADC a from 2 Sps down to 1.2 SpS for B2B scenario and b its penalties at BER = 3.8 × 10−3

in order to capture all the information contained on the continuous signal in the digital domain. The bandwidth of a NRZ signal goes from −Rs to Rs , indicating that the ADC should work at 2Rs or more to satisfy the Nyquist criterion, i.e., at least with two samples per symbol. Narrow-band filtering by devices on the optical and electrical domains allow to loosen the ADC rate requirement and work with less than 2 SpS without significant performance loss. ADCs with lower sampling rates are simpler, cheaper, and more energy efficient than higher rate ones. The relation between the clock frequency of ADCs and power consumption is linear, i.e., a 50% reduction on ADC frequency yields a 50% reduction on power consumption. Consequently, it is desirable that the required ADC sampling rate is as low as possible. In this section, we present the results of an investigation from the effects when working with an ADC with less than 2 SpS and interpolating the signal on the digital domain to 2 SpS for equalization with fractionally spaced equalizers. For a 56 Gbaud signal, it means using sampling rates lower than 112 GSa/s. Figure 14a shows the back-to-back (B2B) performance with ADCs sampling rate varying from 1.2 SpS to 2 SpS in steps of 0.1 SpS (67.2 GSa/s to 112 GSa/s in steps of 5.6 GSa/s). The penalties of the different B2B curves at the hard-FEC BER limit of 3.8 × 10−3 are presented in Fig. 14b. Negligible penalty (≤0.5 dB) occurs when reducing the sample rate down to 1.8 SpS (100.8 GHz), a reduction of 10%. If more penalty is acceptable, then the power consumption and cost of ADCs can be further reduced. As an example, the sampling rate can be reduced by 25% (to 1.5 SpS) if a penalty of 1.5 dB is tolerable.

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5 Conclusions Throughout this chapter, several requirements for 112-Gbps PAM4 transmissions at 1550 nm were evaluated focusing on Data Center interconnects, which is an important topic nowadays driven mainly by the increasing demand due to emerging applications that relies on cloud computing. During the analysis, we could see that: • it is possible to work with an intermediate DSP complexity; • bandwidth limitation is more severe at the transmitter side and it becomes critical for values narrower than half of the transmission rate, i.e., 28 GHz; • chromatic dispersion limits distances greater than 3 km for uncompensated transmissions; • DGD has a significant effect on transmission (penalty above 3 dB) for delays longer than 12 ps and it limits transmission for delays longer than 16 ps; • it is possible to reduce energy consumption when working with an ADC at 1.5 samples per symbol with low-penalty (1.5 dB). Therefore, despite few limitations, four-level pulse amplitude modulation has demonstrated performance consistent with short-reach DC applications requirements at high data rate, where complexity and cost are serious concerns. Acknowledgements The authors thank Jacklyn D. Reis and Luis H. H. Carvalho for their helpful comments. The authors also thank Arley H. Salvador for reviewing a draft of this chapter. This work was partially supported by FUNTTEL/FINEP and by Sao Paulo Research Foundation (FAPESP), grant n.2015/25513-6.

References 1. Cisco (2016) Cisco global cloud index: forecast and methodology, 2015–2020. White Paper 2. Chang F (2017) New paradigm shift to PAM4 signaling at 100/400G for cloud data centers: a performance review. In: ECOC 2017; 43rd European conference on optical communication, pp 1–3 3. Matsui Y, Pham T, Ling W, Schatz R, Carey G, Daghighian H, Sudo T, Roxlo C (2016) 55-GHz bandwidth short-cavity distributed reflector laser and its application to 112-Gb/s PAM-4. In: Optical fiber communication conference postdeadline papers, Optical Society of America, p Th5B.4 4. Kanazawa S, Fujisawa T, Kiyoto Takahata YN, Yamazaki H, Ueda Y, Kobayashi W, Muramoto Y, Ishii H, Sanjoh H (2016) 56-Gbaud 4-PAM (112-Gbit/s) operation of flip-chip interconnection lumped-electrode EADFB laser module for equalizer-free transmission. In: Optical fiber communication conference, Optical Society of America, p W4J.1 5. Zhong K, Zhou X, Wang Y, Huo J, Zhang H, Zeng L, Yu C, Lau APT, Lu C (2017) Amplifierless transmission of 56Gbit/s PAM4 over 60 km using 25 Gbps EML and APD. In: Optical fiber communication conference, Optical Society of America, p Tu2D.1 6. Sadot D, Dorman G, Gorshtein A, Sonkin E, Vidal O (2015) Single channel 112Gbit/sec PAM4 at 56Gbaud with digital signal processing for data centers applications. Opt Express 23(2):991–997

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7. Souza ALN, Figueiredo RC, Júnior JHC, Rossi SM, Chiuchiarelli A (2017) Extended-reach transmission of single-wavelength 112-Gbps PAM4 channel enabled by MLSE for intra data center applications. In: 2017 SBMO/IEEE MTT-S International microwave and optoelectronics conference 8. Kim M, Bae SH, Kim H, Chung YC (2017) Transmission of 56-GB/s PAM-4 signal over 20 km of SSMF using a 1.55-m directly-modulated laser. In: Optical fiber communication conference, Optical Society of America, p Tu2D.6 9. Figueiredo RC, Souza ALN, Ranzini SM, Chiuchiarelli A, Carvalho LHH, Reis JD (2017) Investigation of 56-GBd PAM4 bandwidth and chromatic dispersion limitations for data center applications. In: IMOC 2017; SBMO/IEEE MTT-S International microwave and optoelectronics conference 10. Keysight Technologies (2015) PAM-4 design challenges and the implications on test. Application Note 11. Tektronix (2016) PAM4 signaling in high speed serial technology: test, analysis, and debug. Application Note 12. Anritsu (2016) BER analysis of PAM4 Serdes in 56G, 100G, 200G, and 400G applications. White Paper 13. IEEE (2016) IEEE P802.3bs | 200 Gb/s and 400 Gb/s ethernet task force. http://www.ieee802. org/3/bs/ 14. Eaton JW (2017) GNU Octave. http://www.gnu.org/software/octave/ 15. Seimetz M (2009) High-order modulation for optical fiber transmission, vol 143. Springer, Berlin 16. Savory SJ (2008) Digital filters for coherent optical receivers. Opt Express 16(2):804–817 17. Treichler J, Agee B (1983) A new approach to multipath correction of constant modulus signals. IEEE Trans Acoust Speech Signal Process 31(2):459–472 18. Haykin SS (2008) Adaptive filter theory. Pearson Education India, New Delhi 19. Chiuchiarelli A, Rossi SM, Rozental VN, Simoes GCCP, Carvalho LHH, Oliveira JCRF, Oliveira JRF, Reis JD (2016) 50-GHz+ thin-film polymer on silicon modulator for PAM4 100G-per-wavelength long-reach data center interconnects. In: ECOC 2016; 42nd European conference on optical communication, pp 1–3 20. Chethan B, Ravisimha B, Kurian M (2014) The effects of inter symbol interference (ISI) and FIR pulse shaping filters: a survey. Int J Adv Res Electr Electron Instrum Eng 3(5):9411–9416 21. Ramaswami R, Sivarajan KN (2002) Optical networks: a practical perspective, 2nd edn. Morgan Kaufmann Publishers, Burlington

Ultrafast Electro-Optical Switches Based on Semiconductor Optical Amplifiers Tiago Sutili, Rafael Carvalho Figueiredo, Bruno Taglietti, Cristiano M. Gallep and Evandro Conforti

Abstract This chapter presents results from enhanced semiconductor optical amplifiers based switches to be employed on high-performance applications, which demand ultrafast transition times between operational states together with reduced guard times. A discussion on devices performance is accomplished through experimental characterizations of SOAs’ nonlinear properties and its oscillatory behavior. Switching techniques and mounting schemes are presented to improve switches’ dynamic operation, resulting in rise times below 200 ps and guard times of 650 ps. This performance, when combined with an improved energy efficiency, can offer a viable technical solution for switching in high-rates applications, such as Data Centers and supercomputers.

1 Introduction Semiconductor optical amplifier (SOA) has played different roles in optical communications networks. Its nonlinearities due to carriers’ short lifetime make it less preferable for linear amplification, where erbium-doped fiber amplifier (EDFA) has superior performance. On the other hand, SOA inherently nonlinear behavior combined with its easy integration, wide bandwidth operation, and low fabrication cost make it attractive for several applications, such as wavelength conversion, modulation, optical switching, multiplexing, and optical clock recovery [1, 2]. SOA still finds its place as optical amplifier in O-band applications, as recommended by IEEE 802.3ba-2010 standard [3], where the SOA is employed as a gain element before DEMUX in 100GBASE-ER4 modules, which are developed to attain 30–40 km reach over single mode fiber (SMF) at 1300 nm [4, 5]. More recently, the optimization of fabrication techniques and semiconductor structures resulted in the T. Sutili (B) · B. Taglietti · C. M. Gallep · E. Conforti School of Electrical and Computer Engineering, Department of Communications, University of Campinas, Campinas, SP 13083-852, Brazil e-mail: [email protected] R. C. Figueiredo CPqD, Optical Technologies Division, Campinas, SP 13086-902, Brazil © Springer Nature Switzerland AG 2019 A. Paradisi et al. (eds.), Optical Communications, Telecommunications and Information Technology, https://doi.org/10.1007/978-3-319-97187-2_2

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reduction of SOA nonlinearities, enabling the simultaneous amplification of 250 channels modulated at 64-QAM over an optical bandwidth of 100 nm, comprising S, C, and L bands, adding up to the ultra-wideband amplification of 115.9 Tb/s [6]. At the same time, when it comes to C-band optical switched networks, another promising use of SOA is as optical switch. The increasing data traffic due to emerging applications, like cloud computing and Internet of Things, combined with the increasing demand and video definition of streaming services, will require larger switching capacity for optical interconnects on Data Center (DC) [7, 8]. Since latency includes both propagation and switching times, it is essential to operate with fast and stable switches in DC applications. Extensive research on SOA-based switches has been conducted at the “Optical Communications and Microwave Research Laboratory” (LAPCOM), located at University of Campinas—Brazil. Such research comprises behavior analysis of different commercial devices (linear and nonlinear) and proposals to enhance switching performance through injected pulse optimization and mounting improvements to reduce parasitic elements. This chapter aims to review these studies and serves as guideline for defining the type of SOA and its operation mode according to the desired application. Optimizations on SOA-based switches are proposed, pointing to solutions that can be applied in next-generation networks and Data Centers applications. The rest of the chapter is structured as follows: • • • • • •

Section 2 presents basic background information on SOA-based switches; Section 3 brings results from SOAs dynamic behavior analysis; Section 4 presents a technique to reduce switching time; Section 5 presents a technique to reduce settling time; Section 6 shows mounting optimization to improve switching performance; Section 7 brings a detailed analysis of switching effects on amplitude modulated signals; • Section 8 shows the induced frequency chirp during the on/off switching states; • Section 9 concludes the chapter.

2 Background The SOA is basically a semiconductor laser without a resonant optical cavity. The incident light is amplified as it passes through the active region of the device, which is sandwiched between p-type and n-type layers, through the stimulated emission process driven by an injected electrical current. An amplified spontaneous emission (ASE) noise is added to the output signal during the amplification process [1]. Since this chapter focuses on SOA-based switches, the background section is limited to this matter. An optical switch based on SOA can be configured by setting the amplifier gain through the electrical drive current, switching the device on or off as shown in Fig. 1.

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Fig. 1 Operation of an electrically controlled SOA-based switch: a an electrical current sets the SOAs gain, modulating the b optical input signal, and resulting in a c gated output

The pulses illustrated in Fig. 1 are ideal representations of the switching process. In practice, when an injected current change from state on to off (or vice versa), the photon density takes a nonzero period of time to follow the change of state. Also, due to the energy exchanges between carrier and photons, amplitude oscillations (ringing) will occur at a certain decay rate before the steady state be reached [9]. Amplitude oscillations may induce errors in the receiver by making it difficult to distinguish between the logical high and low levels. The switching rise time is calculated considering 90–10% of the optical power output, the overshoot is calculated as the percentage extrapolating the high level steady state of the optical signal, and the settling time is calculated by the difference between the pulse start and the instant in which the high level reaches the steady state, as illustrated in Fig. 2. The stabilization point characterization depends on the requirements of each application, but usually it is defined as the point where the amplitude oscillations are no longer higher than 5% of its steady-state level, as presented in Sect. 7.

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Fig. 2 Optical response representation highlighting the figures of merit to characterize the switching performance: rise time, overshoot, and settling time

The effects described above can be affected by the waveform of the injected electrical signal and by the physical characteristics of the device. Besides, the switching process can induce distortions in the transmitted signal. All these phenomena that could affect switching performance will be evaluated throughout this chapter.

3 SOA Dynamic Behavior Analysis The SOA operational properties are highly impacted by its constructive characteristics, especially the ones related with its active region geometry and bandgap architecture (i.e., bulk, quantum wire, quantum wells, or quantum dots). In practical terms, these attributes define the device oscillatory behavior, which can be translated in metrics as its rise time, percentage overshoot or settling time, as it will be analyzed in further details in the following sections. In that way, when designing an SOA-based optical space switch, one must analyze and consider the SOA nonlinear behavior, in order to fully understand the device strengths and limitations. This section brings a thorough characterization of four SOAs with different nonlinear properties [10], allowing a deeper understanding of how the device construction affects its performance and the trade-offs that must be considered in order to choose the adequate SOA for each specific application. The experimental setup employed for the proposed characterization is presented in Fig. 3, where the SOA switches a continuous wave optical carrier generated by a semiconductor laser with adjustable output power and wavelength. A variable optical attenuator (VOA) allows the SOA optical output power control, avoiding saturation and amplitude distortions in the photodetection performed by an optical sampling oscilloscope. The acquired signal is averaged to reduce the noise amplitude and then stored for further evaluation through an offline algorithm. The SOA switching is driven by an electrical signal created by combining two synchronized digital signals generated using two ports of the same pulse generator. The first one is composed by a 100-ones sequence followed by 100-zeros in a periodic way, creating 8 ns electrical switching steps, which controls the logical state switch. The second signal, formed by few bits 1s, is synchronized with the first sequence raising edge, creating a pre-

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Fig. 3 Experimental setup employed in order to evaluate the SOA-based spacial switches dynamic behavior performance (© 2015 Wiley. Adapted, with permission, from [10]) Table 1 Characterized SOAs properties and specifications InPhenix CIP-NL CIP-COC Model Packaging Behavior Cavity length Maximum drive current Saturation output power Maximum gain

CIP-XN

IPSAD1503 Packaged Linear 650 µm 350 mA

NL-OEC-1550 Packaged Nonlinear 2 mm 400 mA

NL-OEC-1550 Unpackaged Nonlinear 2 mm 400 mA

XN-OEC-1550 Packaged Ultra nonlinear 2 mm 600 mA

5 dBm

6 dBm

6 dBm

12 dBm

16 dB

34 dB

34 dB

25 dB

impulse to reduce the switch rise time, as presented in Sect. 4 and demonstrated in Fig. 6. Finally, the SOA operating point is controlled by the DC bias current and the electrical switching AC signals amplitudes, which are combined by a bias-T and injected in its active region, where the interaction of electrical and optical carriers will define the device gain and, consequently, the optical output signal power. In order to understand the impact of several constructive factors in the SOA performance, four devices, as specified in Table 1, were selected to be characterized in the proposed comparative analysis. Each of them has a unique set of properties and operational specifications, factors that translate into different linear behaviors, affecting the SOA gain, rise time, and output saturation. The device linearity was defined as a function of its gain fluctuations due to the switching process. However, arising from the intrinsic coupling between optical and electrical carriers, these fluctuations will affect also the optical carrier phase and frequency, as analyzed in Sect. 8. In addition, the SOAs with nonlinear behavior (models NL-OEC-1550) were characterized in their packaged and chip-on-carrier (COC) versions, allowing the inference

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Fig. 4 Characterized SOAs electro-optical conversion response as a function of frequency (© 2015 Wiley. Adapted, with permission, from [10])

from the parasitic elements introduced by the packaging process in the switching performance—a subject that will be further discussed in Sect. 6. The optical carrier is applied to the unpackaged device using microlens-terminated optical fiber and piezoelectric positioning stages [11]. The packaging influence can be noted in the results presented in Fig. 4, where the electro-optical response of the switch is characterized through the analysis of the optical output power as a function of the electrical control signal frequency. The optical power spectra were normalized, allowing a direct comparison of the 3 dB bandwidth of each characterized space switch. To achieve these results, a slightly different experimental setup than the one presented in Fig. 3 was employed, with the substitution of the pulse generator for a sinusoidal generator with constant output power. It is important to highlight in this figure the bandwidth gain attained through the reduction of the mounting parasitic elements, which is made clear by the comparison of the curves related to the unpackaged and encapsulated versions of the nonlinear behavior SOA (i.e., the CIP-COC and CIP-NL, respectively). In practical terms, the device wider bandwidth will be translated in a faster transition and quicker oscillatory behavior stabilization. Both of these factors have directed impact in the reduction of the space switch guard time, as it is presented in Sect. 7. Regarding the SOA switching performance as a function of the AC electrical signals that control its dynamic behavior, two main conclusions arose from the general performance of all characterized devices. First, pre-impulses longer than 960 ps had no significant impact on the switching rise time and induced more drastic overshoots. Next, faster off -on transitions were achieved by applying pre-impulses synchronized simultaneously with the switching step transition from off state to on state, as shown

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(a)

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(b)

Fig. 5 SOA performance as a function of the electrical pre-impulse amplitude in relation with: a the rise time and b the percentage overshoot (© 2015 Wiley. Adapted, with permission, from [10])

Fig. 6 Electrical and optical (compared to the STEP technique) switching pulses employing the PISIC switching technique (© 2002 IEEE. Adapted, with permission, from [13])

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in Fig. 6. Considering these experimental observations, the results presented in Fig. 5 were obtained through the injection of electrical steps with 1 V amplitude and 320 ps pre-impulses. From these results, the trade-off between faster rise times and overshoots amplitude is clear: the greater the pre-impulse amplitude, the greater the overshoot and the faster the rise time. However, excluding the InPhenix (which has linear behavior), the increment in the pre-impulse amplitude seems to have a higher impact increasing the switch overshoot than reducing its rise time. Concerning the comparison between the nonlinear response of each SOA, it is possible to notice that the devices with higher nonlinear behavior presented significantly faster rise times. However, the quicker state transition, once more, resulted in higher overshoots, evidencing the trade-off between the switch response time and oscillatory behavior. A possible solution to this paradigm is provided through the application of multiple impulses during the entire on state switch operation, as it will be detailed in Sect. 5. This comparative analysis shows the importance to carefully define the best operating point and the adequate SOA regarding the specific practical application requirements. More in-depth analyses are presented in the following sections, taking into account other factors that will impact the optical switch performance. However, the results presented here offer an overview that is essential to understand linear and nonlinear phenomena that directly impact the performance of SOA-based switches.

4 Rise Time and PISIC Technique As explained in Sect. 2, an important figure of merit in the evaluation of optical space switches is the time to change from off to on state, which can be defined as its rise time. In practical applications, a shorter rise time can be translated in the possibility to design M × N space switches with improved performance and capable to commute between inputs and outputs in a reduced time period, making it possible to operate in applications requiring ultrashort delays in its dynamic operation. In the specific case of SOA-based space switches, as the SOA is an active optical component, there is a complex dynamic of electrical and optical carriers every time its gain changes, which is in fact exactly the physical process behind its operation as an optical switch. Ideally, this dynamic process is mainly influenced by the finite SOA electrical carriers lifetime [12], which depends intrinsically on the optical input power and carriers density in its active region. However, as it will be discussed in Sect. 6, in commercial devices, the parasitic elements introduced by the SOA packaging have a significant influence on device’s switching velocity and overall performance. The pre-impulse step-injected current (PISIC) is a switching technique introduced by Gallep and Conforti [13] based on the manipulation of the SOA injected current during the switching pulse, allowing the control of its carrier density and, in consequence, the device rise time reduction. This is achieved injecting a narrow electric

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Fig. 7 An experimental approach to generate switching electrical pulses with the PISIC technique (© 2002 IEEE. Adapted, with permission, from [13])

impulse (pre-impulse) at the leading edge of the switching signal, as shown in Fig. 6a, in a way that the abrupt injection of electrical carriers increases the SOA active region carrier density, allowing the device to have faster off -on transitions. One possible experimental setup to the PISIC implementation is presented in Fig. 7, where two independents and synchronized electrical pulse generators are employed, allowing the step and the impulse to be created independently and combined with a microwave coupler with an adequate bandwidth. In this approach, it is fundamental to ensure the generators synchrony through a suitable clock signal, which is also employed as a trigger signal for the reception optical oscilloscope, where the optical switching pulse performance can be evaluated. More advanced experimental setups can be implemented using an electrical pulse generator with two independent outputs or an electrical arbitrary wave generator, ensuring, in both cases, the pulse and impulse synchronization without an external clock signal. Simulations based on the SOA gain modeling using semiconductor laser rate equations adaptation, including the dynamic dependence between the carriers lifetime and density were performed, allowing the optimization of the rise time, which, in ideal conditions (i.e., disregarding parasitic elements) could represent the possibility to achieve rise times in the order of the tens of picoseconds [13]. A reduction of the rise time from 2 ns to approximately 200 ps was experimentally demonstrated using the PISIC technique for a bulk SOA (E-TEK HSOA 200 014 333) [13]. Additional experimental results are presented in Fig. 6b, where it is possible to compare the optical switching pulse for a nonlinear SOA (CIP-NL) with the same bias current being switched simply with the injection of an electrical step or with the PISIC technique. The results show a rise time reduction from 600 to 400 ps, with the drawback of a more pronounced overshoot and increased oscillatory behavior, which is a direct consequence of the drastic injection of electrical carriers in a narrow time period, corresponding to the PISIC impulse.

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5 Settling Time and MISIC Technique The PISIC switching technique presented in Sect. 4, despite its proved transition time reduction effectiveness, increases the oscillatory behavior, leading to an increase of the overshoot and a longer settling time, possibly resulting in SOA saturation and longer guard times (i.e., the rise and settling times sum), respectively. In practical terms, the longer guard time is the impairment with higher impact, once the overshoot deform the transmitted bits during the switching transition. To reduce the practical impact of the settling time and overshoot increase due to the PISIC employment, while maintaining its rise time reduction, the multi-impulse stepinjected current (MISIC) switching technique was proposed by Figueiredo et al. [14]. Its basic operation principle is to add, besides the PISIC impulse synchronized with the switching pulse beginning, short duration electrical impulses located simultaneously with each optical switching pulse oscillation below its stable level, as shown in Fig. 8. In this way, the extra carriers added by each electrical impulse injection allow a momentarily increase in the SOA optical gain, which compensates its oscillations, especially its undershoot. However, its practical implementation requires a careful device characterization, as presented in Sect. 7, in order to evaluate its amplitude oscillations location, duration and intensity for each operating point, allowing the design of the optimum switching pulse that will minimize the optical switching pulse oscillations after the switch transition from off to on operating state. In general, the proposed MISIC pulse can be divided into three main sections, as it can be seen in Fig. 8a. Section A, is a pre-impulse similar to the one applied in the PISIC technique and, as before, its main function is to the accelerate the electrical carriers injection in the SOA active region, allowing its faster transition between operational states. The section B follows section A and is composed by impulses intended to compensate the negative oscillations following the switching transition (mainly the undershoot), thus it should have a duration close to the SOA settling time. Section C is designed to cancel the SOA carriers relaxation [15], which provokes small optical gain fluctuations even after the optical switching pulse stabilization. The relaxation oscillations usually have small amplitude and a well-defined frequency, being compensated by an impulse sequence with the same frequency and inverted phase. The addition of section C impulses also raises the average SOA injected current during its on state operation, resulting in a higher optical contrast and in a smaller percentage overshoot (however its absolute value remains the same) [14]. The optical space switch power consumption increases due to the MISIC application, mainly due to section C impulses, since they must be repeated during the entire period when the switch is operating at on state. Experimental results have shown an energy consumption increase of approximately 15% due to the MISIC in comparison with the PISIC technique [14]. However, if the relaxation oscillations do not represent an impairment to the switch operation, the removal of section C impulses significantly reduces the energy consumption. A performance comparison between the SOA using the PISIC and MISIC techniques can be seen in Fig. 8b, where a CIP-NL is switched at the same operational

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Fig. 8 Electrical and optical (compared to the PISIC technique) switching pulses employing the MISIC switching technique (© 2015 IEEE. Adapted, with permission, from [14])

conditions for both cases. As it can be seen, the MISIC was able to reduce the oscillations amplitude, while increasing the switching pulse optical contrast, which can be an important parameter for some applications. Altogether, each application requirement will define the best switching technique to be applied, but the necessity of faster optical switches indicates a good perspective to the MISIC application despite its higher energy consumption.

6 Mounting Optimization As seen in Sect. 3, the general performance of SOA-based optical switches shows the possibility to achieve rise times of few hundreds of picoseconds, however with significant percentage overshoots and an undesired oscillatory behavior. In this sense, there are two main ways to improve the SOA performance, especially in terms of stability after the transition. The first one, as presented in Sects. 4 and 5, is based

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on the design of the electrical switching signals in order to compensate the oscillations controlling the electrical carriers in the SOA active region. The second one, which is discussed in this section, aims to enhance the electro-optical performance through impedance matching and encapsulation optimization. The comparative analysis between the results achieved by the CIP-NL and the CIP-COC showed above in Fig. 5 (Sect. 3) allows the perception of the mounting optimization importance, once the only difference between them is the absence of encapsulation in the second case. The insertion of parasitic elements due to the encapsulation will affect directly the electrical switching pulses quality, reducing the switch electrical bandwidth and the stability in its dynamic behavior. However, it is difficult to directly characterize the parasitic elements in a complex microwave mounting as the ones employed in the construction of SOA-based components. A valid approach is to infer the mounting elements through the modeling of an equivalent electric circuit with lumped elements, as proposed by Figueiredo et al. in [16, 17]. A possible equivalent circuit scheme is shown in Fig. 9, which was employed in the simulation and optimization of a nonlinear SOA-based space switch without encapsulation (i.e., in a chip-on-carrier mounting) proposed in [18], where each lumped element is discussed in further details. This SOA equivalent circuit is derived from one developed to model semiconductor lasers [19], once both devices are very close in its structure and physical operational principles. The SOA electrical equivalent model is shown in Fig. 9, within the SOA dashed box, representing the SOA carriers’ lifetime and storage, gain compression, spontaneous emission, and heterojunction. An additional electrical network is attached to this circuit, representing the parasitic elements in the SOA encapsulation or COC mounting, as presented in Fig. 9, within the Chip-on-Carrier dashed box. Among these elements, it is possible to highlight inductors and capacitors modeling the microwave wires and plate connections and parasitic elements with dependence on the SOA injected bias current. Lastly, the left arrow in Fig. 9 indicates additional parasitic elements that could be included to emulate connectors and microwave guides that inject the electrical signals into the SOA microwave mounting, affecting the switching performance through its limited bandwidth, induced loss, and phase delays. To extract the estimated value for each lumped element, a fitting between the simulated equivalent circuit and experimental data is heuristically carried out, aiming at matching the model spectral response to the experimental results, as the ones presented before in Fig. 4. Through this analysis, it is possible to identify and quantify each parasitic element in the electro-optical microwave mounting and evaluate its impacted in the overall SOA-based switch performance. Insights derived from this process could represent valid information to optimize the switch mounting over the compensation of the most harmful parasitic elements. A result from this approach is the electrooptical switch proposed by Figueiredo et al. in [18], based on the mounting scheme presented in Fig. 10. In this experimentally characterized switch, a symmetrical thinfilm distributed resistor is employed as a microwave coupler, allowing the combination of two independent and synchronized electrical signals with low loss and high bandwidth. This approach allows the combination of switching steps and impulses

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Fig. 9 SOA and COC equivalent circuits with lumped elements employed in the space switch modeling and optimization (© 2017 IEEE. Adapted, with permission, from [18])

Fig. 10 Top view (not in scale) of the microwave mounting scheme for the electro-optical SOAbased space switch with integrated microwave coupler based on a thin-film resistor (© 2017 IEEE. Adapted, with permission, from [18])

(as required by the PISIC and MISIC techniques presented before in Sects. 4 and 5, respectively) with minimum distortions, enabling a precise control of the SOA active region carriers dynamic, therefore improving its rise time without inducing unwanted oscillations. The performance improvement achieved with the implementation of an integrated microwave coupler directly attached to the COC-SOA mounting is evidenced in the optical switching pulse comparison presented in Fig. 11. In this case, the second optical switched pulse was a result previously published [14] where the same SOA (CIP-NL in a COC mounting presented in Sect. 3) with a microwave mounting based on discrete elements (external microwave coupler and bias-T) was characterized through the implementation of the MISIC switching technique. In both optical pulses presented in this figure, the SOA-based switches were operating under the same conditions (step amplitude of 2.5 V with duration of 8 ns, pre-impulse amplitude of 3.75 V with duration of 480 ps, bias current of 80 mA, and optical input power of 5 dBm). The use of the integrated microwave coupler was able to maintain short rise times (180 ps compared to 160 ps) with a great improvement in its oscillatory

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Fig. 11 Comparison between the here presented electro-optical switch with integrated microwave coupler [18] and the previously mounting employing discrete components [14] under the same operational conditions (© 2017 IEEE. Adapted, with permission, from [18])

(a)

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Fig. 12 Rise time and percentage overshoot as a function of the PISIC pre-impulse amplitude for the optical switch with integrated microwave coupler based on thin-film resistor operating with: a step amplitude of 1.5 V, pre-impulse width of 160 ps, and bias current of 80 mA; b step amplitude of 2.0 V, pre-impulse width of 320 ps, and bias current of 80 mA (© 2017 IEEE. Adapted, with permission, from [18])

behavior, reducing the overshoot from 80 to 66%) and reducing the settling time from 3 to 650 ps. This last improvement alone would represent a more efficient switching performance through the reduction of the switch guard time, enabling the establishing of the desired optical link in a shorter time interval. More detailed results are shown in Fig. 12, allowing the comparison between this switch rise time and percentage overshoot as a function of the PISIC pre-impulse amplitude. Even with rise times below 250 ps, this mounting presented percentage overshoots close to 12%, which do not represent a potential problem for the most practical uses. Even better results can be achieved using the MISIC switching technique, as presented in Sect. 5, with the drawback of a higher energy consumption. The results achieved by this experimental SOA-based switch mounting indicate the

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importance of a higher level of integration between electrical and optical components in complex devices, as the ones analyzed here. The integration of the optical and electrical parts reduces the physical device dimensions, energy consumption, and the parasitic elements from the device encapsulation, enhancing its optical response bandwidth and stability.

7 Amplitude Distortions on Intensity Modulated Optical Signals When evaluating the performance of SOA-based space switches in applications using modulated optical signals, in addition to the performance parameters analyzed on Sect. 6, the transmitted bits vertical aperture and the guard time until the switching pulse stabilization also should be considered. The first one is a metric related with the transmitted bits eye pattern and the receiver capability to differentiate the amplitude level between 0 and 1 when the optical switch is at on state; once it is intrinsically dependent on several other experimental parameters, it will be analyzed in relation to the bits vertical aperture when the optical switch is at off state. The second is related to the time required to the switch to complete its transition from off to on state without generating significant amplitude distortions in the transmitted bits. In practical terms, it represents the period of time when the optical switch is consuming electrical energy without operating properly, reducing its energy efficiency. The experimental setup presented in Fig. 13 shows the modulation scheme of an optical carrier emitted by a laser in continuous wave (CW) through a Mach–Zehnder modulator (MZM) controlled by electrical signals generated by an electrical pulse generator. This optical signal, carrying information through the desired amplitude modulation, is amplified, filtered, and then switched by the SOA operating as a space switch. The SOA operation point is defined by the combination of a DC signal, corresponding to its bias current, and an AC signal, containing the electrical switching pulses, which are formed by the combination of an electrical step and impulses corresponding to the PISIC and MISIC switching techniques, as presented in Sects. 4 and 5, respectively. The SOA optical input and output power were controlled by variable optical attenuators (VOAs) in order to avoid the SOA and photodetector saturation, which could mask some of the amplitude distortions, especially during the switching pulse overshoot. Finally, the switched optical signal modulated in amplitude is photodetected and stored by a real-time oscilloscope, allowing its postprocessing. The received optical signal is postprocessed allowing its evaluation through the extraction and isolation of the optical switching pulse, which carries information regarding its oscillatory behavior, and the transmitted bits, which carries information of its switching performance. Figure 14 presents a typical switching pulse, the extracted pulse without modulation, and the basic parameters employed in the space switches performance evaluation. The oscillatory behavior evaluation is based on the guard time metric, which evaluates the duration of the oscillations that arise from the

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Fig. 13 Experimental setup to evaluate the amplitude distortions imposed by the SOA-based space switch (© 2017 IEEE. Adapted, with permission, from [20])

Fig. 14 Optical switching pulse highlighting the key parameters evaluated in the SOA-based switching (© 2017 IEEE. Adapted, with permission, from [20])

off state to on state transition, until they do not represent severe variations in relation with the on state stationary level. This evaluation is carried out through the switching pulse derivative function analysis, which translates its amplitude variations to a more precise signal. In practical terms, the guard time can be defined as the sum of the rise time and the settling time. On the other hand, the switching performance is based

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on the analysis of the transmitted bits vertical aperture, which can be defined as the optical modulation amplitude (OMA). As this parameter is absolute and intrinsically dependent on the photodetector efficiency and its amplifier gain, the analysis was based on the ratio between the OMA from the bits transmitted when the space switch is on and off. As the analysis is based only on the vertical aperture, the information transmitted through the optical link is a string of interleaved 0s and 1s, facilitating the verification of the OMA through the subtraction of its levels. As the switching performance is evaluated as the OMA ratio, it also represents the switch capability to eliminate information transmitted when it should be on off state. The achieved results show the possibility to improve the space switch general performance through the electrical step amplitude and bias current tuning. Altogether, operating points with high amplitude electrical switching steps and low bias current were able to present a satisfactory compromise between fast stabilization and high OMA ratio, while maintaining the switching pulse energy consumption in low levels. More specifically, regarding the guard time, the parameters with the most crucial impact on the system performance depend on the SOA behavior, the employed switching technique, and the step electrical amplitude. The SOA constructive characteristics define its electrical and optical carriers dynamic, which impacts its recovery time from each oscillation induced by the gain variation controlled by the switching electrical step. In that sense, the SOA with the extremely nonlinear behavior (CIPXN) proved to be capable to achieve its stationary level faster, despite the presence of intense amplitude oscillations. However, in some practical applications, the nonlinearities impairments induced by this kind of device could forbid its implementation, in that case, the SOA with linear behavior (CIP-L) represents the best compromise in terms of its oscillatory behavior and switching time. In this sense, one important observation is the chirp induced in SOAs with more pronounced nonlinear behavior, which can be a crucial impairment in optical links based on phase modulation and coherent reception, as it will be discussed in Sect. 8. The analysis carried out also proved the MISIC technique efficiency in terms of the optical switching pulse oscillatory behavior. The application of impulses during the optical switching pulse undershoot (and others consecutive negative oscillations) was effective in the SOAbased space switch guard time reduction. As the MISIC requires additional impulses with duration times lower than a few hundred picoseconds, the impact on the switch energy consumption should not be a limiting factor for practical applications. These conclusions can be verified in the experimental results presented in Fig. 15, where it is possible to verify the impact of the SOA behavior and the switching technique in the guard time as a function of the bias current. Regarding the OMA ratio, the SOA design is once more a key factor in the switch performance, this time followed by the switching electrical step amplitude and bias current. In fact, these three factors combined impact the SOA gain curve and its operating point. One way to achieve a higher OMA ratio for the switch is to provide higher optical gain variation for the bits transmitted in each state. For that, the SOA must have a steep gain curve as a function of its bias current. Then, when operating far from saturation, the electrical step amplitude can provide a significant gain for the bits transmitted while it remains in high logical level and attenuate the

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Fig. 15 Guard time as a function of the SOA-based space switch bias current for: a three SOAs with different nonlinear behavior switched through the PISIC technique and b the CIP-XN switched through three different switching techniques (© 2017 IEEE. Adapted, with permission, from [20])

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Fig. 16 Optical modulation amplitude ratio for the three characterized SOAs switched through the PISIC technique as a function of: a the SOA bias current and b the electrical switching step amplitude (© 2017 IEEE. Adapted, with permission, from [20])

bits transmitted when it is in low logical level. In practical terms, it translates into an operation region defined by low bias currents and high electrical step amplitudes, as can be seen in the experimental results presented in Fig. 16. This same region also provides the SOA-based space switch satisfactory performance in terms of its oscillatory behavior, allowing the definition of a space switch optimum operation region when transmitting intensity modulated signals. Finally, in order to evaluate the applicability of this kind of space switch in practical optical links, it is also important to verify the switch energy consumption per switching pulse. The experimental results shown in Fig. 17 are related to the combination of SOA behavior and switching technique with overall best performance

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Fig. 17 Electric pulse energy consumption for the CIP-XN switched through the MISIC technique as a function of the SOA bias current in relation with: a the SOA guard time and b the OMA ratio (© 2017 IEEE. Adapted, with permission, from [20])

(CIP-XN switched with the MISIC technique). An optimum operation region can be defined for the switch operating with low bias currents and high electrical step amplitudes. This region presents the lowest guard times, highest OMA ratios, and acceptable overshoot level, while maintaining the energy consumption per 8 ns switching pulse below 5 nJ.

8 Phase Distortions Within the context of electro-optical switching in semiconductor devices, the most important phase distorting phenomenon to consider is the chirp, which is a temporary frequency deviation. The Kerr effect governs such nonlinear behavior in these devices and it can be caused by self-phase modulation (SPM) or due to extrinsic changes in the medium carrier population density, which happens during switching in semiconductor devices [21]. The refractive index of the semiconductor active layer is directly dependent on the carrier density. Thus, the optical or electric injection during switching causes a refractive index change, resulting in an optical carrier frequency deviation. Considering current dense wavelength-division multiplexing (DWDM) with 12.5 GHz channel spacing, a frequency deviation of only a few gigahertz in the optical carrier of one channel could cause significant crosstalk between adjacent channels, which can compromise the overall system performance. Therefore, it is important to consider the frequency chirp peak potential of switching devices in order to avoid this problem. In optical links based on coherent modulation schemes, the interaction between the fiber chromatic dispersion and the frequency chirp can severely impact the information coded in the optical carrier phase. In this case, an efficient digital signal processing (DSP) stage after the electro-optical reception is critical to recover the transmitted information.

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Fig. 18 Filters frequency response and optical carrier tuning of the time-resolved frequency chirp extracting scheme (© 2015 IEEE. Adapted, with permission, from [22])

Fig. 19 Experimental setup responsible for extracting the time-resolved frequency chirp curves (© 2015 IEEE. Adapted, with permission, from [22])

There are different methods to analyze chirp. One of the possible ways to extract the frequency chirp resolved in time is using filters that set the optical carrier in both descending and ascending frequency responses, as seen in Fig. 18. If the optical carrier deviates positively, the output of Filter 1 will attenuate while the output of Filter 2 will increase. The subtraction of these outputs will be proportional to the frequency deviation. The experimental setup pertinent to this analysis is depicted in Fig. 19. In this scheme, the signal is filtered through its reflection in a Bragg grating, being reinserted in the link by an optical circulator. The output signals acquired by the oscilloscope are imported into an offline algorithm to compute the time-resolved deviations. With this setup, it is possible to characterize the frequency chirp on SOA-based switches due to the change of a range of variables, as proposed in [22]. One characterization was due to changes in the switching current injection, employing PISIC switching technique to evaluate effects from step amplitude and pre-impulse amplitude variations on frequency chirp. Selected results are shown in Fig. 20 where the second oscillations in time are related to the switching-on edge, while the first and third oscillations are related to the switching-off edge. The frequency chirp intensity is directly proportional to the switching step amplitude. The peak frequency deviation observed is approximately

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Fig. 20 Time-resolved frequency chirp due to switching step amplitude (© 2015 IEEE. Adapted, with permission, from [22])

3 GHz to both sides for a switching step amplitude of 1 V, which is harmless in a WDM system with 100 GHz channel spacing but can cause significant crosstalk in both adjacent channels in a DWDM of 12.5 GHz channel spacing. The results obtained in [22] also show that the optical input power is inversely proportional to the frequency chirp intensity and that the pre-impulse amplitude does not increase significantly the frequency deviation, but it prolongs settling time from few nanoseconds to tens of nanoseconds.

9 Conclusions The exponential growth in the data volume transmitted through the optical telecommunication infrastructure, currently driven especially by applications as cloud computing and Internet of Things, demands electro-optical devices with optimized performance, allowing the propagation of information with high spectral efficiency and low latency. In this scenario, the optical links general performance require, among other things, electro-optical space switches capable to perform ultrafast switching in a wide bandwidth. In general, the results compiled in this chapter are a summary of SOA-based electro-optical switches performance and enhancements, allowing a more insightful view on this device behavior and the possibilities to optimize its operation. The characterizations discussed in Sects. 3, 7, and 8 provide a deeper understanding of the nonlinear properties and oscillatory behavior of several commercially available SOAs, allowing the definition of the most suitable device for each application requirements. To improve the SOA performance, two switching techniques, namely PISIC

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and MISIC, were presented in Sects. 4 and 5, showing the possibility to control the SOA active region carriers dynamic reducing its rise and settling times. Further improvement can be achieved through a well-designed SOA microwave mounting, as introduced in Sect. 6, proving the importance of the impedance matching and low parasitic elements in the device general performance. Quantitatively, the experimental results show the possibility to design and build electro-optical switches with ultrafast transition time (below 200 ps), low guard time (below 1 ns), and moderate energy consumption considering the simultaneously optical pulse amplification (up to 5 nJ per 8 ns switching cycle). These results are particularly promising when associated with SOA characteristics, as its versatility, ease of integration, low production cost, and wide bandwidth. This performance evidences the possibility to employ SOA-based M × N electro-optical switches [23] as key components in Data Centers with high switching rates [24], high-performance computing [25], all-optical logic gates [26, 27], and supercomputers [28]. Further performance improvements can be achieved in the SOA mounting, especially regarding its impedance matching and energetic efficiency. As demonstrated in this chapter, a complete integration between electrical and optical components is the most promising manner to perform this kind of device performance optimization. Acknowledgements The authors thank Dr. Antonio M. O. Ribeiro for his assistance during the experimental setups and Dr. Napoleão S. Ribeiro and Dr. Adriano Toazza for their helpful discussion during different stages of this work. The authors also thank Dr. Fábio D. Simões for reviewing a draft of this chapter. The works here presented were partially supported by the Brazilian agencies FAPESP (projects 2015/24517-8, 2015/50063-4, 2014/18791-7, 2007/56024-4, and 2005/51689-2), CNPq (projects 400129/2017-5, 301409/2017-0, 402923/2016-2, 150504/ 2015-2, 402184/2014-9, and 574017/ 2008-9), and Capes.

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Coherent Optical Access Networks Andrea Chiuchiarelli and Sandro M. Rossi

Abstract The constant increase in IP traffic, mainly driven by the growth of the number of connected users and the demand for bandwidth per user, has profoundly influenced the evolution of optical communication systems as a whole, including fiber-based access networks, which constitute the last mile of an optical system, directly connecting the edge IP network to the end users. This chapter is devoted to coherent optical access networks. The main intent of the chapter is to analyze different fiber-access technologies, showing the benefits and the main limitations of each of them in assessing the needs for higher bandwidth and higher number of connected users together with the concerns of minimizing the impact on the network cost and complexity. It will be showed that coherent detection offers the highest potential in terms of network efficiency, with recent studies proving its feasibility for the access scenario also in terms of complexity and power consumption.

1 Introduction Fiber-optic based access networks are an essential part of today’s communications networks, as they are responsible for connecting millions of users all over the world to the Internet. The enormous amount of data, audio and video, which are streamed, downloaded and exchanged on a daily basis, is generated from and delivered to an access network. As the demand for bandwidth increases, mainly driven by the fast spreading of fixed and mobile connected devices and by the growth of cloud based services and applications, the need for faster and more reliable connections arises. This demand is reflected on telecommunication networks as a whole, including the access section. However, this cannot come at any price. As common, the end users of a given service are always eager to accept improvements, but only if the impact on the service cost is limited. Furthermore, when more and more people demand access to the same service, old subscribers are not willing to accept paying more to improve the infrastructure in order to allow more users to benefit from the same service. This is true as closer as the service is to the end user, as for the access networks. A. Chiuchiarelli · S. M. Rossi (B) Optical Technologies Division, CPqD, Campinas-SP 13086-902, Brazil e-mail: [email protected] © Springer Nature Switzerland AG 2019 A. Paradisi et al. (eds.), Optical Communications, Telecommunications and Information Technology, https://doi.org/10.1007/978-3-319-97187-2_3

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For this reason, researchers have devoted a great effort to propose and to validate viable solutions to increase the capacity of access networks. In this scenario, coherent technology, which is already established as the primary transmission technology for metro and long-haul communication systems, has been considered as a promising candidate for the access, too. The scope of this chapter is to present an overview on coherent optical networks. The chapter is structured as follows: Sect. 2 will provide an overview and historical background on optical access networks. Section 3 will focus on passive optical networks, which are today the most common type of fiber-optic based access networks. Section 4 will discuss the potential of coherent technology in passive optical networks, and Sect. 5 will focus on research works on coherent passive optical networks, detailing some of the most important results. Finally, Sect. 6 will provide a brief summary along with final conclusions and remarks.

2 Access Networks: An Overview In telecommunications, an access network is the network responsible for delivering the data traffic between the core or backbone network (i.e., the “Internet” network) and the end subscribers (individual users and/or enterprises). Access networks can exist in different types, and are usually divided in wired (or cabled) access networks and wireless access networks. Despite of their inherent higher complexity and cost, wired access networks can provide higher bandwidth and reach compared to wireless networks, making them more suitable to connect a wider number of subscribers over longer distances (up to tens of kilometers). Figure 1 shows the structure of a cabled access network. Access networks have distinct characteristics and requirements, when compared to metropolitan or long-haul networks, which constitute the backbone network. In

Fig. 1 Cabled access network topology

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access networks, reducing cost and complexity is a main concern, more important than upgrading the total network capacity. For these reasons, the first access networks relied on coaxial cable connections with limited reach of a few kilometers, carrying data rates of tens of Mb/s per user. Until the early 2000s, optical fiber was mostly used in metro and long-haul networks, due to the much lower attenuation and higher capacity offered with respect to copper based links. However, with the rapid increase in global data traffic, driven by the increase in the number of connected users and in the quality of the services delivered over the Internet (such as HD video on demand, online gaming and video conferencing), copper based networks began to approach their capacity bottleneck, and optical fiber appeared as the most promising solution for the future of “last mile” technologies. Not only optical fiber is capable to offer higher bandwidth capability than copper, but it also allows to increase the reach of the network as well as the total number of users that a single network could connect, with minimum impact on cost and complexity. This led to a great interest of Internet service providers (ISPs) and operators in optical access solutions, with the optical fiber moving closer and closer to the end user, which started the Fiber To The x (FTTx) era [1], where x could stand for premises (FTTP) more generally, or for curb (FTTC), building (FTTB) or home (FTTH), more specifically. Optical access networks are usually divided in active optical networks and passive optical networks [2]. An active optical network (AON) is structured as a multiple point-to-point (P2P) architecture, in which a central network terminal, also known as optical line terminal (OLT) or central office (CO), is connected to multiple end users via an active switch or router. In this type of network, each optical network terminal (ONT), also referred to as optical network unit (ONU), has its own dedicated fiber line, with the active switch routing the data traffic from the OLT to each ONT (downstream traffic) and vice-versa (upstream traffic). A passive optical network (PON) is a point-to-multipoint (P2MP) connection, in which part of the network is shared between more ONTs by means of passive optical splitters. Therefore, different ONTs receive the same downstream traffic from the OLT, and the data of each user is extracted at the ONT. In a PON, no active element is present inside the network, all being concentrated at the OLT and at the ONTs. Figure 2 shows the typical structure of an AON (a) and a PON (b). Each type of optical network has its own advantages and disadvantages when compared to the other. For example, an AON offers high simplicity, making use of low cost components (optics and electronics), symmetric bandwidth and high scalability. However, the active switch requires inline power feeding, which increases the operational costs for this type of network. On the other hand, a PON has no remotely powered equipment, as it relies on fully passive optical components. Nevertheless, sharing the same optical paths between multiple users requires more complex control protocols, and more expensive burst mode receivers at the OLT to receive the upstream signals coming from different ONTs over the same fiber line. In 1995, the Full Service Access Network (FSAN) working group [3] was formed with the objective of defining the requirements of broadband access networks. Since

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Fig. 2 a Active and b passive optical network architecture

2001, standardization bodies such as ITU-T [4] and IEEE [5] have been defining recommendations for both active and passive optical networks. Today, FTTx connections are present in many countries, with higher density in the Asia-Pacific area, but with massive presence also in several European countries as well as in the United States of America. Despite AON still being deployed, most access networks nowadays rely on passive technologies because of their inherent higher efficiency. For this reason, only PON technologies will be considered in the following sections.

3 Passive Optical Networks As already introduced, optical access networks have some unique requirements that make them different from backbone networks, i.e. metro or long-haul, where the main concern is to maximize capacity and spectral efficiency in order to fully exploit the fiber optical bandwidth. In the access scenario, there is no need for high data rates to satisfy the bandwidth demand of the end users. By proper resource sharing, a single fiber link could serve tens of users by using only one or a few optical carriers with data rates of a few Gb/s per carrier. By doing so, the capital and expenditure costs of the network can be reduced and shared among all the network subscribers, thus minimizing the cost per user, which is the main requirement in access network design. Passive optical networks rely on this concept. As shown in Fig. 2b, a single fiber link

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is shared among multiple users, in a point-to-multipoint configuration. There are different ways in which resource sharing can be realized. The most straightforward solution is to include all the information that is sent from the OLT to the multiple ONTs in one data stream, which is then used to modulate an optical carrier that is sent to the optical fiber and delivered to all the remote end users by means of passive optical splitters. Therefore, each ONT will be receiving the same amount of data, and data associated to a specific user will then be extracted at the ONT node. In a similar manner, for upstream transmission, i.e. from all the ONTs to the OLT, the same wavelength, which is different from the downstream wavelength to avoid crosstalk between the two signals, is used by all remote terminals to carry the information to be sent to the OLT. In order to avoid conflict, time frames are allocated to each ONT to transmit its information, and upstream signal slices (bursts) are then multiplexed based on a time division multiple access (TDMA) scheme [6] and sent to the OLT. A passive optical network based on this configuration is called TDM-PON, and is shown in Fig. 3a. Typically, a TDM-PON can connect the OLT to up to 32 user terminals using a single pair of optical wavelengths for downstream and upstream, but splitting ratios of 1:64 and 1:128 are also allowed. A second solution, shown in Fig. 3b, is to associate a different wavelength (λ) to each user. All optical channels (λ s) are transmitted through the same fiber link by wavelength division multiplexing (WDM) [7]. In this case, no optical splitters are needed, as they are replaced by WDM multiplexers/demultiplexers (MUX/DEMUX), that route each wavelength to the specific user in both directions. The downstream and upstream wavelengths are usually different, to avoid optical crosstalk between the two signals, and their spacing is determined by the MUX/DEMUX free spectral range, i.e., the wavelength (or frequency) interval between two transmission peaks in the filtering profile of each MUX/DEMUX channel. However, many research works were devoted to enable wavelength reuse between downstream and upstream to increase the network efficiency, as discussed in the next section. The main advantage of a WDM-PON is that having a dedicated wavelength per terminal permits to significantly increase the total bandwidth per user. Another advantage of WDM-PON over TDM-PON is that a WDM-PON does not need any control and framing of the upstream signal, as each ONT would have its own dedicated wavelength. This means that each user terminal would be allowed to transmit continuously to the OLT at any time without worrying about the upstream traffic generated by other ONTs. No optical splitters are needed in a WDM-PON, as they are replaced by WDM MUX/DEMUXs, which introduce lower insertion losses, therefore increasing the link budget and maximizing the reach of the network. These advantages come at the price of a higher complexity, as N optical sources are needed at the OLT to connect N user terminals in the network, and WDM MUX/DEMUXs are more expensive than passive optical splitters. Furthermore, to allow for full network reconfigurability, each ONT should be able to be connected to any wavelength. To do so, colorless optical transmitters and receivers are required at the ONTs, i.e., a tunable light source at the ONT transmitter unit and a tunable filter at the ONT receiver side, which also have a high impact on the infrastructure cost. Also, the

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Fig. 3 a TDM-PON versus b WDM-PON architecture. OA: optical amplifier; OC: optical circulator

optical power of the WDM carriers has to be kept below a critical value to avoid nonlinear impairments between channels during propagation [8]. In order to take advantage of the benefits offered by TDM and WDM, an optimal solution consists in joining the two technologies. This PON configuration is known as TWDM-PON. Figure 4a shows the architecture of a TWDM-PON. In this case, a lower number of optical channel pairs are needed to carry the downstream and the upstream signals. Each pair of optical channels is shared between a group of ONTs, in both directions. At the remote node (RN), no WDM MUX/DEMUX is needed, as it can be replaced by a passive splitter. Due to the reduced number of optical channels, the spacing between them can be increased, allowing to increase the launched power per channel with lower nonlinear interference between the WDM carriers. To extend the PON reach, optical amplifiers (OA) can be used at the OLT. TWDM-PON can provide higher bit rates to the end users with limited impact on cost and complexity. They also enable transparent network scalability, as the network

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Fig. 4 a TWDM-PON architecture; b TWDM-PON for LLU

infrastructure can be deployed to carry only one wavelength pair at the beginning, and then adding further pairs as the demand for capacity increases. It is also possible for multiple OLTs to share the same physical infrastructure, as shown in Fig. 4b. By using TWDM technology, different operators could connect their OLTs, using a specific set of wavelengths, to the same fiber, by using a WDM MUX/DEMUX placed at the shared transmitter node. This solution is known as local loop unbundling (LLU). The first international standards for passive optical networks (BPON, EPON, GPON, XG-PON1) [9–12] relied on TDM technology. As the demand for bandwidth per user and the number of connected users increased, it became necessary to evolve TDM systems, leading to the 2015 ITU-T standard for next generation passive optical networks (NG-PON2) [13], where the TWDM-PON architecture was chosen for both

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downstream and upstream transmission. The NG-PON2 standard also included pointto-point WDM (PtP WDM) as an optional technology, with WDM-PON systems being developed by some companies and operators.

4 Non-coherent Versus Coherent Technology in Passive Optical Networks Due to its inherent simplicity and low cost, intensity modulation with direct detection (IM-DD) was chosen as the main technology for the first optical access networks, also considering that the bit rate per optical channel was limited to a few Gb/s and that the requirements in terms of total bandwidth and reach were more relaxed in the early stages of PONs. The physical media dependent (PMD) layer specification in the PON standards released so far relied on IM-DD transmission, making use of directly modulated lasers (DMLs) both at the OLT and at the ONTs. Transmission rates vary from 622 Mb/s downstream and 155 Mb/s upstream per optical carrier in BPON to 10 Gb/s per carrier, both downstream and upstream, in XG-PON and NG-PON2, the latter further allowing four WDM wavelengths for downstream and upstream, yielding a total bit rate of 40 Gb/s. As the number of users keeps growing, as well as the demand for broadband services such as high quality video streaming, online gaming, real-time video conferencing etc., it becomes necessary to upgrade the infrastructure of the optical access networks in order to meet such demand. Internet traffic forecasts predict a threefold increase in global IP traffic between 2016 and 2021 [14], with 71% of the global world population having access to both fixed and mobile connected devices by 2021. It is estimated that 82% of global traffic in 2021 will be represented by IP video. Future optical access networks will face a major challenge as they will have to deliver a much higher amount of data coming from the backbone and metro networks to a higher number of users, distributed over wider areas. In power splitting PONs, such as those described in Sect. 2, where no active elements are present along the optical link, it is important to ensure that each ONT operates above receiver sensitivity, which is the minimum signal power that allows the receiver to operate error-free. This sets a critical trade-off between the maximum reach of the network and the number of connected users, which directly depends on the maximum allowed power splitting ratio. Commercial deployments are usually limited to system reach of 20–40 km, with typical splitting ratios of 1:32 or 1:64 (with the possibility to upgrade up to 1:128), as these are the specifications defined by current PON standards, i.e. GPON and XG-PON1 [11, 12], while NG-PON2 must support a splitting ratio of at least 1:256 [13]. In order to meet the growing demand for user bandwidth, it will be necessary to provide effective solutions to increase the power budget in passive optical networks. The most straightforward way to achieve this goal is to use active reach extenders (optical amplifiers or regenerators) in the middle of the span, as was also considered in ITU-T recommendations, e.g. GPON [11]. However, midspan

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amplification/regeneration stages were not seen as an attractive solution, due to their impact on the network operational costs, and also because an active element in a P2MP network introduces a so-called single point of failure, meaning that any functional issues in a reach extender located at the distribution node of an optical network would inevitably affect all the users connected to that network. To overcome these limitations, WDM-PONs were proposed as a viable alternative, as they required no active elements throughout the link, and dedicating a separated wavelength to each user it was possible to replace the lossy passive optical splitters with low-loss WDM multiplexers increasing the network link power budget, as already described in Sect. 2. WDM-PON also offers higher bandwidth per user compared to TDM-PONs or TWDM-PONs, where the downstream and upstream channels are shared between multiple ONTs. On the other hand, WDMPONs would introduce “color” issues, as each ONT would operate at a different wavelength, affecting the network reconfigurability. One way to solve this problem would be to use tunable lasers at the ONT transmitter, although that would severely affect the cost of the user terminal. For this reason, research started to focus on alternative, cost-effective technologies to make the ONT “colorless”, meaning that each ONT could be able to operate at any given wavelength, thus all network terminals being identical. The most promising technique consisted in generating a remote continuous-wave (CW) optical seed at the OLT to feed a reflective active element at the ONT, typically a reflective semiconductor optical amplifier (R-SOA) [15, 16], a reflective electro-absorption modulator (R-EAM) [17] or an injection-locked Fabry-Perot laser diode (FP-LD) [18]. The remote seed would then be modulated and amplified at the ONT for upstream transmission. Figure 5a shows a WDM-PON with colorless reflective ONT. The main drawback in using remote seeding is the optical crosstalk induced by reflections and Rayleigh backscattering of the CW light back to the OLT, where it superimposes to the incoming modulated upstream at the same wavelength, degrading the system performance and limiting the total link budget [19]. Some works showed effective ways to mitigate the Rayleigh backscattering induced crosstalk [20–23], although at the cost of reduced transmission efficiency. Also, to ensure effective signal re-amplification with limited degradation in the optical signal-to-noise ratio (OSNR), it is necessary that the incoming CW seed at the ONT reflective modulator is sufficiently high. This is another major limitation to the network maximum reach, as low-cost R-SOAs usually exhibit high noise figure (NF) values. As a possible solution, self-seeding of R-SOA or FP-LD at the ONT was suggested [24, 25], as depicted in Fig. 5b, where the broadband light source (R-SOA or FP-LD) at each ONT is sliced by the wavelength selective MUX/DEMUX at the RN and each slice is reflected back to its respective ONT, injecting the reflective active element and locking it to the desired frequency. This technique proved to be rather effective, although a tight control on the polarization state of the self-seeding light was needed, which complicated the network architecture. To further increase the network efficiency, reuse of downstream wavelength at the reflective ONT element was proposed [26–30], as only one wavelength per user would be needed instead of a pair of optical channels for downstream/upstream transmission. However, remodulating the downstream wavelength with the upstream signal requires complex

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Fig. 5 a WDM-PON with reflective ONT; b self-seeded reflective ONTs

modulation suppression methods, such as operating the reflective amplifiers in highly saturated regime [31] or using ad-hoc electronics to erase the downstream signal before upstream modulation [32]. Besides that, crosstalk impairments induced by reflections and Rayleigh backscattering would be even more critical when reusing a modulated downstream wavelength instead of a CW seed [33]. Despite those and other remarkable results achieved in research works on WDMPON, it still was evident that a consistent increase in the PON bandwidth and power budget relying on IM-DD transmission would be extremely difficult to accomplish in a practical scenario, with minimum impact on the architecture and complexity of the network. Coherent technology, already widely used in long-haul and metro networks, was initially not considered for optical access, as it was seen as not commercially viable for low cost PON terminals, due to the higher complexity of the

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optical coherent transmitter and receiver compared to their IM-DD counterpart and to the higher power consumption of the terminal determined by the need of a heavy digital signal processing (DSP) stage. However, recent advances in the integration of optical components as well as in the fabrication technology of semiconductor digital circuits led to an increased interest of the research community and the industry in coherent based PONs. Coherent transmission not only offers the possibility to double the spectral efficiency of the transmitted signal by encoding information also in the phase of the optical carrier, but it can also provide a much higher receiver sensitivity compared to a common IM-DD receiver and it enables the possibility of digitally compensating the linear propagation effects that occur inside the optical fiber (e.g. chromatic dispersion). Therefore, it would be possible to transmit a greater number of WDM channels with tighter spacing in both downstream and upstream directions, in an ultra-dense WDM (UDWDM) configuration. It would also be possible to seamlessly increase the transmission distance beyond 100 km and the splitting ratio to values up to 1:256 and higher. Besides that, in a coherent UDWDM-PON each optical wavelength would be dedicated to a single end user, thus maximizing the user bandwidth, but instead of using ultra-narrow expensive arrayed waveguide gratings (AWGs) as WDM MUX/DEMUX the remote node of the network would still be based on passive optical splitters, with all wavelengths being sent to all ONTs and the local oscillator (LO) at each terminal selecting the desired user wavelength. Figure 6 shows a coherent UDWDM-PON architecture with complex in-phase and quadrature (IQ) modulation. As shown, no change would be necessary in the network link, and legacy PON could be easily upgraded, being necessary only to replace IM-DD terminals with coherent transmitters and receivers, both at the OLT and at the ONTs. Of course, it is important to adapt the structure of the coherent transceivers to the needs and characteristics of an optical access network. In this perspective, only simple

Fig. 6 UDWDM-PON with coherent detection. IQM: in-phase and quadrature modulator

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modulation formats, such as on-off keying (OOK), binary phase-shift keying (BPSK) or quadrature phase-shift keying (QPSK) would be considered. At the receiver side, intradyne detection [34] is usually preferred to homodyne [35] and heterodyne [36] detection schemes, as it relaxes the bandwidth constraints of the receiver and requires no control of the optical phase, leaving the carrier and phase recovery to the electronic DSP circuit. Nevertheless, by properly combining intradyne and heterodyne detection, it could be possible to further simplify the ONT architecture, as discussed in the following section. The DSP circuit can also be designed to reduce its power consumption, as it needs to demodulate low-complex modulation formats and to compensate for propagation effects over much shorter distances than those involved in long-haul or metro optical links.

5 Research Works on Coherent Optical Access In recent years, many research works were devoted to showing the feasibility of coherent UDWDM PONs [37–43]. In this section, we focus on the two most relevant issues that a coherent PON must address. The first one is the implementation of a cost effective DSP with low complexity, both at the transmitter and receiver side, for realtime applications in coherent OLTs and ONTs. The other important concern deals with mitigating interchannel nonlinear propagation effects, which are not negligible in UDWDM passive networks due to the very narrow channel spacing and relatively high launched power per channel. Real-time operation in a bidirectional UDWDM-PON, including performance analysis and DSP design aspects, is presented in Sects. 5.1 and 5.2, while mitigation of four-wave mixing (FWM) induced crosstalk in bidirectional coherent passive optical networks is the subject of Sect. 5.3.

5.1 Performance Investigation of a Coherent UWDM-PON with Real-time Nyquist 16QAM Transmitter It has already been discussed that the role of an access network is to directly connect the end users to the Internet. In a typical real scenario, each user can be seen as independent from the others, and each user just wants a given amount of bandwidth at a fair price, regardless the network capacity or the number of other users connected to the same network. This is a fundamental premise when considering alternative technologies for optical access, since an effective bandwidth of ∼1 Gb/s per user would suffice to meet the needs of most users today. In fact, upgrading an access network is not (or is very little) about increasing the bandwidth per single user, as the primary target is to increase the network efficiency, in terms of system reach, number of connected user terminals, and capital and operational costs (or alternatively cost

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per bit). Coherent transmission, in conjunction with Nyquist pulse shaping [44] that allows to greatly improve the signal spectral efficiency by means of proper digital (or optical) filtering, is a very promising candidate towards this target [45] but, in order to be considered a viable alternative to IM-DD, it should come at the same cost per bit, or lower. In this context, a critical issue is to design the front-end transceivers in the OLTs and ONTs in order to reduce their cost, still making them capable to address the fast-growing demand for bandwidth [46, 47]. Here, we report a detailed performance investigation of a bidirectional coherent UDWDM PON with real-time Nyquist transmitter, as presented in [48], experimentally demonstrating full-duplex (2 × 8λ) transmission at 10 Gb/s per channel based on 2.5 Gbaud 16QAM modulation. Due to Nyquist pulse shaping, it was possible to allocate a symmetric bit rate (downstream and upstream) of 10 Gb/s per user in a 5 GHz bandwidth. Nyquist pulse shaping also improves the tolerance to Rayleigh backscattering (RBS) at lower roll-off factors. In addition, the use of interleaved upstream and downstream Nyquist bands for bidirectional transmission, along with heterodyne coherent detection in the optical network units (ONUs) allowed to reuse, for upstream transmission, the same local oscillator laser used for downstream detection, thus simplifying the network architecture.

5.1.1

Experimental Setup

The network setup is shown in Fig. 7. It is a proof-of-concept network architecture with 16 wavelengths, being 8 for downstream in the OLT and 8 for upstream from the ONUs. Each user has an optical bandwidth of f = 5 GHz, i.e. the channel spacing in either propagation direction is 5 GHz. The upstream and downstream channels are interleaved by f/2 = 2.5 GHz, as depicted in the wavelength assignment in Fig. 7a, so that the back-reflection in each direction falls out of band in the Nyquist limit. The 16 wavelengths are provided by external cavity lasers (ECL) fully-tunable in the C-band with 100 kHz linewidth and 16 dBm output power. All the light coupling is performed using a 1:8 passive coupler (10 dB loss). The ECL sources are modulated with electrical signals from the 2.5 Gbaud real-time transmitter. Figure 7b (top) depicts the real-time Nyquist transmitter operating at 2.5 Gbaud. The DSP, implemented in a field-programmable gate array (FPGA), has the modulation mapping (QPSK, 16QAM, 64QAM and 256QAM) and finite impulse response Nyquist filtering for different roll-off factors: 0.01, 0.1 and 1. The Nyquist filter is implemented using 32-taps raised-cosine shaping at 10 samples per symbol. The DSP is clocked at 156.25 MHz and its 160 lines are interleaved into 4 outputs at 6.25 GHz, connected to a 25 GSa/s DAC with 20 GHz analog bandwidth. The inset eye diagram in Fig. 7a shows the Nyquist signal at 2.5 GBd with 0.01 roll-off. The two RF signals from the DAC outputs are linearly amplified and sent to the IQ modulator. The 8 × 10 Gb/s 16QAM optical signal is then amplified by an erbium doped fiber amplifier (EDFA), and the fiber input power is controlled via a variable optical attenuator (VOA). The optical distribution network (ODN) includes 50 km of standard single-mode fiber (SSMF) followed by a 1:8 passive

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Fig. 7 a Experimental setup of the 2 × 8 × 2.5 Gb/s PON architecture; b real-time 16QAM Nyquist transmitter (top) and off-line receiver DSP (bottom). © 2015 IEEE. Reprinted with permission from [48]

optical splitter, emulated here by a variable optical attenuator set at 10 dB loss. Each ONU has a phase-diversity coherent receiver (optical hybrid + balanced detectors) for heterodyne detection since the local oscillator is shifted by 2.5 GHz with respect to the received signal. After heterodyne coherent detection, the electrical signals are sampled using a real-time oscilloscope at 40 GSa/s with the analog channel bandwidth set to 4 GHz. The off-line DSP block is depicted at the bottom of Fig. 7b. After downsampling the digital signal to 2 samples per symbol (i.e. 5 GSa/s), there is a 2.5 GHz frequency offset (FO) compensation stage, followed by clock recovery (CR), carrier frequency recovery (CFE), carrier phase recovery (CPE), symbol decision and bit demapping (DeMod). The performance is measured in terms of Bit Error Ratio (BER), calculated by counting the bit errors with respect to the transmitted bits. For upstream transmission, the local oscillator is injected into an IQ modulator fed with a 2.5 Gbaud Nyquist 16QAM signal generated by a 64 GSa/s DAC (off-line). f /2 After upstream transmission, the optical channels from the ONUs (λ1,2,...,8 ) hit the coherent receiver in the OLT, where heterodyne coherent detection is performed, i.e. local oscillators are set at λ1,2,...,8 .

5.1.2

Results and Discussion

Bidirectional transmission performance was evaluated for single channel and 2 × 8 UDWDM configuration. Results for measured BER at the ONU coherent receiver are shown in Fig. 8. It is interesting to note that in single channel operation, higher rolloff factors presented the best sensitivity performance, around −39 dBm at BER of 3.8 × 10−3 , which corresponds to the pre-FEC limit for standard hard-decision FEC codes with typical overhead of 7% (Fig. 8a). Nyquist pulses with roll-off factor of 1.0 (black curve) are very close to NRZ pulses, therefore they exhibit higher SNR and more stable clock synchronization in comparison to lower roll-off values, such as 0.1 (red curve) and 0.01 (blue curve), which in turn have a lower bandwidth occupation, and are less affected by linear crosstalk originating from RBS. This is confirmed in the UDWDM transmission case shown in Fig. 8a, where lower roll-off factors show better performance. In this case, the sensitivity is reduced to −36 dBm for

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Fig. 8 a Back-to-back BER versus received power per channel for single channel (dashed lines + circles) and 2×8 UDWDM (solid lines + squares) transmission. b Downstream (DS) BER (4th channel) versus downstream power per channel with upstream (US) launched power of ∼ −7 dBm/channel. c BER (4th DS channel) versus US power with DS power fixed at −7 dBm/channel. d Top: BER per ONU (0.1 roll-off) with DS and US power per channel of ∼ −7 dBm. Bottom: downstream electrical spectra. © 2015 IEEE. Reprinted with permission from [48]

0.01 roll-off (blue curve) and −34 dBm for 0.1 roll-off (red curve). Figure 8b shows the downstream performance (evaluated for the fourth channel only) as a function of the downstream power per channel after transmission over the ODN. For all the three roll-off factors, the optimal performance was achieved with a launched power of around −6 dBm per channel. However, transmitted pulses with 1.0 roll-off (black curve) showed a highly worse performance for all values of transmitted power per channel, due to linear crosstalk and back-reflection from the upstream channels. In order to investigate the tolerance to RBS, Fig. 8c shows the downstream BER results as a function of the upstream power per channel with fixed downstream power per channel of −7 dBm. The benefit of using lower roll-off factors can be verified by observing that the upstream launched power per channel corresponding to a received downstream BER of 3.8 × 10−3 is increased by 8 dB when decreasing the roll-off factor from 1.0 to 0.01. Figure 8d (top) depicts the downstream BER measurements for the eight ONUs, with the transmitter operating with 0.1 roll-off. The launched

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power per channel in both downstream and upstream direction is set to −7dBm. Results show that the center channel has worse performance than the channels at the edge of the spectrum, due to interchannel fiber nonlinearities. At the bottom of Fig. 8d, the downstream electrical spectrum with 0.01 roll-off factor is shown, setting the upstream power per channel to 4 dBm (blue) and −10 dBm (red), to highlight the effect of RBS induced crosstalk. Due to the rectangular spectral shaping limiting the signal occupancy to the Nyquist band, most of the back-reflection falls out of band, thus improving the systems overall performance in full-duplex bidirectional mode. In summary, bidirectional transmission performance of a coherent UWDM-PON with real-time Nyquist transmitter at 10 Gb/s was experimentally evaluated. By interleaving the downstream and the upstream Nyquist bands by f/2 (where f is the channel spacing) and reducing the roll-off factor, it is possible to improve the back-reflection tolerance and to reduce the ONU cost design as only one laser source can be used at the ONU. For a symmetric bit rate of 2 × 10 Gb/s with 5 GHz optical bandwidth per user, an improvement in the tolerance to RBS of up to 8 dB is obtained when using a roll-off factor of 0.01 with respect to 1.0.

5.2 Real-Time DSP for Coherent Passive Optical Networks In [49, 50], the first experimental demonstration of a coherent WDM-PON (16 × 2.5 Gb/s QPSK) with real-time Nyquist OLT transmitter and real-time ONU receivers was presented. In these works, great attention was devoted to the optimization of the DSP units (which are responsible for shaping the modulated signal at the transmitter and decoding the transmitted information at the receiver) in order to allow feasible hardware implementation. Prior to that, 64-channel generation using a fieldprogrammable gate array (FPGA) at the OLT was already demonstrated in [37], however the experimental validation was limited to the back-to-back (b2b) scenario. In [51], real-time DSP operation in the ONU based on 1.25 Gb/s non-return to zero (NRZ) quadrature phase-shift keying (QPSK) was demonstrated. However, all those previous demonstrations did not take into account the challenges related to real-time transmission of Nyquist signals in a WDM-PON, which would provide an effective solution to mitigate crosstalk and to improve the spectral efficiency of the network, as discussed in Sect. 5.1, but also impose critical limitations when compared to NRZ signals. For example, Nyquist signals with low roll-off factors exhibit an increased peak-to-average power ratio (PAPR) in comparison to NRZ or Gaussian signals, and this may limit the usage of simplified DSP architectures, e.g. 8 bits. Furthermore, it was shown that clock recovery at the receiver becomes technically challenging as the Nyquist filter roll-off factor tends to zero [52]. In [49, 50], full real-time operation for generation (at the OLT) and coherent detection (at the ONU) of Nyquist signals in a UDWDM-PON was experimentally demonstrated for the first time, using a simplified 8-bit DSP architecture implemented in FPGA. Transmission of 16 channels over 50 km of SSMF, followed by a 1:16 passive splitter, was successfully achieved, with a bit rate of 2.5 Gb/s per

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channel using 1.25 Gbaud QPSK modulation format. The use of 1.25 Gbaud QPSK simplifies the front-end transceivers, since the SNR requirement is relatively low in comparison to higher-order QAM modulation formats. In addition, the DSP used to generate the 1.25 Gbaud QPSK Nyquist signals at the transmitter and at the receiver is implemented such that additional equalization schemes are not needed. Therefore, the DSP complexity and PAPR are minimized, which in turn relaxes the required effective number of bits (ENOB) in the DAC and in the ADC.

5.2.1

Experimental Setup

The experimental setup is depicted in Fig. 9a. Transmission of 8 and 16 channels was evaluated. The 16 (8) downstream optical channels were generated by an array of 16 (8) tunable external cavity lasers (ECLs, 350 km) repeaterless optical links based on remote optical amplification. The chapter is structured as follows. Section 2 will describe a method for system design in ROPA-based unrepeatered systems, focusing on the main building blocks of the system architecture. Section 3 will report the most important record achievements in unrepeatered transmission of 400G WDM signals. Laboratory demonstrations show the effectiveness of the design method described in Sect. 2 for high-capacity, long-reach repeaterless system optimization. Finally, Sect. 4 will provide conclusions and final remarks.

2 System Design The design of an unrepeatered optical system is a fundamental step, as the application scenario demands a high knowledge of the system parameters, aiming at reducing

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the level of uncertainty to ensure the desired performance after system deployment. The typical architecture of an unrepeatered optical system is depicted in Fig. 2. At the transmitter side, a set of optical channels is multiplexed to generate a WDM signal. Before being sent to the transmission link, the WDM signal is amplified by a booster EDF amplifier (EDFA) followed by a distributed Raman amplification (DRA) stage using co-propagating optical pumping. While the use of a booster EDFA is common in almost all WDM systems in order to ensure a proper level of launched power per channel, the DRA stage at the transmitter is optional and can be omitted in some cases. The transmission link is composed of three fiber stages (F1, F2, and F3) and two ROPAs, the first one being remotely pumped from the transmitter (ROPA Tx) and the other one from the receiver (ROPA Rx). Figure 3 shows three possible ROPA configurations. It is possible to use only a single pump, the ROPA being based on single-stage pumping configuration in this case, with either forward or backward topology, as shown in Fig. 3a, b, respectively. When two pumps are used, the ROPA is said to be based on dual-stage pumping configuration with bidirectional topology, as shown in Fig. 3c. In the architecture shown in Fig. 2, the optical pump light is delivered to the ROPAs through dedicated delivery fibers (F1.1, F1.2, F3.1, and F3.2). Another option is to use the transmission fiber itself to deliver the pump power to the ROPAs [10–12]. However, the use of dedicated delivery fibers makes it possible to extend the unrepeatered transmission reach. This is because it avoids degradation in the transmitted signal caused by the propagation of the pump signal on the same fiber and also allows to deliver more pump power to the ROPA. The main drawback of this approach is the higher cost, so it should be employed only if there is no alternative. At the receiver side, the WDM signal is amplified by an EDFA pre-amplifier combined with a DRA stage with counter-propagating pumping. Finally, the WDM signal is demultiplexed to separate the individual channels. When designing an unrepeatered optical system, the four amplification stages that are shown in Fig. 2 should be considered: (i) a booster amplifier located at the transmitter terminal that could be followed by a first or high-order distributed Raman amplification; (ii) a first ROPA, named ROPA Tx in the following, which is placed

Fig. 2 System architecture

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Fig. 3 ROPA configurations: a forward topology; b backward topology; c bidirectional topology

inside the transmission link at a given distance from the transmitter terminal; (iii) a second ROPA, placed at a certain distance from the receiver terminal (ROPA Rx); and (iv) a pre-amplifier located at the receiver terminal, which could be combined with a first or high-order distributed Raman amplification to set up a Rx hybrid amplifier as well. Considering only single pass ROPAs without any gain flattening filter (GFF), it is possible to define a large number of variables that need to be considered in order to optimize the system performance, such as: the EDFA and distributed Raman amplification configuration for the hybrid amplification stages; the EDF length for the two ROPAs, as well as the distance from the respective optical pump sources located at the terminals. Among all the amplification stages, the optimization of the two ROPAs presents the highest level of complexity. For this reason, an optimization algorithm based on the simulation of all the possible combinations of parameters and selection of the best configuration would demand a great computational effort, even when the hybrid amplification stages are omitted from the optimization process. Therefore, any solution that leads to reduction of design complexity would make unrepeatered system design more feasible. To this aim, it was proposed in [15] to divide the unrepeatered system design in two parts. First, the proposed method focuses on defining the transmitter-side amplifiers, i.e., the Tx hybrid amplifier and ROPA Tx. After that, the amplifiers at the receiver side, i.e., ROPA Rx and Rx hybrid amplifier, are considered. Although there is a strong correlation between the two parts, the authors demonstrated that the proposed approach is capable of achieving the same optimal or suboptimal solution that would be achieved by performing the optimization process on the whole system. For a cascaded optically amplified system with regular spacing between amplification stages, it is well known that the noise figure of the first amplifiers is more significant to the system performance than that of the last amplification stages [5]. Hence, for system design purposes, it should be recommended that the optical ampli-

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fication stages at the beginning of the transmission link have the lowest noise figure, while for the amplifiers at the end of the link, whose noise figure have lower impact on the system performance, the design process is focused on gain improvement. However, this approach does not attain the optimal system performance for unrepeatered systems, where the amplification stages are unevenly distributed, with the Tx stages located closer to the transmitter terminal and the Rx stages concentrated at the receiver side. In fact, an optimal system design for unrepeatered systems should focus only on the gain of the transmitter-side amplifiers (booster/Tx hybrid and ROPA Tx) in order to keep the signal power level as high as possible, also taking into consideration the channel power level limit that is necessary to avoid nonlinear impairments. This is because the power level and OSNR at the input of the transmitter-side amplifiers is very high, thus reducing the influence of the amplifier noise figure on the system performance. On the other hand, for the receiver-side amplifiers (ROPA Rx and preamplifier/Rx hybrid), the system design must be focused on minimizing the amplifier noise figure, as due to the low signal input power and the high gain of the amplifiers, the impact of their noise figure on the system performance is higher. The simplified ROPA design method is summarized in Fig. 4. First, a set of realizable operation points (OPs) is established for the ROPA Tx, from which the OP that yields the highest gain (OPG max ) is selected. Next, the highest channel power (Pmax OP ) associated to OPG max is compared to the nonlinear threshold (NLTH ). If Pmax OP is higher than NLTH , it is eliminated from the set, and the process is repeated. Once the OPG max for the ROPA Tx is defined, the ROPA Rx OP (OPNFeq min ) is selected from the set of realizable OPs for the ROPA Rx as the one that yields the lowest noise figure (NFeq min ) of the equivalent Rx amplifier shown in Fig. 2. If the lowest channel power (Pmin OP ) is lower than the receiver sensitivity (PSEN ), it is eliminated from the set, and the process to select the optimal ROPA Rx OP is repeated. The unrepeatered link design can also consider the ROPA as a gain equalizer element. Although gain equalization is more critical for long-haul than for unrepeatered transmission, some gain equalization may be required along the transmission link to ensure proper detection of the lowest power channel. To achieve this purpose,

Fig. 4 ROPA design heuristics

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the ROPA design needs to balance the compromise between total gain optimization, noise figure optimization and gain equalization.

3 Experimental Demonstrations Figure 5 shows the most important results achieved in unrepeatered WDM transmission in recent years in terms of bit rate × reach product, as summarized in Sect. 1. This section will focus on 400G unrepeatered transmission, detailing the three record results achieved in [15–17] (denoted by red marks in Fig. 5). It will be shown how the use of advanced remote pumping technologies, in conjunction with the design optimization algorithm detailed in Sect. 2, is capable of enhancing the system performance, with each subsection showing a further improvement of the previous record results in terms of system reach and capacity.

3.1 10 × 400G Dual-carrier Transmission over 370 km This section describes a laboratory demonstration, as presented in [15], of unrepeatered WDM transmission of 10 x 400 Gb/s PM-16QAM dual-carrier Nyquist superchannels within a 75-GHz channel grid over 370 km, yielding a spectral efficiency (SE) of 5.33 b/s/Hz. This result represented, at the time of publication, the highest system reach record for dual-carrier 400G WDM unrepeatered transmission using 75-GHz flexible grid.

3.1.1

Experimental Setup

The experimental setup, depicted in Fig. 6, consists of an arbitrary waveform generator (AWG), operating at 63 GSa/s (8-bit resolution), producing four recurrently

Fig. 5 Recently published works on high-capacity unrepeatered optical transmission

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Fig. 6 Experimental setup for unrepeatered transmission of 10 × 400G dual-carrier superchannels. © 2016 IEEE. Reprinted with permission from [15]

repeating raised-cosine (RC) shaped (roll-off = 0.1) 32 GBd four-level signals, which are used as the in-phase (I) and quadrature (Q) components for the X and Y polarization tributaries of the 256 Gb/s (32 × 8) 16QAM signal. Digital pre-emphasis is applied to partially compensate for the digital-to-analog converter (DAC) bandwidth limitations (14 GHz). The AWG has eight differential outputs, with the four positive and the four negative ones driving two LiNbO3 dual-polarization quadrature modulators (DP-IQMs), respectively. Two arrays of ten 75-GHz-spaced external cavity lasers (ECLs) (linewidth = 100 kHz) generate the odd and even optical carriers with mutual spacing of 35 GHz. The odd and even carriers are separately modulated by the two DP-IQMs, and coupled for WDM transmission, where each odd + even carrier pair constitutes a 400G superchannel (line rate 512 Gb/s). In this way, the spacing between superchannels is 75 GHz, while the intra-channel subcarriers are separated by 35 GHz (see inset of Fig. 6). Due to the non-equal optical paths between the two IQMs and the channel multiplexing stage, decorrelation between the two subcarriers of the same superchannel is ensured. The link consists of three fiber spans for signal transmission and two dedicated fibers for remote pumping. Large effective area (Aeff ) ultra-low loss single-mode fiber (LA-ULL SMF) (ITU-T G.654.B, Aeff =110 µm2 , α = 0.169 dB/km at 1550 nm) is used within the first two spans to reduce nonlinear impairments, switching to the less expensive low-loss single-mode fiber (LL-SMF) (ITU-T G.652.D, Aeff = 80 µm2 , α = 0.188 dB/km at 1550 nm) in the last span, where signal power is considerably lower. The use of LL-SMF not only allows to reduce system cost, but its smaller effective area compared to that of LA-ULL SMF also helps to enhance the Raman gain. For ROPA pump delivery, LL-SMF is used at the transmitter ROPA (ROPA Tx), based on the forward-pumping scheme (F-ROPA) depicted in Fig. 3a, while LA-ULL SMF is used to deliver pump power to the receiver ROPA (ROPA Rx) with backward topology (B-ROPA), as in Fig. 3b. The reason for such choice is that the high F-ROPA input signal power causes the amplifier to operate in saturation regime, where small differences in pump power have minor effects on the amplifier gain. For example, for a 50-km fiber length, the pump power difference between LL-SMF and LA-ULL SMF are (0.188 − 0.169) × 50 = 0.95 dB. Conversely, the B-ROPA, operating in linear regime, is extremely sensitive to pump power variations. Also, it is located twice as further from the system terminal as its forward counterpart.

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At the receiver side, the optical power is set to 5 dBm per subcarrier by a variable optical attenuator (VOA), and each 400G superchannel is detected by a wideband polarization-diversity discrete coherent receiver (90◦ optical hybrid followed by four 40-GHz balanced photodetectors with no TIAs). A single local oscillator (15-dBm optical power) is used to detect both subcarriers. The four outputs are sampled at 80 GSa/s by a 4-channel real-time oscilloscope before being sent to the off-line digital signal processing (DSP) stage, which includes downsampling to 64 GSa/s, orthonormalization, chromatic dispersion compensation, and decision-directed least mean squares (DD-LMS)-based dynamic equalization with carrier recovery [18]. For forward error correction (FEC), a soft-decision left-terminated, spatially-coupled lowdensity parity-check (SC-LDPC) code generated from protographs [19] is employed, with syndrome former memory μ = 2. Fine code rate adaptation is achieved by shortening a set of mother codes (as opposed to shortening a single mother code, as, e.g., in [20]) to avoid performance degradation. The amplifier specifications are as follows. Each of the two DRA stages includes two pump lasers with wavelengths between 1445 and 1460 nm, providing a total optical power of 500 mW. The F-ROPA and B-ROPA were designed according to Sect. 2, considering a total launched pump power of 800 and 1300 mW at the delivery fiber input, being 69.3 and 16.7 mW the power reaching the respective ROPA. Figure 7a shows the simulation results for a total system reach of 350 km, considering different combinations of F-ROPA and B-ROPA parameters. The 350-km link

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length was chosen based on computer simulations, as the highest reach that guarantees OSNR ≥ 21 dB, which is ∼2 dB higher than the required OSNR, measured in back-to-back (∼19 dB) for a 32 GBd 16QAM signal at the pre-FEC BER limit of 3.3 × 10−2 . The OSNR at the receiver is shown as a function of the distance of the F/B-ROPA from the Tx/Rx terminal, respectively. For each F/B-ROPA distance value, sixteen different pairs of F-ROPA and B-ROPA EDF lengths were considered, given by all the possible combinations of four values (5, 7, 9, and 11 m) for each of the two ROPAs. The red circle in the figure identifies the optimal OP selected by the design heuristic. The two OPs (for 25:75 km and 25:100 km) with OSNR above that of the optimal OP did not meet the nonlinear threshold requirements. The heuristic, in fact, provides optimal trade-off between OSNR and nonlinear impairments. The obtained optimal OP for the F-ROPA was 5-m EDF length with 50 km distance from the Tx terminal (this OP provides maximum gain with lower-than-threshold channel power). For the B-ROPA, minimum NF was attained with a 9-m EDF length located at 100 km from the Rx terminal. Figure 7b shows the mean subcarrier power profile associated to the optimal OP throughout the transmission link. For the laboratory demonstration, two different scenarios are considered: (1) 350-km transmission with data post-processing using the standard DSP algorithm described above; (2) 370-km transmission (achieved by adding 20 km of standard single-mode fiber in the middle span), using the DSP in conjunction with a DBP algorithm for nonlinear compensation. In the first simulated scenario, the optimal EDF lengths for the F/B-ROPAs are 5 and 9 m, positioned 50 and 100 km from their respective terminals; for the second scenario, the optimal EDF lengths are 5 and 11 m, with the same distance from the terminals as in the 350-km case.

3.1.2

Experimental Results

Figure 8 shows the BER of the 10 superchannels (obtained from the average of the two subcarriers for each channel) for 3 different values of launched power per carrier (−3, 0, and 2.5 dBm), after 350-km transmission with off-line DSP at the receiver. A soft-decision (SD) pre-FEC BER threshold of 3.3 × 10−2 was used, consistent with the LDPC code with 24% overhead and the line rate of 512 Gb/s. The optimal trade-off between OSNR and nonlinearities was achieved with 0-dBm carrier launched power. Figure 8 also shows the BER for the 370-km transmission case, with and without nonlinear compensation, considering a launched power per carrier of 2.5 dBm. BER values below FEC limit were achieved for all channels after applying digital nonlinear compensation using a DBP algorithm with 21 steps distributed along the link as follows. The first 50-km LA-ULL SMF was divided into two portions of 20 and 30 km, with 5 and 6 equally spaced DBP steps, respectively. The following 220-km LA-ULL SMF span was compensated using 10 equally spaced steps. For the last 100-km LL-SMF, only linear distortion was compensated because of the low optical power levels. Figure 9 shows the estimated post-FEC BER results for the individual superchannels after 370-km transmission with nonlinear compensation (solid blue) and with

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Fig. 8 BER performance for all channels transmitted for 350 and 370 km. © 2016 IEEE. Reprinted with permission from [15]

Fig. 9 Post-FEC BER versus required per-channel FEC overhead. © 2016 IEEE. Reprinted with permission from [15]

linear compensation only (dashed red). Each channel is represented by a different marker. The post-FEC BER was estimated using the method proposed in [21]. Using nonlinear compensation, a SD-FEC overhead of 19.5% is sufficient for error-free operation of all channels, resulting in a net bit rate of 434 Gb/s. When only linear compensation is used, four channels required SD-FEC overhead higher than 24%. For these channels, the net rate of 400 Gb/s was not achieved. However, it can be observed that in an unrepeatered transmission all channels essentially share the same source-destination terminals. For this reason, traffic sharing techniques can be used to efficiently distribute the information between the channels, and guarantee equivalent overall WDM capacity.

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3.2 16 × 400G Single-Carrier Transmission over 403 km This section describes the laboratory demonstration of unrepeatered WDM transmission, as presented in [16], of 16 × 400 Gb/s single-carrier channels (66-GBd DP-16QAM) within a 75-GHz grid over 403 km (64.7 dB span loss), yielding a net capacity-reach product of 2.58 Pb/s km. At the date of publication, the achieved transmission distance represented the highest value demonstrated in 400G unrepeatered WDM transmission.

3.2.1

Experimental Setup

The experimental setup is depicted in Fig. 10. At the transmitter side, two groups of eight 150-GHz-spaced external cavity lasers (ECLs) with linewidth of 100 KHz are combined and independently modulated by a 29-GHz dual-polarization in-phase quadrature modulator (DP-IQM). Each DP-IQM is fed by four independent raisedcosine-shaped four-level electrical signals (roll-off = 0.1), representing each of the I and Q components of the two 16QAM signals for the X and Y polarizations. The electrical signals are generated using an arbitrary waveform generator (AWG) operating at 92 GSa/s with electrical bandwidth of 32 GHz. The symbol rate was optimized to achieve the best system performance, as detailed in the following section. Channel power pre-equalization was carried out at the optical transmitter, to achieve the same received OSNR for all channels. The transmission link consists of four spans. For the first two spans, 50 and 47 km of very-large effective area ultra-low loss single-mode fiber (VLA-ULL SMF) (ITUT G.654.D, Aeff =150 µm2 and α = 0.157 dB/km) were used, to reduce nonlinear impairments that would arise from the high input power per channel. The last two segments are 211 and 95 km of LA-ULL SMF (ITU-T G.654.B, Aeff = 112 µm2 and α = 0.157 dB/km), where the signal power is lower. For remote pumping of the two ROPAs, LA-ULL SMF was also used. The backward/forward ROPAs (B/F-ROPAs) were designed based on the procedure presented in [15], considering a total launched power into the two dedicated pump delivery fibers of 1.38 W and 880 mW, with optimal EDF lengths of 11 and

Fig. 10 Experimental setup for unrepeatered transmission of 16 × 400G single-carrier channels over 403 km

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13 m, respectively, positioned at 50 and 95 km from their respective terminals. At the DRA stages, two Raman pumps with wavelengths between 1445 and 1460 nm were transmitted into the transmission link. At the receiver side, each channel is selected by a tunable filter. Then, the 400G channel is detected using a discrete coherent receiver based on a 90◦ optical hybrid, a local oscillator (100-kHz linewidth), and four 40-GHz balanced photodetectors (PDs). The electrical signals at the output of the PDs are sampled by a four-channel real-time oscilloscope (80 GSa/s, 35 GHz electrical bandwidth). A standard DSP algorithm is used for off-line processing. The DSP includes resampling to two samples per symbol and orthonormalization. Static equalization is performed based on frequency domain equalizer (FDE) to mitigate CD only or DBP algorithm for joint compensation of nonlinear effects and CD. Polarization demultiplexing is performed by a two-stage equalizer. The first stage uses a 30-tap DD-LMS-based dynamic equalizer with carrier recovery. For FEC, a SC-LDPC code generated from protographs [19] is employed, with syndrome former memory of 2. When the DBP algorithm is used, the SC-LDPC outputs are demapped and fed back to DD-LMS equalizer in the second stage of equalization, acting as a training sequence. When linear FDE is considered, no FEC feedback is used at the polarization demultiplexing stage.

3.2.2

Experimental Results

To achieve the best system performance, the symbol rate was optimized in terms of required OSNR and implementation penalty in back-to-back (B2B), as depicted in Fig. 11. The symbol rate was swept from 62 to 70 GBd and the SC-LDPC overhead was calculated considering a net bit rate of 400 Gb/s with 1%-overhead for harddecision FEC. For the symbol rate of 66 GBd, 31%-OH with pre-FEC BER limit of 5 × 10−2 yielded the lowest required OSNR, i.e., 19.7 dB, with an OSNR penalty below 2 dB with respect to the theoretical limit. The total number of steps used in the DBP algorithm was optimized in terms of average Q2 gain per channel. Two different values of average launched power per

Fig. 11 Symbol rate and SC-LDPC overhead optimization in B2B

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channel (3 and 6 dBm) were considered, the optimum number of steps being 30 for both cases [22]. The channel performance in terms of pre-FEC BER after 403-km transmission for both 3 and 6-dBm average launch power per channel is depicted in Fig. 12. When using FDE for static equalization, all channels achieved BER values below the SDFEC limit (5.0 ×10−2 ) for 3-dBm/ch launch power. Increasing the launch power to 6 dBm/ch, channels 2, 4, 12, 14, and 16 exhibit BER values above the FEC limit. When using DBP and FEC feedback as described in the previous section, the performance of all channels satisfies the FEC limit requirement for both channel launch power values with increased system margin. Figure 13 shows the counted post-FEC BER for each channel after 403-km transmission, calculated similarly as proposed in [21]. For 3 dBm of launch power per channel (blue curves), the SC-LDPC is able to ensure error-free operation for all channels with OH below 30%, which corresponds to the SD-FEC limit of 5.0 × 10−2 . For 6-dBm/ch launched power (red curves), the worst-performing channel requires around 33%-OH to achieve error-free operation, effectively reducing the net bit rate to ∼394 Gb/s. Fig. 12 Pre-FEC BER versus channel index after 403-km transmission

Fig. 13 Post-FEC BER versus required overhead for 3 dBm/ch (blue) and 6 dBm/ch (red) average launch power

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3.3 24 × 400G Single-Carrier Transmission over 443.1 km This section describes the laboratory demonstration of the distance record in unrepeatered WDM transmission, as presented in [17], of 24 × 400 Gb/s single-carrier channels (64/66 GBd DP-16QAM) over 443.1 km (73.1-dB span loss), yielding a net capacity-reach product of 4.25 Pb/s×km. As shown in Fig. 5, this result is still the highest bit rate × reach record in unrepeatered WDM transmission to date.

3.3.1

Link Design

Following the methodology described in Sect. 2, the link design for the unrepeatered WDM transmission of 24 × 400 Gb/s single-carrier channels was carried out. The simulation setup used in the link design phase is depicted in Fig. 14. At the transmitter side, a WDM signal is generated by multiplexing 24 continuous-wave (CW) single-carrier channels (λ’s) starting at 191.65 THz with channel spacing of 75 GHz. The WDM signal is amplified by an EDFA booster combined with distributed Raman amplification (DRA) using two forward laser pumps at 1452 and 1457 nm, giving 700 mW total launched pump power into the fiber. The WDM signal transmission link is composed of three fiber stages (F1, F2, and F3) and two ROPAs (Tx and Rx). Each ROPA is based on a dual-stage pump configuration with bidirectional topology, as the one shown in Fig. 3c. The two ROPA pumps are generated by 1480-nm high-power Raman fiber lasers. The input pump power per delivery fiber was 3.2 W for the Tx ROPA and 3.6 W for the Rx ROPA. At the receiver side, the WDM signal is amplified by an EDF pre-amplifier combined with a DRA using a counter-propagating Raman fiber laser at 1455 nm with 1-W optical power. Finally, the WDM signal is demultiplexed, and the OSNR for each channel is evaluated.

Fig. 14 Simulation setup for unrepeatered transmission of 24 single-carrier channels

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Table 1 Simulation scenarios with different combinations of fiber types

Table 1 shows the simulation scenarios used in the link design phase. Four different scenarios, each corresponding to a different combination of fiber types, were considered. The first one (Setup 1) was entirely composed of LA-ULL SMF (ITU-T G.654.B, Aeff = 112 µm2 , α = 0.157 dB/km). The other three scenarios (Setup 2–4) were different combinations of LA-ULL SMF, VLA-ULL SMF (ITU-T G.654.D, Aeff = 150 µm2 , α = 0.157 dB/km), and LL-SMF (ITU-T G.652.D, Aeff = 82 µm2 , α = 0.183 dB/km). Limiting our analysis to Setup 2–4, for all of them the first span (F1) consisted of VLA-ULL SMF, in order to reduce fiber nonlinear impairments due to the high launched optical power per channel in the transmission link. At the second span (F2), only LA-ULL SMF was considered. In the other spans (F3, F1.X and F3.X) either LA-ULL SMF or LL-SMF was used. For the last transmission span (F3), LA-ULL SMF and LL-SMF were compared to find out which one performs best because of the trade-off between fiber attenuation and Raman gain. VLA-ULL SMF was not considered because the signal power per channel is considerably lower in the last section of the link. The scenario depicted in Setup 1 was used as performance reference, as it was the configuration that yielded the best performance among the considered scenarios. However, it was not possible to experimentally reproduce this setup, due to unavailability of the required amount of LA-ULL SMF. In all scenarios, the fiber attenuation curve as a function of the channel frequency was taken into consideration. The link design optimization process was executed considering two values of total launched optical power, i.e., 17 and 20 dBm. Table 2 summarizes the obtained results in terms of optimal EDF length and distance from transmitter/receiver for ROPA Tx/Rx, minimum received OSNR among all the WDM channels, and minimum received OSNR after equalization among all the WDM channels. The equalization of the OSNR at the receiver was performed by adjusting the channel power levels at the input of the EDFA booster. The reference Setup 1 scenario showed the best performance in terms of minimum OSNR (without and with equalization) at the receiver due to exclusive use of LA-ULL SMF. By analyzing the three other viable

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Table 2 Link design results for 17/20 dBm of total launched power

Fig. 15 Launched optical power per channel for 17 and 20 dBm of total launched power

scenarios, it can be seen that scenario Setup 4 presented the best performance, i.e., the highest value of the minimum equalized OSNR, therefore this scenario was chosen for the experimental demonstration. Figure 15 shows the launched optical power for each channel in all scenarios, without (all setups) and with OSNR equalization at the receiver. As can be seen, to achieve the equalization of the OSNR at the receiver (as shown in Fig. 16), it is necessary to decrease the launched power for all the channels from 1 to 15 and to increase the power of the other channels. The main reason behind this is the non-flat gain profile of the amplifiers along the link. However, it is important to point out that increasing the launched power per channel may cause signal degradation due to fiber nonlinear effects. The received OSNR for each channel in all scenarios, without and with OSNR equalization, is shown in Fig. 16. Based on the experimental BER versus OSNR curve of the single-channel system in B2B (Fig. 20), one can see that scenarios Setup 3 (equal.) and Setup 4 (equal.) exhibit the minimum OSNR exceeding the required OSNR of about 20 dB. Due to other degradation effects on the signal that were not considered in the link design, Setup 4 is a better choice as it has a higher OSNR margin relative to the required OSNR. Figure 17 illustrates the simulated optical power profile of channels 1 and 24 along the transmission link for the scenario Setup 4, without and with OSNR equalization at the receiver. In the equalized case, it is worth noting that the difference between

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Fig. 16 Received OSNR for 17 and 20 dBm of total launched power

Fig. 17 Simulated power profile map along the transmission link for 17 and 20 dBm of total launched power

the power levels of channels 1 and 24 is large only in the first link, being greatly reduced after the ROPA Tx and further decreasing as the channels propagate along the link.

3.3.2

Experimental Setup

The experimental setup is depicted in Fig. 18. At the transmitter, two arrays of 12 external cavity lasers (ECLs) with 100-kHz linewidth are combined and independently modulated by a 29-GHz dual-polarization in-phase quadrature modulator (DPIQM). The two DP-IQMs are fed by independent electrical signals generated using an arbitrary waveform generator (AWG) operating at 92 GSa/s, with 8-bit resolution and 32-GHz electrical bandwidth. The AWG generates four-level signals with raised-cosine pulse shape, which are used as the I and Q components of the 16QAM signals in the X and Y polarizations. In this work, two symbol rate values were considered: 66 GBd (1.39 oversampling, roll-off = 0.1) with 75-GHz channel spacing, and 64 GBd (1.43 oversampling, roll-off = 0.05) with 68.75-GHz channel spacing, resulting in spectral efficiencies of 5.33 and 5.81 b/s/Hz, respectively. Before being sent to the fiber link, the WDM signal was amplified by a hybrid amplifier (HYB Tx) based on an EDFA booster combined with a distributed Raman amplification (DRA) stage. Two different levels of total launched signal optical power

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Fig. 18 Experimental setup for unrepeatered transmission of 24 × 400G single-carrier channels over 443.1 km. © 2017 IEEE. Reprinted with permission from [17]

Fig. 19 Measured launched power and received OSNR per channel at a 64 and b 66 GBd for 17 (empty marker) and 20 (solid marker) dBm of total launched power. © 2017 IEEE. Reprinted with permission from [17]

after HYB Tx were considered, i.e., 17 and 20 dBm. As previously done in the link design phase, channel power pre-equalization before the HYB Tx amplification stage was carried out in order to attain similar per channel OSNR values at the receiver. Measured launched power and received OSNR per channel are shown in Fig. 19a for 64 GBd and in Fig. 19b for 66 GBd. The transmission link is composed of three fiber stages, as well as the delivery fiber links. At the beginning of each delivery link, optical filters (OFs) centered at 1480 nm were used to mitigate stimulated Raman scattering (SRS) induced by propagation of the high pump power into the delivery fiber. By doing so, it was possible to maximize the pump power level reaching the two ROPAs. The two ROPAs (Tx and Rx) were designed according to the characteristics of the chosen scenario Setup 4 showed in Table 2. Due to the limited amount of fiber available for the laboratory demonstration, it wasn’t possible to exactly reproduce the transmission link design depicted in the scenario Setup 4 in Table 1. However, the required changes in the experimental setup were minor and carefully chosen in order to keep the transmission link as close as possible to Setup 4. More in detail, a combination of VLA-ULL SMF and LA-ULL SMF was used for the first span, as their attenuation versus frequency curves are practically the same. At the ROPA Tx output, a ∼22-km span of VLA-ULL SMF was used to reduce nonlinear impairments. In the pump delivery fiber links, the use of some spans of few kilometers of LA-ULL SMF or LL-SMF was necessary to attain the exact distances from the terminals for the two ROPAs.

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At the receiver, the single-carrier 400G channel is selected by a tunable optical filter with 100-GHz bandwidth. Each channel is then detected using a discretecomponent polarization-diversity coherent receiver comprising a local oscillator (100-kHz linewidth ECL), 90◦ optical hybrid and 40-GHz balanced photodetectors (PD). The electrical signals at the output of the four PDs are sampled by a 4-channel real-time oscilloscope operating at 80 GSa/s, with electrical bandwidth of 35 GHz, and then processed by an off-line DSP stage. The DSP algorithm includes resampling to 2 samples per symbol and orthonormalization. Static equalization is performed using either a frequency domain equalizer (FDE), to mitigate chromatic dispersion (CD) only, or a digital backpropagation (DBP) algorithm for joint compensation of CD and nonlinear effects. For polarization demultiplexing, a 36-tap DD-LMSbased dynamic equalizer with carrier recovery is used. For FEC, a soft-decision left-terminated, spatially-coupled low-density parity-check code is employed.

3.3.3

Experimental Results

The back-to-back (B2B) curves of BER as a function of OSNR for single-channel (SC) and WDM signal at 64 GBd (red curves) and 66 GBd (blue curves) are shown in Fig. 20. The curves exhibit negligible penalty between the single-channel and the WDM case (with BER measured only at the central channel), being the required OSNR ≈ 20 dB at the FEC limit (inset) for both the considered signaling rates. The WDM transmission performance, evaluated in terms of received BER as a function of channel index, is depicted in Fig. 21. For 17 dBm of total launched power, all channels achieved BER values below the SD-FEC limit at both the considered symbol rates. When increasing the launched power to 20 dBm, BER values below the 4.4 × 10−2 pre-FEC limit are not attained for channel 8 and for channels 16–24 at 64 GBd. At 66 GBd, BER values below 5.0 × 10−2 pre-FEC limit are not achieved for channel 12 and for channels 16–24. The BER degradation is a consequence of the nonlinear effects arising from transmission of the WDM channels into the optical fiber. However, when using the DBP algorithm for nonlinear impairments

Fig. 20 Pre-FEC BER in B2B. © 2017 IEEE. Reprinted with permission from [17]

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Fig. 21 Pre-FEC BER after 443.1 km and Q2 gain with DBP. © 2017 IEEE. Reprinted with permission from [17]

compensation, it can be seen that almost all channels (the only exception being channel 23) achieve a BER value below the pre-FEC threshold. Figure 21 shows the Q2 gain per channel provided by the DBP algorithm at the two considered launched power values, with 40 steps equally distributed in the first four fiber spools of the transmission link (10 steps per spool), where the optical power per channel is higher (linear compensation only was performed in the remaining spools). It is worth noting that as the channel power increases, the nonlinear compensation gain becomes more significant.

Fig. 22 Post-FEC BER versus OH at 64 (red curves) and 66 (blue curves) GBd for 17 dBm of total launch power. © 2017 IEEE. Reprinted with permission from [17]

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Figure 22 presents the counted post-FEC BER as a function of the overhead (OH) (calculated similarly as in [16]) for all channels after 443.1 km with 17 dBm of total launch power at both symbol rates. Considering 64 GBd, error-free operation could be achieved for all the 24 channels with an OH of 27%, which corresponds to the pre-FEC limit of 4.4 × 102 . At 66 GBd, error-free operation could be attained with an OH of 31%, corresponding to the 5.0 × 102 pre-FEC limit.

4 Conclusions In a context where global connectivity is the ultimate goal for Internet and system providers, it is important to address the challenges arising from trying to deliver high-speed reliable connections to remote or hostile regions. Unrepeatered optical transmission appears today as the most promising technology towards this goal, as it provides a viable trade-off between system performance and capital and operational costs. In this scenario, system design becomes crucial. This chapter presented a low-complexity approach to unrepeatered system design, proving its effectiveness by means of laboratory demonstrations. The high number of record results achieved in the past few years, the most significant of which were presented here, highlights the enormous potential of repeaterless optical transmission for future high capacity (400G per channel and beyond) connections in difficult access environments. Acknowledgements The authors would like to thank Rafael C. Figueiredo for reviewing this chapter. This work was supported by Brazilian Ministry of Science, Technology, Innovation and Communications (MCTIC), FUNTTEL/FINEP.

References 1. Clesca B, Perrier P, Fevrier HA, Chang DI, Burtsev S, Pedro HD, Pelouch W (2014) Field deployment of advanced photonic technologies for ultra-high bit rate and ultra-long reach terrestrial WDM transmission in Brazil. In: Asia communications and photonics conference 2014, Optical Society of America, p ATh4E.4 2. Agrawal GP (2005) Lightwave technology: telecommunication systems. Wiley, New York 3. Bromage J (2004) Raman amplification for fiber communication systems. IEEE J Lightwave Technol 22(1):79–93 4. Chang D, Pelouch W, Burtsev S, Perrier P, Fevrier H (2015) Unrepeatered high-speed transmission systems. In: 2015 optical fiber communications conference and exhibition (OFC), Optical Society of America, p W4E.3 5. Desurvire E (1994) Erbium-doped fiber amplifiers. Wiley, New York 6. OIF-Tech-Options-400G-01.0 (2015) Technology options for 400G implementation. Standard, Optical Networking Forum (OIF) 7. Mongardien D, Bastide C, Lavigne B, Etienne S, Bissessur H (2013) 401 km unrepeatered transmission of dual-carrier 400 Gb/s PDM-16QAM mixed with 100 Gb/s channels. In: ECOC 2013; 39nd European conference on optical communication, pp 1–3

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8. Downie JD, Hurley J, Roudas I, Pikula D, Garza-Alanis JA (2014) Unrepeatered 256 Gb/s PM-16QAM transmission over up to 304 km with simple system configurations. Opt Expr 22(9):10256–10261 9. Bissessur H, Bastide C, Dubost S, Etienne S, Mongardien D (2014) 8 Tb/s unrepeatered transmission of real-time processed 200 Gb/s PDM 16-QAM over 363 km. In: ECOC 2014; 40nd European conference on optical communication, pp 1–3 10. Bissessur H, Bastide C, Dubost S, Etienne S (2015) 80x200 Gb/s 16-QAM unrepeatered transmission over 321 km with third order Raman amplification. In: 2015 optical fiber communications conference and exhibition (OFC), pp 1–3 11. Mongardien D, Bastide C, Bissessur H, Etienne S (2015) 15.4 Tb/s C-band only unrepeatered transmission of real-time processed 200 Gb/s PDM-16 QAM over 355 km. In: Asia communications and photonics conference 2015, Optical Society of America, p AM3D.2 12. Bissessur H, Bastide C, Etienne S, Dupont S (2017) 24 Tb/s Unrepeatered C-band transmission of real-time processed 200 Gb/s PDM-16-QAM over 349 km. In: 2017 optical fiber communications Conference and Exhibition (OFC), Optical Society of America, p Th4D.2 13. Huang YK, Ip E, Aono Y, Tajima T, Zhang S, Yaman F, Inada Y, Downie JD, Wood W, Zakharian A, Hurley J, Mishra S (2017) Real-time 8x200-Gb/s 16-QAM unrepeatered transmission over 458.8 km using concatenated receiver-side ROPAs. In: 2017 optical fiber communications conference and exhibition (OFC), Optical Society of America, p Th2A.59 14. Zhang J, Yu J, Chien HC (2017) 1.6Tb/s (4x400G) unrepeatered transmission over 205-km SSMF using 65-GBaud PDM-16QAM with joint LUT pre-distortion and post DBP nonlinearity compensation. In: 2017 optical fiber communications conference and exhibition (OFC), Optical Society of America, p Th2A.51 15. Januário JCSS, Rossi SM, Ranzini SM, Parahyba VE, Rozental VN, de Souza ALN, Bordonalli AC, de Oliveira JRF, Reis JD (2016) Unrepeatered transmission of 10 x 400G over 370 km via amplification map optimization. IEEE Photonics Technol Lett 28(20):2289–2292 16. Januário JCSS, Rossi SM, Junior JHC, Chiuchiarelli A, Souza ALN, Felipe A, Bordonalli AC, Makovejs S, Oliveira JRF, Reis JD (2017a) Unrepeatered WDM transmission of single-carrier 400G (66-GBd PDM-16QAM) over 403 km. In: 2017 optical fiber communications conference and exhibition (OFC), Optical Society of America, p Th4D.1 17. Januário JCSS, Rossi SM, Junior JHC, Chiuchiarelli A, Souza ALN, Felipe A, Bordonalli AC, Makovejs S, Mornatta C, Festa A, Golovchenko E, BuAbbud G, Reis JD (2017b) Singlecarrier 400G unrepeatered WDM transmission over 443.1 km. In: ECOC 2017; 43rd European conference on optical communication, pp 1–3 18. Savory SJ, Gavioli G, Killey RI, Bayvel P (2007) Electronic compensation of chromatic dispersion using a digital coherent receiver. Opt Expr 15(5):2120–2126 19. Mitchell DGM, Lentmaier M, Costello DJ (2015) Spatially coupled LDPC codes constructed from protographs. IEEE Trans Inf Theor 61(9):4866–4889 20. Zhang Y, Djordjevic IB (2014) Staircase rate-adaptive LDPC-coded modulation for high-speed intelligent optical transmission. In: 2014 optical fiber communications conference and exhibition (OFC), Optical Society of America, p M3A.6 21. Schmalen L, Buchali F, Leven A, Brink ST (2012) A generic tool for assessing the soft-FEC performance in optical transmission experiments. IEEE Photonics Technol Lett 24(1):40–42 22. Júnior JHC, Souza ALN, Janurio JCSS, Rossi SM, Chiuchiarelli A, Reis JD, Makovejs S, Mello DAA (2017) Single-carrier 400G unrepeatered WDM transmission using nonlinear compensation and DD-LMS with FEC feedback. In: 2017 SBMO/IEEE MTT-S international microwave and optoelectronics conference (IMOC), pp 1–5

Impact of Nonlinear Effects and Mitigation on Coherent Optical Systems Stenio M. Ranzini, Victor E. Parahyba, José Hélio da C. Júnior, Fernando Guiomar and Andrea Carena

Abstract This chapter presents an overview of modeling and mitigation of nonlinear effects on coherent optical systems. The Gaussian Noise (GN) is presented as an efficient method to analyze the nonlinear propagation in an uncompensated link and used to estimate the system performance. In order to compensate for the nonlinear impairments, four digital techniques were investigated: Digital Back-Propagation (DBP), DBP with coupled equations, Volterra series, and Maximum Likelihood Sequence Estimator (MLSE). Different scenarios were used to validate the algorithms. Finally, a nonlinear estimation algorithm based on Steepest Descent Algorithm (SDA) is shown and experimentally validated in an unrepeatered optical system.

1 Introduction The evolution of Internet traffic combined with migration to cloud-based services are forcing a complete change in the optical networks industry, urging for high-bitrate solutions. In this context, there are few commercial alternatives to increase the system capacity. For instance, (i) single-carrier systems can scale up the symbol rate, (ii) multi-subcarrier systems at constant symbol rate may explore higher number of optical subcarriers, and finally, (iii) it is always possible to augment the cardinality of the modulation format. Regarding the first approach, there are works reporting baud rates up to 128.8 GBd [1]. However, this solution requires high bandwidth components, and Digital-toAnalog/Analog-to-Digital Converter (DAC/ADC) operating with high sample rates. The second alternative is to employ parallel optical processing, grouping multiple optical subcarriers independently modulated with low baud rate, combining to S. M. Ranzini (B) · J. H. C. Júnior CPqD, Optical Technologies Division, Campinas, SP 13086-902, Brazil e-mail: [email protected] V. E. Parahyba CEA, CEA Grenoble - 38054, Grenoble, France F. Guiomar · A. Carena Politecnico di Torino, Optical Communication Group, 10129 Torino, TO, Italy © Springer Nature Switzerland AG 2019 A. Paradisi et al. (eds.), Optical Communications, Telecommunications and Information Technology, https://doi.org/10.1007/978-3-319-97187-2_5

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generate a multi-carrier signal called super channel [2]. The main techniques considered in the literature are Coherent Orthogonal Frequency-Division Multiplexing (Co-OFDM) [3] and Nyquist Wavelength-Division Multiplexing (WDM) [4]. Both implementations of super channels require modifications in the optical front-end. Even more, increasing the number of subcarriers will induce nonlinear impairments, degrading the performance of optical systems. Recent works evaluated the application of up to 12 subcarriers [5]. Finally, the third approach considers the use of high-order modulation formats. Some experiments were demonstrated employing up to PM-1024QAM [6]. However, the spectral efficiency of dense constellations comes at the cost of lower tolerance of nonlinear effects and noise, which reduces the performance of optical systems. Recent advances in coherent Digital Signal Processing (DSP) technology are shifting the fiber-optic communication paradigm, enabling to mitigate linear effects such as Chromatic Dispersion (CD) and Polarization Mode Dispersion (PMD) in the digital domain. Today, nonlinear impairments induced by the Kerr effect in optical fibers are the most significant factor limiting the transparent reach of optical systems, and the Digital Back-Propagation (DBP) algorithm is the reference to nonlinear compensation [7]. However, the DBP presents a high computational complexity, motivating the search for an efficient and low-complex alternatives like Volterra series [8] and Maximum Likelihood Sequence Estimator (MLSE) [9]. The nonlinear compensation techniques mentioned before assuming full knowledge of optical fiber parameters. However, this can be difficult or impossible to obtain in legacy systems or under dynamic environments. In order to overcome this challenge, blind-adaptive algorithms are available in the literature to estimate the nonlinear parameter [10]. It is also of the interest of the community to have methods to accurately predict the system’s performance over a wide range of scenarios. In this way, the Gaussian Noise (GN) model was proposed and proved to be an efficient method to model nonlinear propagation, and has been extensively experimentally validated [11]. The chapter is organized as follows. Section 2 introduces the reader to the major key nonlinear aspects of optical fibers and reviews the modeling approach of GN. Section 3 presents an overview of the most conventional digital techniques to compensate the nonlinear effects such as DBP, DBP coupled equations, Volterra series, and Maximum Likelihood Sequence Estimator (MLSE). Finally, Sect. 4 demonstrates an adaptive algorithm to estimate the fiber nonlinear parameter.

2 Gaussian Noise (GN) Model In recent years, a large number of models for nonlinear propagation in optical fibers have been introduced. Most of them rely on the new link paradigm introduced by coherent systems, where CD is fully compensated electronically in the DSP receiver module. The impact of nonlinearity due to Kerr effect in the fiber material, is usually labeled as Nonlinear Interference (NLI). An additive Gaussian noise that is added

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to propagated signals, independent from the optical noise, is a good approximation of NLI. Under this assumption, at any link section the system performance can be directly related to a Quality of Transmission (QoT) parameter that can be defined for each transmitted channel and it is an equivalent OSNR for the link taking into account both ASE noise accumulation and NLI generation: O S N Rlink =

Pch . PAS E + PNLI

(1)

Models based on this assumption are well known as GN models. The final goal of GN models is to derive the power spectral density for NLI, G NLI ( f ), needed to calculate PNLI . In [12], it has been introduced for the first time the name GN model and a full derivation for the general expression of NLI power spectral density: 16 2 γ G NLI ( f ) = 27



+∞ −∞



+∞ −∞

G T x ( f 1 )G T x ( f 2 )G T x ( f 1 + f 2 − f )

(2)

   1 − e−2αL S e j4π 2 |β2 |( f1 − f )( f2 − f ) 2   ·   2α − j4π 2 |β2 |( f 1 − f )( f 2 − f )    sin2 2N S π 2 ( f 1 − f )( f 2 − f )|β2 |L S   d f1 d f2 · sin2 2π 2 ( f 1 − f )( f 2 − f )|β2 |L S

where • • • •

G T x ( f ) is the transmitted signal spectrum; N S is the number of spans; L S is the span length; α, β2 and γ are the fiber parameters: attenuation, chromatic dispersion, and nonlinearity, respectively.

This is a very general expression valid for any system, with the simplifying assumption that the signal has a Gaussian distribution at the link input. However, this is not completely true unless a pre-distortion is applied to the signal. The PNLI estimation obtained with this method for channel modulated with state-of-the-art symbol rate of 32 GBd has an error in the first spans that for PM-QPSK can reach up to several dB but it reduces to less than 2 dB after 20 spans. A positive point is that the Eq. 2 always leads to an overestimation of NLI, so that any design based on it will guarantee a conservative approach with a certain level of margin. It has also been shown that for higher order modulation formats, like PM-16QAM and further, the accuracy is much better and asymptotic errors for long distances are halved to less than 1 dB [13]. In Fig. 1, it is reported an example of the accumulation of NLI along a periodically amplified link. We have considered a normalized PNLI because it is a parameter independent from channel power, defined as ηNLI =

PNLI . 3 Pch

(3)

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Fig. 1 Normalized NLI (ηNLI ) for a periodical link with EDFA amplification recovering span loss. Solid blue: GN model. Dashed blue: IGN model. Solid red: simulation. System parameters: 15 channels, PM-QPSK, 32 GBd, 33.6 GHz of channel spacing, standard SMF, spans of 100 km

It can be clearly observed (Fig. 1) that the NLI estimation error reduces when the number of span increases. As discussed above, this case considers only a few channels and PM-QPSK, thus the gap at the beginning of the link is quite large but it quickly decreases below 2 dB. The same figure also reports a curve referring to the Incoherent GN model (IGN). It is a simplified approach to the GN model that allows to reduce the computational speed. IGN assumes that NLI accumulates incoherently along the link, so it can be evaluated using Eq. 2 for a single span and then it scales up linearly. Under this assumption, the IGN provides the evolution of the PNLI along the link with a single calculation of Eq. 2. This avoids the evaluation of the last factor of the integrand function, the so-called array-factor, which requires notable computational effort slowing down the whole calculation. The simpler IGN model shows an improved accuracy compared to the standard GN model, but it is not supported by any theoretical evidence. It is just by chance that IGN provides a better NLI estimation due to the linear accumulation that partially compensates for the transient error in the initial dispersion. As we have shown, the GN model has good accuracy. However, in some conditions (short distances, low-order modulation formats, and few channels), the GN model can deliver only a rough approximation of NLI. Nonetheless, it is important to point out that any error on PNLI evaluation is strongly mitigated when it comes to system performance optimization. In particular, it must be noted that, due to the fact that 3 , performance parameters like maximum reach (L M AX ) PNLI is proportional to Pch or maximum link OSNR (O S N Rlink,M AX ) evaluated at the optimal launch power, depend on PNLI as follows:

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 L M AX ∝

3

 O S N Rlink,M AX ∝

3

1 PNLI

(4)

1 . PNLI

(5)

This implies that inaccuracies in NLI estimation are mitigated by a factor of 1/3 in logarithmic scale. This means that an error of 1 dB in the estimation of PNLI leads to only 1/3 dB error in L M AX and O S N Rlink,M AX estimation, equivalent to 8%. This basic version of the GN model has been extensively validated both with simulations and experiments [14–16]. In case further accuracy is needed for the NLI estimation, the standard GN model in Eq. 2 can be improved to an Enhanced GN model (EGN) [17]. EGN ignores the hypothesis that the signal has a Gaussian distribution at the link input and introduces an additive correction term in the GN model: EGN GN ( f ) = G NLI ( f ) + G corr G NLI NLI ( f ).

(6)

As it can be seen in Fig. 2, the accuracy of NLI estimation is strongly enhanced and the estimation error is almost negligible after the first span. However, a classical tradeoff arises because higher accuracy implies higher model complexity, which increases computational effort. Indeed, EGN requires to evaluate a larger set of integrals than

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Fig. 2 Normalized NLI (ηNLI ) for a periodical link with EDFA amplification recovering span loss. Solid blue: GN model. Solid green: EGN model. Solid red: simulation. Main system parameters are listed in the following. Modulation format: PM-QPSK, symbol rate: 32 GBd, number of channels: 15, channel spacing: 33.6 GHz, fiber type: SMF, span length: 100 km

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GN to determine the correction term [17]. For long distances, an asymptotic closedform expression for the correction term is available [18] and it provides high accuracy without requiring to evaluate the whole set of integrals in the EGN model. The EGN model is a valuable approach to study in depth the NLI generation; it shows that NLI has a dependence on the symbol rate. Indeed, the work in [19] demonstrates that through Symbol-Rate Optimization (SRO) is possible to minimize the amount of NLI generated in a link. Considering standard fibers and typical link lengths, optimal symbol rates always fall in the range between 2 and 4 GBd. As a matter of fact, employing such low symbol-rate values to deploy optical channels is not a practical solution: it would generate an exaggerated increase in the number of transceivers needed to fill up the available bandwidth with the same spectral efficiency. For example in the C-band, we could fit thousands of channels. An help comes from the DSP at transmitter side, normally employed for spectral shaping: it allows to generate Multi-subcarrier (MSC) signals electrical signals. Each optical carrier is then modulated with several electrical subcarriers slicing the spectrum in subchannels working at the optimal symbol rate for the considered link. This approach has proven its efficiency [19] and can be combined to other nonlinear mitigation techniques, like DBP. Given that the GN model provides low accuracy for low symbol rate signals, NLI evaluation for MSC channels requires to employ EGN, otherwise the benefits obtained using SRO cannot be observed. This is mainly due to the slow impact of chromatic dispersion that takes very long distances to impose a Gaussian distribution to the signal, that is the main hypothesis used in the derivation of the GN model. As it has been pointed out before, in general EGN evaluation is quite complex but for the specific case of MSC with low symbol rate the NLI accumulation has been found to be almost linear with respect to the number of spans [20]. In Fig. 3, we report NLI for a MSC system showing both the EGN, with its proper coherent accumulation and also a simplified EGN incoherent approach where the NLI accumulates linearly along the link. Similarly to the IGN concept introduced above, the I-EGN is a simplified approach to the EGN model that assumes that can be evaluated using Eq. 6 for a single span and then scaling it up linearly. Despite its simplification, such approach leads to very small errors ( 1 fiber spans and EDFAs. Considering a step-size L = Ns L s (length of each optical link section), each inverse VSTF step is applied as



 A˜ x (ωn , z − L) = Dˆ A˜ x (ωn , z), L + Nˆ A˜ x (ωn , z), A˜ y (ωn , z), L ,

(14)

where A˜ x and A˜ y are the frequency-domain optical field envelopes in the x- and y-polarizations, evaluated at the discrete angular frequency, ωn , and at propagation distance z. As evidenced by expression (14) and Fig. 8, the inverse VSTF requires ˆ and nonlinear ( Nˆ ) operators, which are the independent evaluation of linear ( D) fully applied in frequency domain. Note that the equalization of the y-polarization is simply obtained by commuting the x/y indices in (14). For simplicity, in this chapter, we will consider the specific case of an homogeneous optical link composed of uncompensated uniform fiber spans (the same fiber parameters and length across ˆ is given by all spans). 1 In that case, the linear dispersive operator, D,

1 Nevertheless,

fiber link.

the inverse VSTF can also be easily generalized to any other heterogeneous optical

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Dˆ A˜ x (ωn , z), L = K 1 (ωn , L) A˜ x (ωn , z).

as

(15)

Neglecting higher order dispersive terms, the multi-span linear kernel, K 1 , reads   β2 2 (16) K 1 (ωn , z) = exp − j ωn z , 2

where α and β2 are the attenuation and group velocity dispersion coefficients, respectively. In turn, the nonlinear operator, Nˆ , is obtained from a double summation over N samples corresponding to each Fast Fourier transform (FFT) block, 

Nˆ A˜ x (ωn , z), A˜ y (ωn , z), L = N N 8 − j ξ γ K 1 (ωn , L) K 3 (ωn , ωk , ωm )F(ωn , ωk , ωm ) 9 m=1 k=1   × A˜ x (ωk , z) A˜ ∗x (ωm , z) + A˜ y (ωk , z) A˜ ∗y (ωm , z) A˜ x (ωn+m−k , z),

(17)

where γ is the nonlinear coefficient and 0 < ξ ≤ 1 is a free optimization parameter. K 3 is the third-order intra-span nonlinear kernel, K 3 (ωn , ωk , ωm ) =

  1 − exp αL s − jβ2 (ωk − ωn )(ωk − ωm )L s −α + jβ2 (ωk − ωn )(ωk − ωm )

,

(18)

F(ωn , ωk , ωm ) is a multi-span phased-array factor [33], which takes into account the coherent accumulation of nonlinearities over L/L s fiber spans,   β2 (ωk − ωn )(ωk − ωm ) (L − L s ) F(ωn , ωk , ωm ) = exp − j 2 sin (β2 (ωk − ωn )(ωk − ωm )L/2) . × sin (β2 (ωk − ωn )(ωk − ωm )L s /2)

(19)

Being based on entry-wise matrix multiplications, the inverse VSTF algorithm is highly parallel, favoring real-time implementation. However, with numerical complexity evolving as O(N 2 ) per equalized sample, where N is the FFT block-size, as defined in expression (17), the DSP resources required for parallel real-time implementation quickly scale up to unfeasibly large values, hindering practical application. This issue is addressed in the literature [40–45] with proposals that exploit advanced cascaded structures for the inverse VSTF [43, 45], as well as aggressive pruning of the K 3 coefficients [46, 47], enabling to achieve implementation complexities as low as O(log(N )) per equalized sample. In order to explore other degrees of freedom for complexity reduction, an equivalent time-domain realization of a frequency-flat inverse VSTF is derived in [48] and experimentally demonstrated

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in [49]. Interestingly, these latest time-domain approaches enabled the implementation of structures that resemble the well known split-step Fourier method, with the notable advantage of enabling nonlinear compensation in separate parallel branches with larger step-sizes [49]. The inverse VSTF and its simplified versions were widely experimentally demonstrated over 100G [39, 47] and 400G [49] transmission systems based on several modulation formats such as PM-QPSK, PM-16QAM, and PM-64QAM. In the following, we briefly review the experimental results reported in [47], corresponding to PM-64QAM transmission over Pure Silica Core Fiber (PSCF). The transmitted signal is composed of 10 channels modulated at 10.4 GBaud PM-64QAM (124.8 Gb/s) with root-raised cosine pulse shaping (0.05 roll-off factor). The signal is then propagated over an optical recirculating loop composed of 2 identical spans of 150 µm2 PSCF with 54.44 km each, attenuation of 0.161 dB/km, and dispersion parameter of 20.7 ps/nm/km. The signal performance (in terms of Q-factor, obtained from counted BER) after chromatic dispersion equalization (CDE) and nonlinear compensation with the inverse VSTF is depicted in Fig. 9a and b, respectively. The obtained results demonstrate that the inverse VSTF yielded an improvement of ∼30% on the maximum reach (from ∼1200 to ∼1550 km) at a threshold Q-factor of 5.7 dB (BER of 2.7 × 10−2 ). Most interestingly, these results were obtained with a singlestep inverse VSTF (step-size, L, equals to the full transmission length), which was able to achieve the same performance as a highly iterative SSFM-based DBP approach.

(a)

(b)

Fig. 9 Performance of a 100G PM-64QAM signal with linear and nonlinear compensation. The contour maps indicate the Q-factor versus launched power and transmission distance. The dashed lines indicate the estimated maximum reach for a threshold Q-factor of 5.7 dB. a Chromatic Dispersion Equalization (CDE), b Inverse VSTF (IVSTF)

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3.4 Maximum Likelihood Sequence Estimation (MLSE) The MLSE was initially proposed for digital Pulse-Amplitude-Modulated (PAM) sequences in the presence of finite intersymbol interference and white Gaussian noise [50]. Its structure comprises a whitened matched filter along with a recursive nonlinear processor, the Viterbi Algorithm [51]. MLSE- based equalization is now widely used in 10 Gb/s On-Off Keying (OOK) modulation systems. Recently, they have attracted attention as an alternative approach to the problem of nonlinearity compensation, having as main advantage the fact that it does not need the knowledge of the channel (i.e. its parameters of α, β, and γ ) [52]. Nonlinear effects in conjunction with CD and PMD can be understood as a specific form of intersymbol interference that distorts the optical signal so that symbols overlap with their neighbors. The set of algorithms responsible for the linear equalization of the received optical signal, which has as its last element an estimator and phase corrector, can be seen as approximately equivalent in principle to the whitened matched filter. The outcome of the set of algorithms is then viewed as a signal sampled at one sample per symbol corrupted with intersymbol interference, derived from the nonlinear effects, and white Gaussian noise and can then be treated with the Viterbi Algorithm.

3.4.1

The Viterbi Algorithm

The Viterbi Algorithm is implemented by establishing a library of M n possible sequences, or states, where M is the number of constellation points of the transmitted signal and n refers to the memory of the channel, that is, the number of symbols that are considered to be interdependent. We then proceed to a training phase, where a probability distribution function (PDF) is established at reception for each possible state transmitted. There are several alternatives for these PDF estimations, a common approach is to consider them as approximately Gaussian [53]. Although this is not a completely valid premise, it allows PDF determination with just the information of the mean and variance of the signal. In this work, however, we decided to construct a histogram of the received signal and to have a more accurate estimation of the signal’s PDF. Figure 10 represents the decision process of the Viterbi Algorithm for an example of four stages. After receiving a new symbol, the algorithm takes into account the sequence already established in order to compute the new sequence which has the highest probability according to the PDFs. Unlike other possible solutions for the mitigation of nonlinear effects, MLS does not suffer with high computational cost. It only needs M n additions and M n−1 comparisons per received symbol. The main drawback is the high amount of memory potentially needed to store the PDFs. In order to alleviate this issue, we consider the symbols of each polarization, in a polarization modulation scheme, as independent. In doing that, we could establish

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Fig. 10 Example of the Viterbi Algorithm for a case of four stages. Green circles represent the chosen sequence, while the red ones represent possible alternatives that were rejected following the criteria of maximum likelihood

M = 2 × K , where K is the number of constellation points in each polarization, instead of M = K 2 .

3.4.2

Experimental Setup

Being just at the final symbol decision part, MLSE could be used alongside with other nonlinear compensation methods, such as the classical DBP. The experimental verification of the MLSE equalization potential was performed in the context of a single channel transmission modulated at 224 Gb/s PDM-16QAM with launch power varying from −3 to 3 dBm. The link consists of an optical recirculation loop of approximately 72 km of pure silica fiber and an EDFA adjusted to fully compensate for the attenuation of the link. The transmitted signal circulated 10 times inside the loop, leading to an equivalent distance of 720 km. Please refer to [9] for more details about the experimental setup.

3.4.3

Experimental Results

Figure 11 shows a comparison using three different techniques: MLSE, DBP, and MLSE applied together with DBP. For 720 km, it was impossible to obtain a BER below FEC Limit using only linear equalization techniques. As expected, for launch power values above −1 dBm, BER increases indicating the inability of the method to completely compensate for nonlinear effects, even in this single-channel context. This is due to different effects such as IXPM, IFWM, or even the interaction between ASE noise and nonlinearity, as well as insufficient representation of DBP to compensate for SPM, i.e., more equalization blocks would be needed. It is interesting to note that better results are obtained with MLSE than with DBP. This behavior may have two explanations. First, the lack of an exact knowledge of the parameters of the fiber (i.e, α, β, and γ ), which can impact DBP’s performance; second, the unwanted optical filtering of the devices used (transmitter, receiver, etc.) may be larger than expected, causing high intersymbol interference. The joint appli-

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Fig. 11 BER comparison using three methods for an experimental system PM-16QAM 224 Gb/s with variable launch power for one fixed distance of 720 km transmission

Launch power [dBm]

Fig. 12 Comparison of BER by varying the distance to a fixed launch power of 3 dBm: linear equalization (blue); DBP algorithm (black); MLSE (red) and combination of the last two (green)

Fiber lenght [km]

cation of DBP and MLSE produced even better results: a gain of approximately 0.65 dB was noted in comparison with a pure MLSE implementation. In a variation of the experiment, we set a launch power of 3 dBm and look for the maximum distance achieved with DBP and MLSE. In Fig. 12, we observe the results presented by the MLSE are again better than the DBP, allowing the system to reach up to 600 km. We also notice that the difference between the MLSE and the DBP is large even at short distances, this is another indication that the system may be limited by optical filtering, regardless of the distance transmitted, and are partially compensated by this method. The combination of the two methods results in an extension of the reach: 640 km, almost three times the value of that reached using only linear compensation.

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4 Nonlinearity Estimation in Digital Back-Propagation (DBP) Algorithm Most of DBP schemes rely either on full knowledge of optical fiber parameters or even on brute-force optimization to define, for instance, the nonlinear parameter γ [54, 55]. However, legacy systems or dynamic environments with unknown and time-varying fiber information prevent a straightforward determination of the fiber parameters, which leads to a degradation of the performance of the DBP algorithm. In such scenarios, it would be highly desirable to adopt a Blind-Adaptive DBP (ADBP) method to estimate the fiber parameters, preferably with a low computational effort to meet the specifications for practical implementations. Some works on ADBP were reported using different Cost-Functions (CFs) to estimate the optimum nonlinear parameter γ (γopt ) [10, 56–59]. All the works adopted the Steepest Descent Algorithm (SDA) to determine γopt . This section will describe the principle and experimental results of a fully blind A-DBP algorithm to estimate the nonlinear parameter γopt in single-carrier 400 Gb/s unrepeatered optical system. The A-DBP method uses the Bit Error Rate (BER) estimated from decision-directed Error Vector Magnitude (EVM) as CF based in [58].

4.1 Principle of Adaptive Digital Back-Propagation (A-DBP) Algorithm The block diagram of DSP subsystems employing A-DBP is depicted in Fig. 13. First, the received signal is sampled by high-speed ADC, and then is subject to the orthonormalization, aiming to compensate for inaccuracy in the optical front-end and equalize the in-phase and quadrature components on each received polarization. Next, the A-DBP is used for joint compensation of CD and nonlinear impairments. The nonlinear compensation stage is performed using the initial value γ (0). Subsequently, dynamic equalization is performed by adaptive time-domain 2 × 2 Multiple-Input-Multiple-Output (MIMO) Finite Impulse Response (FIR) filters, whose purpose is to carry out polarization demultiplexing. After this, the carrier recovery block performs the frequency offset compensation, to identify and compensate frequency mismatches between transmitter and receiver, and phase noise compensation from transmitter and local oscillator lasers. Then, the CF is calculated to estimate the γopt , which is defined as C F(γ ) = B E R est where B E Rest is the estimated BER and is given by [60]

(20)

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Fig. 13 Block diagram of DSP subsystems employing A-DBP

B E Rest =

  −1 1−M 2 1 log2 M 2

 er f c

3/2 (M − 1) E V Mr2ms

 (21)

where M is the QAM constellation order and E V Mr ms is the decision-directed Error Vector Magnitude (EVM), and can be expressed as [60]

E V Mr2ms

 2  1 N     i=1 E r,i − E d,i N  =   N  2 i=1 E d,i

(22)

where N is the number of symbols and Er,i and E d,i are the received and decided symbols vectors, respectively. After CF calculation, the algorithm checks if CF is minimized. If not, the proposed method updates γ following the SDA given by γ (i + 1) = γ (i) ± μ∂C F(i)

(23)

where i is the iteraction index, μ is the convergence speed factor, ∂C F(i) is the gradient of CF at the step i, γ (i) and γ (i + 1) are the nonlinear parameter at iteraction i and i + 1, respectively. After N iteractions, defined by the μ, the CF is minimized (i.e., ∂C F=0) obtaining the γopt .

4.2 Experimental Setup The experimental setup is the same presented in [61]. At transmitter side, 16 External Cavity Lasers (ECLs) with linewidth of 100 kHz and spaced by 75 GHz are separated in odd and even channels and independently modulated by a pair of PolarizationMultiplexing In-phase Quadrature Modulators (PM-IQMs). An Arbitrary Waveform

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Generator (AWG) (Keysight M8196A) operating at 92 GSa/s with electrical bandwidth of 32 GHz generates 66 GBd raised cosine shaped 16QAM electrical signals (roll-off = 0.1). The symbol rate was optimized and includes 31 and 1%-overhead (OH) for Soft-Decision (SD) and Hard-Decision (HD)-FEC, respectively. The transmission link consists of four sections. The first two segments are 50 and 47 km of submarine-grade Corning® Vascade® EX3000 large effective area ultra-low loss fibers (Ae f f = 150 µm2 , α = 0.157 dB/km and γ = 0.56 km−1 W−1 ). The last two segments are 211 and 95 Km of submarine-grade Corning® Vascade® EX2000 fibers (Ae f f = 112 µm2 , α = 0.157 dB/km and γ = 0.76 km−1 W−1 ). Also, the transmission link includes submarine-grade Corning® Vascade® EX2000 fibers to transport the Remote Optically Pumped Amplifiers (ROPAs) pumps. The counterpropagating ROPA, defined by B-ROPA, is positioned at 50 km from the transmitter. The co-propagating ROPA, called F-ROPA, is positioned at 95 km from the receiver. In addition, two Raman pumps were transmitted along the WDM signal with wavelengths between 1445 and 1460 nm. At the receiver side, the channel is selected by a tunable filter before the discretecomponent coherent receiver. Then, the electrical signals are sampled by real-time scope operating at 80 GSa/s, with electrical bandwidth of 35 GHz. After this, a standard DSP is used for offline processing. The DSP subsystems consist in a resampling to 2 samples/symbol, orthonormalization, frequency domain CD equalization, DBP or A-DBP, dynamic equalization enhanced by FEC feedback, carrier recovery and bit error correction employing spatially coupled Low-Density Parity-Check (SC-LDPC) codes.

4.3 Experimental Results The fully blind A-DBP was evaluated using the experimental setup described before. First, an example of CF in terms of the estimated γ is depicted in Fig. 14a, considering 6-dBm average launch power. Given an initial γ (0), the algorithm self-adjusts the γ and the CF is minimized after less than 10 interactions. For this case, the optimum γ is 0.74 km−1 W−1 . If the estimated γ shifts away from this optimum value, the nonlinear compensation is degraded, increasing the estimated BER. Figure 14b shows the optimization of number of steps used by the DBP and ADBP in terms of average Q 2 gain per channel, for 3 and 6-dBm average launch powers. The DBP and A-DBP steps are uniformly distributed along of the first three fiber segments. In the last segment only linear impairments are compensated, because of the low optical power. Considering the trade-off between complexity and average Q 2 gain per channel, the optimum number of total A-DBP and DBP steps for both average launch powers is 30. This result demonstrates a good convergence of ADBP algorithm independently of number of total steps with comparable or even better performance than DBP with full knowledge of optical fiber. Figure 15 shows the WDM transmission performance for 30 steps in terms of pre-FEC Q 2 per channel index with DBP, A-DBP, and Linear Compensation (LC).

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(a)

(b)

Fig. 14 Experimental results: a Example of CF versus estimated γ ; b Average Q 2 gain per channel versus number of total steps for DBP and A-DBP compared to the case with only linear compensation (LC) Fig. 15 Pre-FEC Q 2 versus channel index after 403 km for DBP, A-DBP, and LC

3 dBm/channel with DBP 3 dBm/channel with ADBP 3 dBm/channel with only LC 6 dBm/channel with DBP 6 dBm/channel with ADBP 6 dBm/channel with only LC

Considering 3-dBm average launch power with only LC, all channels achieved errorfree transmission. However, for 6-dBm average launch power, Q 2 levels above the FEC limit are not attained for channels 2, 4, 12, and 16. Considering both launch powers with A-DBP, all channels achieved error-free operation.

5 Conclusion This chapter presented a summary of modeling and mitigation of nonlinear impairments applied to coherent optical systems. The GN model was defined as a sufficiently reliable tool for performance prediction in uncompensated optical coherent links over realistic scenarios. However, when the GN model is used to present a

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detailed Nonlinear Interference (NLI) noise accumulation along a link, the predictions can be influenced by substantial errors, mainly in few-span systems. In this way, an alternative was presented to correct this overestimation error, which is called the EGN model. In order to compensate for the nonlinear effects, four digital techniques were detailed: DBP, coupled equations, Volterra series, and MLSE. The DBP algorithm was reviewed in an experiment of 32 GBd PDM-16QAM transmission. The gain was compared in terms of distance using 1, 2, and 4 steps per span. We demonstrate that using a more complex algorithm (4 steps per span) it was possible to obtain, in a single-channel transmission, a 96% gain of transmission distance. Using a less complex algorithm (1 step per span), we showed a gain of 35% on the maximum reach. The usage of coupled equations is reviewed in an experiment of a WDM transmission with 20 × 56 GBd PDM-16QAM using a spectrally sliced receiver. The transmission distance gain was 150 km, for 0 dBm per channel, and 250 km, with 1 dBm per channel. The Volterra series presented, with a single step, ≈30% gain on the maximum reach (from ≈1200 to ≈1550 km) for a PM-64QAM transmission over PSCF. Subsequently, the MLSE results showed a better performance than DBP. We infer that this is due the lack of knowledge of the exact fiber parameters and the unwanted optical filtering of the devices used. Using the MLSE combined with the DBP, we presented a gain of 0.65 dB compared to the MLSE implementation only. Finally, the fully blind A-DBP algorithm is detailed and experimentally evaluated. The results showed that A-DBP required less than 10 iteractions to converge to the nonlinear parameter, and error-free operation was achieved for both average launch powers considered. In addition, we reviewed experimental results showing a comparable or even better performance than DBP with full knowledge of optical fiber parameters. Acknowledgements The authors thank Dr. Miquel Garrich Alabarce for reviewing a draft of this chapter.

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High-Order Modulation Formats for Future Optical Communication Systems André L. N. Souza and José Hélio da C. Júnior

Abstract Transceivers must evolve to cope with the ever-increasing traffic demand on optical networks. Some of their new features include using high-order modulation formats combined with more complex forward error correcting codes, nonlinear compensation, and probabilistic shaping. Beyond performance enhancement, power consumption is also an issue. This chapter focuses on some simulation results of using supervised phase recovery algorithm for complexity and power consumption reduction and experimental results on probabilistic shaping for performance enhancement.

1 Introduction A new generation of 100 Gb/s transceivers using the dual-polarization quadrature phase shift keying (DP-QPSK) modulation was enabled by the combination of coherent detection, high-order modulation, forward error correction (FEC), and digital signal processing (DSP). Now, research efforts are being made to implement 400-Gb/s systems, whose transceiver complexity is still under discussion in standardization bodies [1]. In this context, the main option considered by the industry relies on the dual-carrier approach (2 × 200 Gb/s) using the dual-polarization 16 quadrature-amplitude modulation (DP-16QAM). However, the spectral efficiency of DP-16QAM comes at the cost of lower nonlinear effects and noise tolerance, reducing the transparent reach of future 400-Gb/s systems. In the context of high-speed optical transmissions, single-carrier 400 and 600 Gb/s are attractive solutions compared to multi-carrier schemes, considering transceiver complexity. The main single-carrier options relies on dual-polarization (DP) 16QAM and 64QAM modulation formats with symbol rates up to 64 GBd [2–4]. However, to achieve higher symbol rates, systems would need to employ digital-to-analog/analogto-digital converters (DAC/ADC) with higher sample rates and bandwidth, increasing the overall power consumption, and equipment cost. In this way, increasing the A. L. N. Souza (B) · J. H. C. Júnior Optical Technologies Division, CPqD, Campinas, SP 13086-902, Brazil e-mail: [email protected] © Springer Nature Switzerland AG 2019 A. Paradisi et al. (eds.), Optical Communications, Telecommunications and Information Technology, https://doi.org/10.1007/978-3-319-97187-2_6

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modulation format and using higher order QAM formats such as DP-256QAM is an interesting alternative [5]. The high spectral efficiency provided by High-order modulation formats (HOMFs) such as quadrature-amplitude modulation (QAM) make them good candidates for future high-speed optical systems. A M-QAM constellation has M complex symbols that convey up to k = log2 (M) information bits per symbol. Rising the modulation format order (k) increases the spectral efficiency, but the minimum distance between constellation symbols (d) decreases, as shown in Fig. 1, where the minimum distance between symbols is represented by the dashed red lines and is given in terms of the mean signal power (E). As a consequence of this reduction, higher order QAM formats are less robust to the effects of ASE noise, phase noise, nonlinearities, and narrow-band filtering. Therefore, advanced digital signal processing techniques should be employed when transmitting high-rate high-order QAM signals to compensate for the different impairments and allow long-distance transmission. On the other hand, HOMFs require more rigorous specifications of the electrooptic components such as laser and DAC/ADC. The effective number of bits (ENOB), one of the specifications of DAC/ADC, has been studied in [6]. Xi et al. show that the ENOB requirement for 64QAM and 256QAM are 4.9 and 6.9, respectively. Another critical impairment for HOMFs is the phase noise. In [7], Pfau et al. show the impact on carrier recovery with different laser linewidths on a QAM receiver using the blind phase search (BPS) algorithm. The BPS is normally used as a benchmark for other phase recovery algorithms due to its robustness to ASE noise and its highly parallelized hardware implementation. Unfortunately, to use BPS with HOMFs the number of necessary test phases grows and the complexity and power consumption of the algorithm becomes an issue. Moreover, as the BPS algorithm depends on symbol decisions to estimate the phase deviation, it does not perform well with HOMF in low optical signal-to-noise ratios (OSNRs), as more decision error occurs. The BPS is also affected by 90◦ rotations of the received constellation during transmission (cycle-slips). These rotations are caused by constellation symmetry, requiring the use of differential coding (which is undesirable because of the inherent performance loss) or other cycle-slip identifications and elimination techniques, possibly reducing the algorithm performance. Supervised phase recovery algorithms, on the other hand, are a promising solution to maintain reasonable complexity and power consumption of future high-speed optical transceivers without reducing performance even with HOMFs. Supervised phase recovery approaches are normally based on a periodic insertion of time-division multiplexed pilot symbols to estimate the phase error and avoid differential decoding. A crucial issue is the choice of the rate at which pilot symbols are multiplexed with the information data sequence, which depends on the linewidth of the received carrier and on the signal-to-noise ratio (SNR). In [8], Magarini et al. investigate the impact of the pilot rate by using experimental data for a longhaul 100 Gb/s polarization-multiplexed (PM) quadrature phase shift keying (QPSK) wavelength-division multiplexing (WDM) signal in different transmission scenarios. Many strategies are considered to compensate the reach limitations of high-speed optical systems employing HOMF, from advanced FEC schemes [9, 10] to nonlinear

High-Order Modulation Formats for Future Optical … Fig. 1 Quadratureamplitude modulation formats with different orders k. The red dotted line represents the smallest distance between neighboring symbols, E is the constellation mean energy

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compensation using digital back-propagation (DBP) [11, 12]. A technique to improve the link capacity and/or reach is probabilistic shaping (PS) [13]. PS shapes the symbol probability according to its amplitude. In this way, lower energy symbols occur more frequently than symbols with higher energy. As consequence, PS offers a modest gain in transparent reach at the cost of an extra constellation mapper and demapper with a properly FEC scheme. Considering that all constellation points in DP-QPSK have the same modulus, PS could not be applied. However, for HOMFs, it becomes a viable option. Some works on PS have been reported. In [13], the simulation of a WDM system with a symbol rate of 28 GBd using 16QAM and 64QAM is presented. The PS and DBP are evaluated showing comparable performance. In [14], the simulation of a WDM system with symbol rate of 28 GBd using a novel coded modulation scheme is demonstrated. The PS is applied in 16QAM and 64QAM modulations, increasing the reach in 8 and 15%, respectively, compared with the case without PS. In [15], the transmission of 384 Gb/s (32 GBd DP-64QAM) is presented. Using the PS, the reach was extended in 25 and 43% compared with DP-64QAM and DP16QAM without PS, respectively. In [16], the potential network cost savings enabled by probabilistic shaping in DP-16QAM 200-Gb/s systems are evaluated based on experimental measurements and analytical derivations. In [17], the dual-band C+L transmission of 65 Tb/s (179 × 363.1 Gb/s DP-64QAM) is demonstrated. Using PS, digital nonlinear compensation, and spatially coupled low-density parity-check (SCLDPC) codes, the system achieved a transparent reach of 6600 km with a spectral efficiency of 7.3 b/s/Hz. In [18], a single-carrier 400 Gb/s transmission using 64QAM within 50 GHz grid over standard single-mode fiber (SSMF) is presented. Using PS, up to 300% reach enhancement is achieved compared to regular 64QAM. In [19], the transmission of probabilistically shaped DP-256QAM is showed with spectral efficiencies from 14.1 to 8.9 b/s/Hz at reaches from 500 to 4000 km, respectively. In [20], the field trial of probabilistically shaped 64QAM at 7.46 b/s/Hz over a 5.523 km in service EDFA-only amplified trans-Atlantic cable is presented. The rest of the chapter is organized as follows. Section 2 introduces the concept of supervised phase recovery. The rest of the section points out a strategy to select the pilot-symbol sequence to be time multiplexed with the original signal and some of the issues to be considered. Section 2.3 compares the performance of a supervised algorithm to the BPS in terms of BER in back-to-back. Section 3 describe the principle of PS and the generation of nonuniform constellations. The performance of PS is also investigated for different digital signal processing (DSP) algorithms, using the supervised and non-supervised blind phase search algorithm (BPS) for phase recovery. Finally, Sect. 4 summarizes the presented informations and concludes the chapter.

2 Supervised Phase Recovery Algorithms Supervised phase recovery algorithms are normally based on the insertion of pilot symbols in the information data sequence to help estimate the phase error and avoid cycle-slips.

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On the transmitter side, a block of pilot symbols is periodically time multiplexed with the information symbols. The rate at which these blocks are inserted is defined N as R p = Nsp , where N p is the number of pilot symbols per block and Ns is the number of information symbols between two consecutive blocks. Higher pilot insertion rates improve the error correction capacity of the algorithm, at the expense of using higher symbol rates to accommodate the redundancy and maintain the information rate. Higher rates require more rigorous specifications of the electro-optic components such as DAC/ADC bandwidth and, based on the relation between SNR and OSNR [21], signals with higher bandwidth require a bigger OSNR to achieve the same SNR, i.e., the same error rate. The supervised phase recovery algorithm on the receiver side has three distinct operation modes: identification, synchronization, and error correction. Considering that the signal was previously equalized and the frequency offset was ideally compensated, the pilot blocks are identified and synchronized for phase error estimation. The error is calculated as the phase difference between the received pilot symbol and its original position. The value of phase correction applied to the information symbols can be interpolated from the estimated values. In this section, some simulation results are shown to help in choosing a suitable pilot-symbol sequence. In addition, the performance of a supervised phase recovery algorithm is compared through simulations to some implementations of the BPS with different complexities for high-order modulation formats.

2.1 Simulation Setup The kth sample of the discrete-time received signal at the input of the carrier recovery circuit can be modeled as xk = ak · e j (θk +k·2π f f r eq Ts ) + n k ,

(1)

where ak is the unitary average energy- transmitted symbol sequence, including pilot symbols and n k is a zero mean complex additive white Gaussian noise (AWGN) sequence with variance SNR−1 . The unknown time-varying phase noise sequence θk of the incoming carrier is a Wiener process with variance ω2p = 2π νTs , where Ts is the sampling time and ν is the sum of the transmitter and receiver linewidths.  f f r eq is the difference between the transmitter and local oscillator laser frequencies, known as frequency offset.

2.2 Pilot-Symbol Sequence Selection When developing a transmission system using supervised phase recovery, attention should be given to the choice of the periodic pilot-symbol sequence to avoid unattended effects such as the advent of a DC level and the enhancement of nonlinearities

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Fig. 2 Possible pilot sets for different high-order modulation formats

during transmission. Some values of frequency offset between the transmitter and receiver lasers can create a DC level on the analog electrical signal that is sampled by the analog-to-digital converter and, if this DC level is blocked before frequency offset correction, the effect is catastrophic on the performance of DSP algorithms, especially for HOMFs. Moreover, if the chosen pilots excessively elevate the mean power of the transmitted signal, more nonlinear effects will impair the signal, degrading the overall system performance. These effects will be thoroughly explained in the following sections. First, we make the assumption that the pilot symbols must be symbols of the transmitted modulation format, to maintain the same DSP blocks of the non-supervised scenario (except the phase recovery algorithm) even without the knowledge of the pilot positions. Another assumption to reduce the number of possible pilot positions without losing performance is that there must be only one possible pilot position per quadrant. For square constellations, the obvious choice would be the symbols on the corners, but to reduce the mean energy of the pilots, we can also choose to use any pilot on the diagonal. To avoid the creation of DC values, all pilots must have the same absolute in-phase and quadrature components. Figure 2a, b shows the possible set of pilots for 256QAM.

2.2.1

Pilot Absolute Value Effects on Phase Estimation

The farther the pilot symbol is from the origin, the better is the phase noise estimation, because the phase deviation effect of additive noise is small when compared to the effects on constellation points near the origin. Unfortunately, pilots with high absolute values increase the signal mean energy, enhancing the nonlinear effects during fiber transmission. Consequently, the chosen radius of the transmitted pilot symbols must be a trade-off between performance in back-to-back and energy increase.

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Fig. 3 Back-to-back performance of possible pilot sets for different high-order modulation formats

To illustrate this effect, in Fig. 3 back-to-back curves with AWGN and phase noise for different pilot sets for 64QAM and 256QAM at 45.5 and 34 GBd. ν was set to 100 kHz and  f f r eq remained equal to zero. N p = 1 and Ns = 15. Figure 3 shows the performance of different pilot sets for 64QAM (a) and 256QAM (b). For 64QAM, Pilot sets 7 and 5 have the same performance at the soft-FEC limit of B E R = 2e−2 , other sets had too many convergence problems. In the 256QAM case, the pilot sets 15, 13, 11, 9, and 7 have roughly the same OSNR required for the soft-FEC limit, and the performance degrades rapidly for lower sets. To avoid an unnecessary increase on the signal mean energy, the Pilot sets 5 and 7 seem to be good choices for 64QAM and 256QAM, respectively. Pilot set 5 increases the mean energy of the 64QAM constellation by 1.2%. Pilot set 7 actually reduces the mean energy of the 256QAM constellation by 3%.

2.2.2

Effects of Frequency Offset

Some values of frequency offset between the transmitter and receiver lasers change the distribution of those pilots in the quadrants and create a DC level on the electrical signal that is sampled by the analog-to-digital converter. If this DC level is blocked before frequency offset correction the signal becomes tilted, leading to higher error ratios. For HOMFs, the effect is catastrophic on the performance of DSP algorithms. As an example, we simulate 106 symbols of a 64QAM signal at 32 GBd with one pilot symbol inserted every 15 information symbols. ν was set to 0 kHz and  f f r eq was varied. Let us choose the following 4-symbol sequence as pilots: α · 3π 7π ]), where α is a constant. These four symbols also allow the correct ex p( j · [ π4 5π 4 4 4 estimation of carrier phase, without 90◦ ambiguity. Without frequency offset, the pilot symbols are equally distributed among the four quadrants yielding signals in the quadrature and in-phase with zero mean as can be seen in the density plot of Fig. 4. In this case, specific values of frequency offset on

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Fig. 4 Pilot-symbol distribution for different values of frequency offset

s the form  f f r eq = k · 4·(NRs +N with k integer, may alter the distribution of pilots in p) space and generate DC values on the components of the signal, as can be seen on the density plots of Fig. 4 for different values of  f f r eq . For frequency offsets that are not on the form presented before as 250 and 800 MHz, the pilot symbols have mean values on the quadrature and in-phase components lower than 1e−3 . On the other hand, for k = 1, 2 and 3 ( f f r eq = 500, 1000, and 1500 MHz) the resulting signals are clearly biased.

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To avoid this effect, the use of long pseudo-random sequences to determine the pilot symbols quadrant position is recommended.

2.2.3

Pilot-Symbol Sequence Selection, Insertion and Synchronization

To use a simple method for identification and synchronization of pilots on the receiver, pseudo-random sequences can be used to determine the pilot quadrant to be sent and avoid any biasing of the signal, as indicated on the previous section. As an example, suppose that one pilot symbol is time multiplexed for every 15 information symbols. During the identification phase, the pilots can be identified by correlating the absolute value of consecutive blocks of 16 received symbols, sum the correlation values for a certain number of blocks (e.g., 16) and choose the position with the highest correlation value. Due to the 90◦ phase ambiguity, the PRBS sequence must be synchronized after the position identification. It can be done by trial and error: consider that four consecutive pilot symbols are correct and use them to calculate the next pilots; compare the received pilot symbols with the calculated ones and, if any prediction error occurs, rotate the received signal by 90◦ and start over until the error rate is sufficiently low. For high-order modulation formats (16QAM and beyond) that have higher required OSNR values, the rate of quadrant error is very low, enabling the use of the preceding technique for synchronization because the number of wrong pilot reception is very close to zero.

2.3 Performance Comparison of Phase Recovery Algorithms In this section simulations, the transmitter has two configurations, depending on the phase estimation algorithm are used on the receiver. The system implementing the blind phase search algorithm with 2 stages works with signals modulated with 64QAM and 256QAM at 43 and 32 GBd, respectively, yielding a net bit rate of 400 Gb/s and differential coding to avoid cycle-slips. When using the supervised phase recovery algorithm, one pilot symbol was added after each 15 information symbols. The system uses signals modulated with 64QAM and 256QAM at 45.5 and 34 GBd, respectively, to accommodate the pilot symbols and sequential coding. ν was set to 200 kHz and  f f r eq remained equal to zero. The performance of the supervised algorithm and the BPS with 6, 8, and 10 phase tests per stage are presented in Fig. 5a, b. In the 64QAM case, all BPS implementations have the same behavior and the supervised algorithm is 0.3 dB which is better than at the FEC limit of B E R = 2e−2 . For 256QAM, we observe that the performance of the supervised algorithm is equivalent to the BPS with 10 phase tries per stage at the soft-FEC limit, with the advantage of being much simpler and more power efficient. To reduce the BPS complexity, the number of phase tries per stage

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Fig. 5 Back-to-back performance of various phase recovery algorithms for different high-order modulation formats

can be reduced, but the performance degrades rapidly when going from 10 to 8 or 6 phase tries.

3 Probabilistic Shaping This section will describe the principle of PS and the generation of nonuniform constellations. The experimental setup and performance analysis in back-to-back are made in 200 Gb/s systems per channel with DP-16QAM modulation. The performance of PS is also investigated for different digital signal processing (DSP) algorithms, using the blind phase search algorithm (BPS) supervised and unsupervised for phase recovery.

3.1 Information-Theoretic Aspects In information theory, the mutual information (MI) is a measure of mutual dependence between two random variables. Given a discrete input alphabet with M elements Ak , the MI between channel input X and channel output Y , in bit/symbol, is given by [22]

I (X ; Y ) =

M−1  k=0

 Pr(Ak )

∞

−∞

 ρY |Ak (y|Ak ) · log2  M−1 l=0

ρY |Ak (y|Ak ) Pr (Al )ρY |Al (y|Al )

 dy (2)

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where Pr(Ak ) is the probability of generating symbol Ak and ρY |Ak (y|Ak ) is the probability density function (PDF) of channel output given the symbol Ak . For an additive white Gaussian noise (AWGN) with variance σ 2 , the PDF is given by ρY |Ak (y|Ak ) =

−|y−Ak |2 1 2σ 2 e 2π σ 2

(3)

In a conventional optical transmission approach, all the symbols occur with the same probability. In this case, the constrained capacity C is defined as the maximum MI for a given modulation format and can be expressed as C = maxPr(Ak ) I (X ; Y )

(4)

In an ideal case, the symbol probabilities can be modeled as a Gaussian distribution, resulting in the maximum capacity allowed for an AWGN channel, defined as Shannon limit. The capacity C can be approximated to the Shannon limit shaping the input constellation. In this case, a viable option is the probabilistic shaping, since it is possible to apply the same DSP algorithms used in uniform constellations. In this way, the symbol probabilities can be shaped applying the Maxwell–Boltzmann distribution is given by [23] Pr(Ak ) = 

1 −λ|Ak |2 ,λ ≥ 0 2 e −λ|A | k Ak e

(5)

where Ak is the symbol amplitude and λ is a constant. For λ = 0, the constellation will be uniform. However, for λ > 0, the constellation will be nonuniform, whereas the symbol probabilities are inversely proportional to the symbol amplitudes. Consequently, the symbols of less energy occur more frequently than symbols of higher energy. The constant λ can be numerically optimized as a function of signal-to-noise ratio (SNR). For each SNR, the constant λ is swept, choosing the optimum value to maximize the MI, as presented in Fig. 6a. The optimum values of λ in terms of SNR for DP-16QAM modulation is depicted in Fig. 6b. Figure 7 shows the performance of PS in terms of MI versus SNR, for different modulation formats. The use of PS yields a maximum SNR gain of ≈0.5 dB and ≈1 dB for DP-16QAM and DP-64QAM, respectively. The results depicted in Fig. 7 motivates the use of higher order modulation formats with higher redundancy overheads [24], instead of lower order modulation schemes combined with lower redundancy, as in conventional optical networks. The application of common FEC techniques increases the computational complexity. However, the implementation of an appropriately coded modulation scheme can provide better performance with almost the same computational complexity. In general, the required number of dimensions to achieve the shaping gain is smaller than the number of dimensions of coding gain [25]. Furthermore, the computational complexity of PS implementation is small. The combination of shaping

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Fig. 6 Optimization of Maxwell–Boltzmann distribution for DP-16QAM Fig. 7 Mutual information for DP-16QAM and DP-64QAM modulation formats with and without probabilistic shaping

and coding can be used in variable-code-rate transceivers with low complexity just choosing the appropriately coded modulation technique. Several techniques were proposed to allow the application of nonuniform constellations. Assuming the transmission of a binary source output with same probabilities and without memory, one way to implement the probabilistic shaping is to assign the source output to variable length codewords. Therefore, the codeword probabilities are given by a dyadic distribution [26] Pr(Ak ) = 2−li

(6)

where li is the codeword length. In this way, lower number of bits, that is more frequent, are mapped into symbols with lower energy, and higher number of bits, that is less frequent, are assigned to symbols with higher energy. This procedure is called Huffman coding [27]. In this work, the Maxwell–Boltzmann distribution

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Fig. 8 Mutual information for DP-16QAM and DP-64QAM modulation formats using Maxwell– Boltzmann and dyadic distributions

is approximated by a dyadic distribution, using the Huffman procedure mentioned before. Figure 8 shows the performance for DP-16QAM and DP-64QAM with PS using Maxwell–Boltzmann and dyadic distributions. As expected, the shaping gain decreases using the dyadic approximation. Based on Fig. 8, for higher order modulation formats, the number of degrees of freedom allows a better approximation, decreasing the difference compared to the ideal distribution.

3.2 Generation of Nonuniform Constellations This section will detail the generation of nonuniform constellations, which is described by a flowchart in Fig. 9. The first step to generate nonuniform constellations is to optimize the parameter λ numerically, choosing the value that maximizes the MI in each SNR, as presented in Fig. 6a, b. With the optimum values of λ are calculated, for each SNR the symbol probabilities using the Eq. 5. Figure 10 shows an example of the probabilities for the 16QAM modulation with different SNRs. For higher SNRs, the difference between the symbol probabilities of inner and outer radius is small, approximating to a uniform constellation, as presented in Fig. 10a. However, for lower SNRs, the difference between the symbol probabilities of inner and outer radius is evident, generating a nonuniform constellation, depicted in Fig. 10b.

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Fig. 9 Flowchart of the generation of nonuniform constellations

Fig. 10 Maxwell–Boltzmann distribution and binary codes for DP-16QAM

Using the probabilities calculated before, the Huffman procedure is applied, generating a binary code, as depicted also in Fig. 10. Figure 10a shows the binary code for a uniform constellation with high SNR. In this way, codeword lengths are equal for all symbols. However, for lower SNRs, the difference between the symbol probabilities generates different binary sequences, coding the inner and outer symbols with lower and higher number of bits, respectively. Despite the inner symbols present the same probabilities, the codewords are generated with a different number of bits, which is a consequence of Huffman coding. Finally, using the binary codewords, is generated a binary sequence, mapping the bits from Huffman to Gray code, and after this to complex symbols. Figure 11 is depicted as an example of nonuniform constellation. As a consequence of the difference between codeword length of inner symbols, an asymmetrical density of constellations points is seen. This phenomenon is not seen in higher order modulations, because of higher degrees of freedom used in the Huffman procedure.

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Fig. 11 Comparison between uniform and nonuniform 16QAM constellations

3.3 Experimental Setup The experimental setup is the same presented in [28]. At transmitter side, an external cavity laser (ECL) centered in 1549.55 nm and with linewidth of 100 kHz is modulated by a dual-polarization in-phase quadrature modulator (DP-IQM). A digital-toanalog converter (DAC) operating at 64 GSa/s with electrical bandwidth of 18 GHz generates 32 GBd raised-cosine shaped 16QAM electrical signals (roll-off = 0.1). After transmitter, the optical signal is generated and coupled with amplified spontaneous emission (ASE) noise. The ASE source is based in an erbium-doped fiber amplifier (EDFA) combined with variable optical attenuator (VOA), controlling the ASE level to be added into the optical signal. The coupler output is taken to a second coupler, splitting the optical power for a coherent receiver and a fraction for an optical spectrum analyzer (OSA), where the optical signal-to-noise ratio (OSNR) is monitored. In this way, after optical signal generation, the OSNR is verified to configure the VOA, setting an appropriate ASE noise power. At receiver side, the optical signal is detected using an integrated coherent receiver based on polarizing beam splitters (PBSs), 90◦ optical hybrids, and balanced photodetectors (PD). After this, the 4 electrical signals were sampled by an analog-to-digital converter (ADC) operating at 80 Gsa/s with bandwidth of 35 GHz. Then, the sampled signals are processed using a standard DSP including a resampling to 2 samples per symbol, deskew, time recovery, radius-directed dynamic equalizer (RDE), carrier recovery, and error vector magnitude (EVM) estimation. Based on EVM, the SNR is calculated as in [29]. Subsequently, the experimental capacity is estimated using the theoretical curves presented in Fig. 8.

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3.4 Experimental Results This section will describe the performance in back-to-back of probabilistic shaping applied to 200 Gb/s DP-16QAM system. Based on experimental setup described in Sect. 3.3, the OSNR is varied and the optical signal is collected at receiver. As presented in Sect. 3.2, for each SNR is generated a different nonuniform constellation. In this way, the first step is to define the OSNR range. For the transmission of 32 GBd DP-16QAM, the OSNR range was from 6 to 20 dB. Next, the SNR was calculated as in [21]. Then, the nonuniform constellations are generated and loaded at DAC. After the generation of 32 Gbd DP-16QAM electrical signals, the optical carrier is modulated and amplified. At the receiver, for each OSNR, we made 5 measurements. The performance of PS is investigated for different DSP algorithms. First, it was applied the DSP algorithms described in Sect. 3.3 with the supervised blind phase search (BPS). The experimental SNR for the transmission of 32 GBd DP-16QAM with and without PS and using supervised BPS is depicted in Fig. 12a. For values of OSNR above 8 dB, the experimental SNR, in each case, is the same. A different behavior is seen for values of OSNR below 8 dB. In this case, the experimental SNR diverges, as a consequence of limitations of DSP algorithms. Using the experimental SNR, the experimental capacity was estimated using the theoretical curves. Figure 12b depicts the experimental and theoretical capacities versus OSNR using supervised BPS. Considering higher OSNRs, the experimental capacity stays below of maximum theoretical mutual information, as a consequence of DAC and ADC limitations. For lower OSNRs, the experimental curves diverge, as a result of DSP limitations. For OSNRs below 6 dB and above 20 dB, the nonuniform constellations approached to uniform constellations, resulting in the same mutual information.

Fig. 12 Experimental results for the 32 GBd DP-16QAM transmission using supervised BPS

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Because of this, this range was not evaluated in this experiment. Therefore, the gain region for PS is between 8 and 20 dB. In this region, the maximum capacity and OSNR gains were 0.34 bit/symbol and 0.4 dB, respectively. The results achieved are close to the theory. Figure 12b also presents the received constellations after DSP algorithms for different values of OSNR. We can see a higher density of points at inner radius. Furthermore, for higher OSNRs, the distribution approached to the uniform case, justifying the same mutual information described before. Figure 13 shows the capacity gain as a function of OSNR. The curve illustrates the gain region of probabilistic shaping applied to the transmission of 32 GBd DP16QAM using the supervised BPS. Some fluctuations are seen as a consequence of variations in the measurements. However, the average gain is 0.25 bit/symbol, showing the consistency of experiment. After the performance evaluation of 32 GBd DP-16QAM using the supervised BPS, the next step is to apply non-supervised phase recovery. The non-supervised BPS is based on a forgetting factor (FF), which consists in calculating the weight of the phase values, and can assume values between 0 and 1. In this way, the first step was to optimize the FF for the cases with and without PS. Varying the FF from 0.994 to 0.999 with step of 0.001, the SNR was estimated as a function of OSNR for the case without PS, and depicted in Fig. 14a. Increasing the FF, the estimated SNR is improved for lower OSNRs. This behavior is not seen for higher OSNRs. The same investigation was conducted for the experimental capacity. Figure 14b shows the mutual information versus OSNR. As described before, for higher OSNRs, the capacity stays below the maximum mutual information, as a consequence of DAC and ADC limitations. Also, increasing the FF, the capacity is improved for lower OSNRs. In this way, the optimum FFs for the non-supervised BPS are 0.999 and 0.998, considering the capacity gain for lower OSNRs. The FF optimization was made for the case with PS. Figure. 15a presents the experimental SNR versus the OSNR. For lower OSNRs, the estimated SNR is very

Fig. 13 Capacity gain for 32 GBd DP-16QAM using supervised BPS

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Fig. 14 Experimental results for 32 GBd DP-16QAM without PS using non-supervised BPS. M-B stands for Maxwell–Boltzmann

low, as consequence of phase recovery degradation. Even after increasing the FF, the calculated SNR is not improved, which is different for the case without PS. Using the values of SNR estimated in Fig. 15a, the experimental capacity was calculated. Figure 15b depicts the mutual information versus OSNR for the case with probabilistic shaping. The results present the same behavior as described before, where the capacity is limited by the experimental components. Increasing the FF, the capacity is not improved for lower OSNRs, proving the inconsistency of nonsupervised BPS. Based on Fig. 15b, the optimum FFs are 0.999 and 0.998.

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Fig. 15 Experimental results for 32 GBd DP-16QAM with PS using non-supervised BPS

Figure 16 presents the comparison between the cases with and without PS using non-supervised BPS and FF equal to 0.998. The optimum FF was chosen based on the higher SNR gain for lower OSNRs. The difference in performance is clear for lower OSNRs. Even for higher OSNRs, the capacity with PS degrades, reduced the gain compared to the uniform distribution. The received constellations are also presented. Based on the results in Fig. 16, we concluded that the non-supervised phase recovery presents a negative impact in probabilistic shaping. The inconsistency in phase estimation is a consequence of decision process realized in the BPS algorithm, where the decision is based on minimum distance, not considering the a priori symbol prob-

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Fig. 16 Experimental capacity comparison for 32 GBd DP-16QAM with and without PS using non-supervised BPS and FF = 0.998

abilities, degrading the performance of probabilistic shaping. For the case using the supervised phase recovery, the decision is replaced by a training sequence, justifying the better performance.

4 Conclusion This chapter presented the main concepts and advantages of supervised carrier phase recovery and probabilistic shaping. Simulation results of using a supervised phase recovery algorithm with HOMF for complexity and power consumption reduction and experimental results on probabilistic shaping for performance enhancement were presented. In the section about supervised phase noise estimation, some problems that should be considered in the choice of the pilot sequence were pointed out. The simulations were performed focusing on 400 Gb/s systems, using signals modulated at 64QAM and 256QAM. According to the analysis, pilots with intermediate absolute values should be used combined with long pseudo-random sequences to select the quadrant of the pilot symbols to avoid some undesired effects. The performance results in comparison to the classic blind phase search algorithm corroborate that supervised phase recovery algorithms are good candidates for future, low-power high-speed optical systems. Although this chapter focused on square constellations, supervised phase recovery can be applied to any modulation format.

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The probabilistic shaping is presented and experimentally evaluated applied to 200 Gb/s DP-16QAM optical systems. The first experimental analysis considered the transmission of 32 GBd DP-16QAM with supervised BPS. The results showed maximum capacity and OSNR gains of 0.34 bit/symbol and 0.4 dB, respectively. The performance of non-supervised phase recovery was investigated for the cases with and without probabilistic shaping, showing the impact of non-supervised BPS for lower OSNRs, as a result of the decision process realized in the algorithm. Acknowledgements This work was partially supported by FUNTTEL/FINEP and by Sao Paulo Research Foundation (FAPESP), grant no. 2015/25513-6. The authors thank Dr. Giovanni Beninca de Farias for reviewing a draft of this chapter.

References 1. Reis JD, Shukla V, Stauffer DR, Gass K (2015) Technology options for 400G implementation. Technical report, Optical Networking Forum (OIF) White Paper 2. Rahman T, Rafique D, Spinnler B, Bohn M, Napoli A, Okonkwo C, de Waardt H (2016) 38.4 Tb/s transmission of single-carrier serial line-rate 400 Gb/s PM-64QAM over 328km for metro and data center interconnect applications. In: Optical fiber communications conference and exhibition (OFC), IEEE, pp 1–3 3. Rios-Müller R, Renaudier J, Brindel P, Simonneau C, Tran P, Ghazisaeidi A, Fernandez I, Schmalen L, Charlet G (2014) Optimized spectrally efficient transceiver for 400-Gb/s single carrier transport. In: 2014 European conference on optical communication (ECOC), IEEE, pp 1–3 4. Geyer J, Doerr C, Aydinlik M, Nadarajah N, Caballero A, Rasmussen C, Mikkelsen B (2015) Practical implementation of higher order modulation beyond 16-QAM. In: Optical fiber communications conference and exhibition (OFC), 2015, IEEE, pp 1–3 5. Chien HC, Yu J (2016) On single-carrier 400G line side optics using PM-256QAM. In: Proceedings of 42nd European conference on optical communication ECOC, VDE, pp 1–3 6. Chen X, Chandrasekhar S, Randel S, Gu W, Winzer P (2016) Experimental quantification of implementation penalties from limited ADC resolution for nyquist shaped higher-order QAM. In: 2016 optical fiber communications conference and exhibition (OFC), pp 1–3 7. Pfau T, Hoffmann S, Noé R (2009) Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations. J Lightwave Technol 27(8):989–999 8. Magarini M, Barletta L, Spalvieri A, Vacondio F, Pfau T, Pepe M, Bertolini M, Gavioli G (2012) Pilot-symbols-aided carrier-phase recovery for 100-G PM-QPSK digital coherent receivers. IEEE Photon Technol Lett 24(9):739–741. https://doi.org/10.1109/LPT.2012.2187439 9. Rafique D, Rahman T, Napoli A, Calabró S, Spinnler B (2014) FEC overhead and fiber nonlinearity mitigation: performance and power consumption tradeoffs. OFC 2014:1–3. https://doi. org/10.1364/OFC.2014.W2A.32 10. Rahman T, Rafique D, Napoli A, Man E, Kuschnerov M, Spinnler B, Bohn M, Okonkwo CM, Waardt H (2014) FEC overhead optimization for long-haul transmission of PM-16QAM based 400 Gb/s super-channel. In: European conference on optical communication (ECOC), pp 1–3 11. Ip E, Kahn J (2008) Compensation of dispersion and nonlinear impairments using digital backpropagation. J Lightwave Technol 26:3416–3425 12. Mussolin M, Rafique D, Mårtensson J, Forzati M, Fischer JK, Molle L, Nölle M, Schubert C, Ellis AD (2011) Polarization multiplexed 224 Gb/s 16QAM transmission employing digital back-propagation. In: European conference on optical communication (ECOC), pp 1–3 13. Fehenberger T, Alvarado A, Bayvel P, Hanik N (2015a) On achievable rates for long-haul fiber-optic communications. Opt Express 23:9183–9191

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14. Fehenberger T, Bocherer G, Alvarado A, , Hanik N (2015b) LDPC coded modulation with probabilistic shaping for optical fiber systems. In: Optical fiber communication conference and exposition (OFC/NOFC), pp 1–3 15. Buchali F, Bocherer G, Idler W, Schmalen L, Schulte P, Steiner F (2015) Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM. In: European conference on optical communication (ECOC), pp 1–3 16. Diniz C, Hélio J, Souza A, Lima T, Lopes R, Rossi S, Garrich M, Reis JD, Arantes D, Oliveira J, Mello DAA (2016) Network cost savings enabled by probabilistic shaping in DP-16QAM 200-Gb/s systems. In: Optical fiber communication conference and exposition (OFC/NOFC), pp 1–3 17. Ghazisaeidi A, Ruiz IFJ, Müller RR, Schmalen L, Tran P, Brindel P, Meseguer AC, Hu Q, Buchali F, Charlet G, Renaudier J (2017) Advanced C+L-band transoceanic transmission systems based on probabilistically shaped PDM-64QAM. J Lightwave Technol 35:1291–1299 18. Zhu Y, Li A, Peng WR, Kan C, Li Z, Chowdhury S, Cui Y, Bai Y (2017) Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping. In: Optical fiber communication conference and exposition (OFC/NOFC), pp 1–3 19. Chandrasekhar S, Li B, Cho J, Chen X, Burrows E, Raybon G, Winzer P (2016) High-spectralefficiency transmission of PDM 256-QAM with parallel probabilistic shaping at record ratereach trade-offs. In: European conference on optical communication (ECOC), pp 1–3 20. Cho J, Chen X, Chandrasekhar S, Raybon G, Dar R, Schmalen L, Burrows E, Adamiecki A, Corteselli S, Pan Y, Correa D, McKay B, Zsigmond S, Winzer P, Grubb S (2017) Transatlantic field trial using probabilistically shaped 64-QAM at high spectral efficiencies and single-carrier real-time 250-Gb/s 16-QAM. In: Optical fiber communication conference and exposition (OFC/NOFC), pp 1–3 21. Essiambre RJ, Tkach RW (2012) Capacity trends and limits of optical communication networks. Proc IEEE 100:1035–1055 22. Ungerboeck G (1982) Channel coding with multi-level/phase signals. IEEE Trans Inf Theory 28:55–67 23. Wachsmann U, Fischer RFH, Huber J (1999) Multilevel codes: theoretical concepts and practical design rules. IEEE Trans Inf Theory 45:1361–1391 24. Gho GH, Kahn J (2012) Rate-adaptive modulation and low-density parity-check coding for optical fiber transmission systems. J Opt Commun Netw 4:760–768 25. Forney GD, Ungerboeck G (1998) Modulation and coding for linear gaussian channels. IEEE Trans Inf Theory 44(6):2384–2415. https://doi.org/10.1109/18.720542 26. Kschischang F, Pasupathy S (1993) Optimal nonuniform signaling for gaussian channels. IEEE Trans Inf Theory 39:913–929 27. Huffman DA (1952) A method for the construction of minimum redundancy codes. Proc IRE 40:1098–1101 28. Hélio J (2016) Avaliação experimental da formatação probabilística aplicada a sistemas ópticos DP-16QAM a 200 Gb/s. Master’s thesis, Universidade Estadual de Campinas, Brasil 29. Shafik RA, Rahman MS, Islam AR (2006) On the extended relationships among EVM. BER and SNR as performance metrics. In, International conference on electrical and computer engineering (ICECE)

Soft-Decision Forward Error Correction in Optical Communications Alexandre Felipe and André L. N. Souza

Abstract In order to effectively design good error-correcting codes for a given application, it is important to know how they work, how to assess the reliability of a given implementation and to be aware of the available codes and its features. In this chapter, a background about error correction is given so the reader can grasp the ideas behind error-correcting codes. Derivations about the confidence of error rate estimates are presented. These derivations turn out to be useful in the assessment of a system reliability when it is not possible to simulate enough codewords to observe a considerable number of errors. Finally, a brief historical review is presented and the authors present their view about promising codes for optical communications.

1 Introduction Communication is the action of transferring information between two points through a channel. This is a broad definition and contains all common sense forms of communications, e.g., this book serves as a channel when the message is encoded as text that modulates the light on a display or the ink on the paper. The final result is that the message produced by us, here at CPqD, is being received by you at this moment. Another everyday example is a conversation in which one of the interlocutors encodes a message in words that are modulated in acoustic waves and propagates through the air reaching the ears of the other that decodes the message. These are two examples of natural language communication, however, many applications rely on communications using electronic devices. Formally, a communication system can be divided into four elements: transmitter, receiver, channel, and code. The transmitter is the entity that creates the message based on some information. The receiver extracts underlying information from the message. The channel is a medium that propagates events caused at the transmitter to the receiver. Finally, the code is a set of rules that associate information to events A. Felipe (B) · A. L. N. Souza CPqD Optical Technologies Division, Campinas, SP 13086-902, Brazil e-mail: [email protected] © Springer Nature Switzerland AG 2019 A. Paradisi et al. (eds.), Optical Communications, Telecommunications and Information Technology, https://doi.org/10.1007/978-3-319-97187-2_7

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that are sent to the receiver, it can be a simple mapping rule or a more sophisticated code that involves error correction or encryption. A big revolution in communications happened with the use of electromagnetic waves to transport information, initiating the era of telecommunications. The air itself serves as a channel, it is necessary only one transmitter and some receivers, and the message is delivered as fast as possible (the speed of the light). Unfortunately, the transmitter of this communication system is not the only entity able to generate electromagnetic waves that can be observed at the receiver. Several sources produce electromagnetic waves as well and all of them are added together in what is observed by the receiver. The signal reaching the receiver other than the transmitted signal is called “noise” or “interference”. A great advance in telecommunications happened with the introduction of optical communications. In optical communications, electromagnetic waves are the physical phenomena used to transport information as well, but instead of transmitting over the air, it employs optical fibers that are able to guide the light preventing it from causing or suffering interferences. In spite of having many advantages, optical communications are susceptible to a variety of impairments. Several of them can be compensated employing digital signal processing (DSP) algorithms in the transmitter and the receiver. Due to limitations of DSP compensations or the nature of the impairments, such as random noise added by the amplifiers or by the components at the endpoints of the transmission, the received signal is noisy. Error-correcting codes are responsible to recover the message from the noisy signal after all feasible DSP compensation techniques were employed. In practical applications, error-correcting codes usually operate close to its limit. The signal is as noisy as it can be because the signal is transmitted as far as possible. In such conditions, error correcting codes are required to distinguish from the correct and incorrect codewords by considering a large number of bits at once. As a result, efficient codes will have to use large blocks of data and establish many dependencies between its bits. Section 2 is intended to give the reader an intuition about how error-correcting codes work, without any deep mathematical analysis. Section 3 presents results about the confidence of event frequency estimates that are applied for bit and word error rate estimation via simulation. Section 4 presents the evolution of the error correcting codes and an explanation about why we think Low-density Parity-check (LDPC) and polar codes are the most promising codes for optical communications.

2 Error-Correcting Codes The amazing fact about error-correcting codes is that they enable a system to read a string of symbols (usually binary symbols) and correct errors occurred during transmission. Given a random string of bits at the receiver, determining whether it is correct or corrupted is not possible, in principle, without knowing the transmitted

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data. But a system that requires the knowledge of the transmitted symbols to ensure that the received symbols are correct is useless. One possibility is to transmit a string multiple times, so the receiver has multiple unreliable copies of the same string, but to combine them to produce an arbitrarily reliable output is not possible. The first thing to notice is that, even for unreliable error detection, additional information is required to be transmitted. The second thing to notice is that even if it is known that good codes exist, most of the clever ideas to construct an errorcorrecting code will fail. In 1949, Claude Shannon showed mathematically that it is possible to communicate reliably using a noisy channel in a time when all the scientific community were skeptic about that [1]. The Shannon information theory provided the ground for the invention of many error correcting codes in the following years. In Sect. 2.1, the Shannon codes are briefly discussed and in Sect. 2.2 examples of everyday life that can be interpreted as error-correcting codes are given.

2.1 Shannon Codes In digital communications, binary data must be transported between two electronic devices. If there is noise in the channel, there is a fixed probability that some bit is wrongly detected at the receiver. This way it becomes almost impossible to transmit a large file without errors. Claude Shannon proved that reliable communication through a noisy channel is possible even for a random dictionary code. The code consists in choosing randomly 2k unique strings of n bits with k ≤ n and creating a bijection from k-bit messages to the strings in the code. The code has 2k codewords that are n-bit strings, the success of the code depends on the number of codewords being negligible compared to the number of possible n-bit strings. If the noise corrupts some bits of a valid string, it still resembles the original codeword, and the probability that it resemble any other codeword is small since there are few valid codewords among the possible strings. For illustration, consider a binary channel and a codebook consisting of 2k sequences of k ≤ n bits randomly chosen. A k bits message is transmitted using a n bits codeword. This code is said to have a rate R = k/n. If a codeword is transmitted through a noisy channel some bits will be corrupted, but hopefully few bits. There are 2n possible received sequences, however, only 2k are valid, i.e., for each 2n−k codewords, there is only one valid codeword. Consider now that R = 1/2, k-bit messages are encoded as codewords with n = 2k bits, e.g., if messages of 32 bits are transmitted there are 232 codewords consisting of 64 bits each, for each valid codeword there are 232 − 1 invalid codewords (more than 4 × 109 ). Now keeping the code rate but using messages of 100 bits encoded in sequences of 200 bits, there exists approximately 1.27 × 1030 invalid codewords for each codeword. An error occurs when the signal received is more similar to a valid codeword different from that encoded at the transmitter. As the code length increases at a fixed rate the valid codewords becomes relatively more rare, so that the probability of error becomes negligible.

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2.2 Interpreting Things as Error-Correcting Codes Even if it is proven that random codes perform very well as the size of the codeword is increased, the number of codewords grows exponentially with the length of the message (there are 2k codewords) so the dictionary with large codewords cannot be stored on a computer memory, for instance, a code of rate 0.5 with a 32-bit message would take 8 GB to be stored. In the sequence, examples of codes are presented. In Sect. 2.2.1, an orthographic corrector is interpreted as a dictionary code whose codewords are listed. Section 2.2.2 presents code used for detecting typing errors to illustrate how a code can be defined by rules instead of a list of codewords. Last, in Sect. 2.2.3, a Sudoku is interpreted as a recursive code where each puzzle is interpreted as a codeword transmitted through an erasure channel.

2.2.1

A Practical Dictionary Code

In spite of the storage limitation, even a dictionary error correcting code may be effective in some applications. Perhaps, the most comprehensible dictionary based errorcorrecting code is an orthographic corrector, and even a human can read a text with a lot of orthographic errors. Consider the English language, on average the English words are about eight letters long,1 it is possible to write 268 = 208, 827, 064, 576 arrangements of eight letters. The Second Edition of the 20-volume Oxford English Dictionary contains full entries for 171,476 words in current use,2 that is a very small subset of all possible arrangements letters. The majority of us have a much less extensive vocabulary, so that most of the times a word written incorrectly is still more similar to the intended word than to any other word in the English vocabulary.

2.2.2

Error-Detecting Codes

It is desirable to have a method to verify errors in a received string using only the information in the string itself. This is precisely what error detecting codes are meant to do. A code can be defined as a set of codewords formed by strings of symbols. Each codeword is associated to a single message. Conversely, a string is valid if and only if it belongs to the set of codewords. But instead of constructing a code storing all possible codewords, one can use a set defined as “all strings that satisfy some simple rule”, and instead of looking for the string in a set, the rule of formation of the set can be used to decide if a string is valid. In addition to being testable, it is desirable that a

1 http://www.ravi.io/language-word-lengths. 2 https://en.oxforddictionaries.com/explore/how-many-words-are-there-in-the-english-language.

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code is efficiently encodable, i.e., given a message it is possible to easily determine a corresponding codeword, and efficiently decodable, i.e., given a codeword is easy to determine the message that originated the codeword. For instance, credit card numbers are validated by the code introduced by Luhn [2] that is expressed by Eq. 1. It is a very simple code that may detect the most common typing errors: single digit changes and inversions of two contiguous digits. Thus, when using some e-commerce site you enter your credit card incorrectly if the error consists on a single digit error or swapping two contiguous digits, the error can be detected before attempting to proceed the transaction. However, the error-detecting scheme is not reliable in the sense that a number chosen randomly has a 10% chance of being valid. Equation 1 expresses mathematically the Luhn verification for a number written as an an−1 . . . a2 a1 , where ai is one single digit. Given a numeric sequence, a verification digit can be appended so that the extended sequence is valid. ⎧ ⎛ ⎞  ⎨ (ai ) if i is odd, ⎝ ⎠ ≡ 0 mod 10 (2ai ) if i is even and ai < 5, ⎩ (2ai − 9) if i is even and ai ≥ 5. 2.2.3

(1)

The Sudoku Puzzle

Sudoku is a puzzle consisting of a 9 by 9 grid, partitioned in 3 by 3 blocks, all numbers must appear exactly once in each column, each row and each block. There are N = 6, 670, 903, 752, 021, 072, 936, 960 > 272 valid solutions, thus in a Sudoku puzzle it is possible to encode a message of 72 bits as solutions of the Sudoku puzzle, for each of the 272 possible 72-bit message one assigns a different solution. The code is the set of all possible Sudoku solutions, each solution is a codeword, the codewords are transmitted through an erasure channel. If the received partially filled board is uniquely solvable it means that the received codeword can be determined, and the message recovered readily. Let x be a solution, possibly with erasures, r(x, i, j) represents the jth element in the ith row, c(x, i, j) the jth element in the ith column, b(x, i, j) the jth element in the ith block, defined in terms of a vector x ∈ {1 . . . 9}81 . r(x, i, j) := x9·i+j c(x, i, j) := x9·j+i b(x, i, j) := x9·(3i/3+j/3)+(9(i/3−i/3)+3(j/3−j/3)) The code can be defined in terms of the Sudoku rules, let the indexes I = {(i, j1 , j2 ) ∈ {0..8}3 | j1 = j2 }

(2)

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Fig. 1 Transmission of a solution to a Sudoku puzzle over an erasure channel that causes few erasures

and a vector x ∈ {1..9}81 , Eq. 3 expresses the constraints that must be satisfied in order to x to represent a valid solution to the puzzle. ⎧ ⎨ c(x, i, j1 ) = c(x, i, j2 )∀(i, j1 , j2 ) ∈ I r(x, i, j1 ) = r(x, i, j2 )∀(i, j1 , j2 ) ∈ I ⎩ b(x, i, j1 ) = b(x, i, j2 )∀(i, j1 , j2 ) ∈ I

(3)

Figure 1 illustrates how an erasure channel may affect the solution to a Sudoku puzzle resulting in an unsolved Sudoku puzzle in the receiver. The example may be filled easily since there is only one possible value for each of the erased cell. The puzzle can be interpreted as a recursive code [3], the underlying code of all check nodes is set of permutations of the vector of integers from 1 to 9, 

P = x ∈ {1 . . . 9}9 |xi = xj ⇐⇒ i = j .

(4)

There are 27 check nodes: one for each column, one for each row and one for each block. The code P is limited to correct a single erasure however it is used to produce a code that can correct multiple erasures in the same check node. Important codes such as Turbo Codes, LDPCs and Polar Codes are examples of recursive codes.

2.2.4

Iterative Decoding

The example in Sect. 2.2.3 presents a code consisting in the set of all solutions of a Sudoku puzzle transmitted under an erasure channel and should convince the reader that any Sudoku solver could be employed as a decoder for this code. In that example, the transmitted codeword can be recovered by simply filling the squares with the only possible number at that position given the numbers that were not erased. This section illustrates how iterative decoding is able to recover more difficult codewords.

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Consider the received codeword of Fig. 2. It is not possible to decide the value of some squares based on the puzzle constraints and the currently filled squares, e.g. the first empty square (corresponding to the 5 in the first row) accepts 3 or 5. However, it is possible that some squares can be determined by checking the constraints of the puzzle. After filling such squares it is possible that more squares can be filled. Possibly the board is completely filled by repeating this procedure. Figure 3 shows the evolution of the board during the execution of the algorithm for the received codeword in the Fig. 2.

3 Error Probability Measures In order to measure the reliability of a communication system, statistics about the errors observed are usually considered. For simple channels, some measures such as bit error probability, symbol error probability and even frame error probability can be estimated analytically. For complex systems, there is no known methods for estimating these probabilities other than measuring, possibly by simulation. Particularly for coherent optical communication systems the channel is fairly complex, the channel is much more than the optical fiber, it includes analog-to-digital/digital-toanalog converters and DSP algorithms, including precompensations and impairment estimation/compensations, e.g., clock recovery, frequency offset compensation, and phase recovery. Section 3.1 shows how to calculate the confidence about some upper bound on error probability and Sect. 3.2 gives one possible lower bound on error probability based on mutual information measures.

3.1 Simulation-Based Error Probabilities Estimates The most common measure of reliability of a communication system is a failure probability. Specifications generally say “the failure probability must be less than ”

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where  is a tiny number. Failure may be a single bit error or a frame error, or a word error for the error-correcting codes. Systems without error-correcting codes generally present a nonnegligible error rate and it is possible to simulate until a large number of errors is observed and the ratio of failures in the observations (e.g., ratio between bits with errors and all bits tested) can be estimated with a good precision. On high-speed optical communications a very low error rate is required because the errors become more frequent with the increase of the transmission rate, for instance, a bit error rate of 10−15 on a system operating at 600 Gbps means that on average two errors will occur every hour. Checking the presence of an error floor by plotting an error curve is even more difficult since bit error probability must be estimated for different noise levels with very low error probability.

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Ensuring that such low error rates are achieved is one of the biggest challenges while designing an error-correcting code for optical communications. The traditional approach to simulate until some dozens of errors are observed could delay the tape out of a chip and lead to the loss of the market window. What is presented in this section is a result that enables the designer to make decisions based on the tests already performed.

3.1.1

Estimating Density of Probability of the Event Probability

It is well known that if one event is observed η times in a number θ of tests, as the number of tests increases the value η/θ approaches the probability of that event. The event may be, for instance, a bit error or an uncorrected frame error. Let F be the probability of the event E. Let T (η, θ) represent the event E being observed η out of θ tests, its probability is given by p(T (η, θ)|p(F) = x) =

θ η x (1 − x)(θ−η) . η

(5)

The probability p(F) is not known, but we can define p(p(F) = x), the probability of the probability of the event F being equal to x, and after some tests are performed it can be predicted by the Bayes rule p(p(F) = x|T (η, θ)) =  1 0

p(T (η, θ)|p(F) = x)p(p(F) = x) p(T (η, θ)|p(F) = u)p(p(F) = u)du

.

(6)

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.

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(8)

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(9)

By integrating the probability density function it is possible to determine the probability of the error rate being in an interval. This will be explored in the sequence.

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By observing few errors it is not possible to give a good estimate of error probability, however, it is possible to determine the confidence that the requirement will be met based on that experiment 



p(p(F) = x|T (η, θ))dx  (θ + 1)!  η x (1 − x)(θ−η) dx. θ!η! 0

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(17) (18)

Soft-Decision Forward Error Correction in Optical Communications

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(21)

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Even if the number of tests and observations are small, the method presented will determine how confident one can be that a specification is met. In fact, it can calculate the confidence that the error probability is below an arbitrary threshold using the results of the simulation.

3.1.3

Confidence About Error Probability Upper Bound Without Event Observation

An interesting feature of the Eq. 21 is that it can be applied even without observing any error. Consider one test of frame errors in which no error was observed, the confidence of frame error probability upper bound is given by Eq. 21 with η = 0   p(FER <  | T (0, θ)) = 1 − (1 − )(θ+1) .

(23)

An approximation for large θ is p(FER <  | T (0, θ)) = 1 − exp(−θ)).

(24)

In fact, when θ is very large, Eq. 24 may give a better approximation than Eq. 23 when using standard floating point computations. Figure 4 depicts the probability that the frame error rate is less than a given value.

3.2 Error Measures in Terms of Mutual Information The mutual information is the maximum information that can be recovered from a source given a “noisy” observation. The mutual information is measurable given a

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Confidence

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joint distribution of transmitted and received signal using the Eq. 25. Given two random variables (X , Y ) and its respective domains (X , Y) the marginal probabilities (p(x), p(y)) and the joint probability p(x, y) must be determined. In optical communications the signals are continuous, but fortunately the systems of interest are digital, thus the quantized signals can be considered.

 p(x, y) (25) p(x, y) log I (X ; Y ) = p(x)p(y) x∈X y∈Y Without loss of generality, consider X = {1, . . . , |X |} and Y = {1, . . . , |Y|}. The probability p(x) can be precomputed using O(|X |) memory and time; the probability p(y) can be precomputed using O(|Y|) memory and time. Storing p(x, y) may require O(|X × Y|) memory so it is better to calculate it on demand. Another important measure is the entropy given by the Eq. 26, that indicates how uncertain is the value of a random variable X ∈ X . For a binary variable, the entropy can be expressed in terms of the probability of one of the values as H (X ) = h(p(X = 1)), with h(x) defined as in Eq. 27. H (X ) = −



p(x) log (p(x))

(26)

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(27)

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(28)

For sake of illustration, consider the relation I (X ; Y ) = H (X ) − H (X |Y ) in the scenario where X is a binary variable with probability p, and p(y = x) = pe the

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bit error probability. The information that is available in the receiver is I (X ; Y ) = h(p) − h(pe ), where h(x) is the binary entropy function defined in Eq. 27, by the data processing inequality, given the mutual information between the transmitted and received signal one can easily check the minimum achievable error probability. The reverse procedure can be used as well, if one known how to achieve some bit error probability I (X ; Y ) ≥ h(p) − h(pe ) gives a handy proxy for the mutual information between the transmitted and the received signal.

4 Evolution of Error-Correcting Codes After the publication of the Shannon Information Theory, the scientific community was motivated to try to invent some effective and efficient error-correcting codes, many of them find application even in our days. In 1955 Peter Elias proposed what we know as Convolutional Error-Correcting Codes, which use a finite state machine to produce redundant bits [4]. The next important class of codes over binary groups was proposed by Hocquenghem [5] and, one year after, independently by Bose and Chaudhuri [6], known as BCH codes. A more general class of codes over finite fields was proposed in [7], the well known Reed–Solomon codes. Differently from the above-mentioned codes that are defined in terms of polynomial over finite fields, Robert Gallager presented the LDPC codes, defined as a set of linear equations over finite fields along with an iterative algorithm whose iteration requires a number of operations that grows linearly with the size of the codeword [8]. A framework for efficient decoding BCH and Reed–Solomon codes was established by [9–13], in the next years, and Viterbi delineated an algorithm to determine the maximum likelihood symbol sequence for each possible final decoder state [14] at the same time. With the BCH and Reed–Solomon large block codes, for the standards of that time could be encoded and decoded, with good guarantees about the error curves. By the other hand convolutional codes decoded with Viterbi algorithm can take advantage of information about the probability of each received symbol, known as soft information. Convolutional codes are able to operate with more noise than Reed–Solomon or BCH codes. However, it can not deliver a very low output error probability. A natural solution is to concatenate one convolutional error code that takes advantage of soft information, and one BCH/Reed–Solomon code that can deliver negligible error probability. A very effective coding scheme known as Coded Modulation (CM) was proposed by Ungerboek in 1982 [15]. Coded Modulation splits the symbol space into cosets, and the encoder produces symbols determining first the coset then the symbol inside the coset, this procedure increases the Euclidean distance of the encoded sequence, and can be decoded with Viterbi algorithm. In spite of the effectiveness of the previous error-correcting codes, there was still a considerable gap between the performance achieved by the practical codes and the theoretically reachable Shannon limit. The difference was mainly because

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the complexity of the most simple soft-decision decoders at the time, the Viterbi algorithm, still grows exponentially with the number of bits in the decoder state. The Turbo Codes introduced in 1993 [12] accompanied with an efficient iterative decoding algorithm, enabled the implementation of codes with large blocks, thus reducing considerably the gap to the Shannon Limit. Back in the 1960s, Gallager proposed an efficiently decodable error-correcting code but, due to the lack of a concise representation of the code and the poor performance with small blocks, they were ignored. In 1981, Tanner introduced low complexity recursive codes [3], with a proof that those codes could be efficiently decoded and approach the Shannon capacity as the block length increases, providing a generalization to the concatenation of codes. The tanner representation served later for explaining the message passing decoding algorithm for LDPC codes. After the observation that the distribution of the degrees of the variable nodes is a freedom degree that could be explored [16] for hard-decision decoding, a more general design approach was proposed in [17], namely irregular LDPC design, along with an efficient encoding algorithm [18], and demonstrated experimentally to produce codes that definitively closed the gap to the Shannon limit for AWGN channels [19]. In a single year, LDPC codes became the center of attention. In practical applications, LDPC codes received little attention for a long time after being discovered, since it required a large frame to become competitive, and required a large computational power both for encoding and decoding. The most effective solution for reducing the complexity of the description of an LDPC code is to use quasi-cyclic structure that enables hardware reuse both for encoding and decoding LDPC codes. In the last decades, in the computer era, the requirement for data transmission increased dramatically. Many of the traditional solutions are well suited for applications where the electronic processing speed is higher than the transmission rate, and multiple logic operations can be performed at the time required to transmit one single bit. For high rate optical communications, these solutions are adapted using multiple instances of one encoder or decoder, such solutions provide high throughput but increase considerably the circuit area and power consumption. LDPC codes can easily take advantage of soft information, and have much more flexibility in terms of word length and rate. There exists LDPC codes for every (k ≤ n, (k, n) ∈ N). In addition, the message passing decoding complexity increases linearly for a fixed number of decoding iterations. As the codeword length increase, LDPC overcomes all previously known codes in terms of error correction ability and, since every decoding iteration can be completely parallelized, they can deliver a corrected codeword with a much lower latency, thus becoming the principal candidate for high speed optical communications. More recently, polar codes were discovered [20]. They are defined for n being an integer power of 2, they can be encoded more efficiently than LDPC without requiring a special design of the codes for that, and more important, they have an efficient decoding procedure that can take advantage of soft information. The most attractive feature of the polar codes is that its decoder is not iterative, thus an implementation will have a low latency, and differently from iterative message passing algorithm it

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is fixed something very suitable for optical communications that generally operate continuously. The original decoding algorithm for Polar codes does not provide competitive results when compared to LDPC. However, employing a technique based on list decoding and word selection based on a inner error detecting code [21] makes the polar codes a strong candidate for applications in optical communications as well.

5 Conclusion This chapter presented the basic concepts on how error-correcting codes work. To facilitate understanding of these concepts, simple practical examples have been given, e.g. credit card numbers validation and iterative resolution of Sudoku puzzles. Deductions were also made on confidence of error rate measures when few errors were observed. This method can be applied for bit and frame error rates and is useful for shortening the tapeout time of a chip as it helps predict the performance of an error-correcting code with few error observations. Finally, we present a brief history of the development of FEC that culminated in the emergence of the two most promising codes in optical communications at the present time: Low-density Parity-check and Polar codes. Acknowledgements The authors thank Dr. Rafael Carvalho Figueiredo for reviewing a draft of this chapter.

References 1. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(4):623–656 2. Armonk Luhn HP (1954) Computer for verifying numbers. US Patent 2,950,048, 6 Jan 1954 3. Tanner R (1981) A recursive approach to low complexity codes. IEEE Trans. Inf. Theory 27(5):533–547 4. Elias P (1955) Coding for noisy channels. IRE Convention Record 4:37–46 5. Hocquenghem A (1959) Codes correcteurs derreurs. Chiffres 2(2):147–56 6. Bose RC, Ray-Chaudhuri DK (1960) On a class of error correcting binary group codes. Inf Control 3(1):68–79 7. Reed IS, Solomon G (1960) Polynomial codes over certain finite fields. J Soc Ind Appl Math 8(2):300–304 8. Robert G (1962) Low-density parity-check codes. IRE Trans Inf Theory 8(1):21–28 9. Chien R (1964) Cyclic decoding procedures for bose-chaudhuri-hocquenghem codes. IEEE Trans Inf Theory 10(4):357–363 10. Forney G (1965) On decoding BCH codes. IEEE Trans Inf Theory 11(4):549–557 11. Berlekamp ER (1967) Nonbinary BCH decoding. 1967 12. Berrou C, Glavieux A, Thitimajshima P (1993). Near shannon limit error-correcting coding and decoding: turbo-codes. 1. In: IEEE international conference on communications, 1993. Technical program, conference record ICC’93 Geneva, vol 2. IEEE, pp 1064–1070 13. Massey J (1969) Shift-register synthesis and bch decoding. IEEE Trans Inf Theory 15(1):122– 127

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14. Viterbi AJ (1967) Error bounds for convolutional codes and an asymtotically optimum decoding algorithm. IEEE Trans Inf Theory 13:260–267 15. Ungerboeck G (1982) Channel coding with multilevel/phase signals. IEEE Trans Inf Theory 28(1):55–67 16. Luby M, Mitzenmacher M, Shokrollah A, Spielman D (1998) Analysis of low density codes and improved designs using irregular graphs. In: Proceedings of the thirtieth annual ACM symposium on theory of computing. ACM, pp 249–258 17. Richardson TJ, Shokrollahi MA, Urbanke RL (2001) Design of capacity-approaching irregular low-density parity-check codes. IEEE Trans Inf Theory 47(2):619–637 18. Richardson TJ, Urbanke RL (2001) Efficient encoding of low-density parity-check codes. IEEE Trans Inf Theory 47(2):638–656 19. Chung S-Y, David Forney G, Richardson TJ, Urbanke R (2001) On the design of low-density parity-check codes within 0.0045 db of the shannon limit. IEEE Commun Lett 5(2):58–60 20. Erdal A (2009) Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels. IEEE Trans Inf Theory 55(7):3051–3073 21. Tal I, Vardy A (2011) List decoding of polar codes. In: 2011 IEEE International symposium on information theory proceedings (ISIT). IEEE, pp 1–5

Challenges Toward a Cost-Effective Implementation of Optical OFDM Mônica L. Rocha, Rafael J. L. Ferreira, Diego M. Dourado, Matheus M. Rodrigues, Stenio M. Ranzini, Sandro M. Rossi, Fabio D. Simões and Daniel M. Pataca

Abstract We present a review of concepts and challenges to implement the OFDM technique in the all-optical domain so that it may emerge, in a near future, as a technically and economically feasible option to meet, with spectral efficiency and energy saving, the ever-increasing demand of capacity in data transmission systems. Keywords Optical communication · Optical OFDM · Optical fast fourier transform · Coherent detection

1 Introduction Since the disruptive advent of erbium-doped fiber amplification and wavelength division multiplexing (WDM) in the early 1990s, it became common to justify most of the research on high capacity optical transmission systems as being motivated by the need to meet the ever-growing demand for bandwidth [1–3]. Nowadays, as services and applications continue to evolve, the growth in bandwidth demand still holds this argument valid, although in a more complex scenario that incorporates other equally important requirements such as increase of spectral efficiency (SE) and reduction (or better control) of energy consumption [4–9]. In this context, two multiplexing techniques stood out, among other advanced technologies that emerged, to meet the desired high spectral efficiency: optical orthogonal frequency division multiplexing M. L. Rocha (B) · R. J. L. Ferreira · D. M. Dourado University of São Paulo, Av. Trabalhador São-carlense, 400, São Carlos, SP 13566-590, Brazil e-mail: [email protected] M. M. Rodrigues Idea! Electronic Systems, Av. José Rocha Bonfim 214, Campinas, SP 13080-650, Brazil S. M. Ranzini · S. M. Rossi · F. D. Simões CPqD Foundation, R. Ricardo Benetton Martins 1000, Campinas, SP 13086-902, Brazil D. M. Pataca Universidade Paulista, Av. Comendador Enzo Ferrari 280, Campinas, SP 13045-770, Brazil e-mail: [email protected] © Springer Nature Switzerland AG 2019 A. Paradisi et al. (eds.), Optical Communications, Telecommunications and Information Technology, https://doi.org/10.1007/978-3-319-97187-2_8

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Fig. 1 a O-OFDM and b N-WDM signals represented in the frequency in time domains (Rs and T s represent the symbol rate and duration, respectively)

(O-OFDM) and Nyquist WDM (N-WDM) [11, 12]. Both allow subcarrier overlapping—in the frequency and time domains, respectively, as illustrated in Fig. 1. Furthermore, both are typically associated with coherent detection and electronic processing that, by one hand, allow fulfilling the bandwidth specification but, on the other hand, increase the energy consumption [13, 14]. Note that, strictly speaking, there are two competing ways for implementing an OFDM signal in the optical domain: one refers to the electronic generation of an OFDM data stream (RF OFDM) that will modulate the optical carrier, usually called coherent OFDM (CO-OFDM) and more commonly investigated for access networking applications [10]. The other is associated to the modulation of optical subcarriers provided by an optical comb generator, thus comprising an all-optical OFDM data stream, hereby referred to as O-OFDM [12]. Despite the reciprocity in frequency and time of the two multiplexing techniques seen in Fig. 1, N-WDM with an adequate pulse shaping, in frequency, and overlapping, in time, has been proved to be a more reliable solution [14]. In fact, when compared to O-OFDM, N-WDM is a more mature technology that requires, among other advantages, a less complex transceiver and a lower ratio between transmitted peak power and average power [14–17]. Being able to minimize the occurrence of inter-symbol and inter-carrier interferences, ISI and ICI, respectively, N-WDMbased techniques usually employ wavelength selective switches (WSS) for optical filtering and channel selection with a reduced guard band between carriers. However, they still require a finite guard band between carriers, and whenever the need of a higher SE is more stringent, O-OFDM may represent a better option since it does not

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require guard band—on the contrary, it allows spectral overlapping of subcarriers [12, 18, 19]. With that perspective in mind, in this chapter, we present an overview of concepts, challenges, and technological approaches for implementing the O-OFDM technique. The chapter focuses, mainly, on interferometric methods for the all-optical processing performed at the receiver side and at intermediate nodes [20–24]. This special attention is necessary because, as far as O-OFDM principles are concerned, demultiplexing, routing, adding, and dropping of optical subcarriers must be performed by mechanisms that do not violate the orthogonality condition. That is a feature intrinsic to the technique, and thus requires more sophisticated schemes allied to the conventional WSS. Mathematically, the interferometric methods operate similarly to the fast Fourier transform (FFT) and the inverse fast Fourier transform (IFFT) algorithms for providing a time-to-frequency conversion and a frequency-to-time conversion, respectively. To simplify the interferometric implementation in cases where the number of subcarriers increases, Hillerkuss et al. [21] proposed the use of optical filters combined with optical couplers, Mach–Zehnder interferometers (MZIs), phase shifters, and delay lines (DLs) and their proposal is explored in this chapter aiming at the design of more compact structures. Our main goal is to introduce a level of abstraction into a discussion that takes into account the fundamentals behind O-OFDM and N-WDM and disregards their present degrees of technological maturity. That could lead to a comparison between them based on the hypothetical assumption that both can be implemented by state-of-the-art technologies combining optoelectronics, optical/electronic processing of signal and integrated photonics. In that case, one could establish a pattern that, ultimately, relies on the energy consumption as a key factor for determining which technique should be employed in a case to case basis. This chapter is organized as follows. Section 2 presents a review of OFDM fundamentals illustrated by the implementation of an electrical (RF) OFDM data stream that modulates an optical carrier and is recovered by a coherent receiver, comprising the so-called coherent OFDM (CO-OFDM). Section 3 describes briefly three common techniques used to generate an optical comb from a seed laser and the subsequent modulation of subcarriers, adequate to generate the mutually orthogonal subcarriers, i.e., the O-OFDM data stream. Section 4 focuses on the all-optical FFT and IFFT implementation. It starts by describing the complete interferometric technique before presenting Hillerkuss’ simplification (Sect. 4.1), which leads to another approach based on the AWG technique [25] (Sect. 4.2). In Sect. 4.3, as a proof of concept, we describe an experiment configured with discrete components for demonstrating Hillerkuss’ proposal applied for the drop of a subcarrier out of a fourchannel O-OFDM [26]. In Sect. 4.4, the experimental results are used to calibrate a system simulator that performs the whole operation, thus including an all-optical IFFT for the insertion of a subcarrier [26]. Section 5 deals with synchronism and optical clock recovery of phase-modulated signals, illustrated by a technique based on the use of a four-wave mixing (FWM) process [27, 28]. In Sect. 6, we propose a node architecture, similar to those in [29–39] (Sect. 6.1) that summarizes what could be incorporated into a reconfigurable optical add and drop multiplexer (ROADM)

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to enable the new functionalities. Finally, in Sect. 6.2, we present a brief discussion on energy consumption in Mach–Zehnder modulators implemented with integrated photonic technology [31–35], which will be necessary for allowing O-OFDM to become a cost-effective technique [36].

2 OFDM Fundamentals The concept of (RF) OFDM was first introduced by R. W. Chang, in 1966, whilst the term “OFDM” first appeared in Chang’s patent, in 1970 [37]. The most potential applications of the technique, however, would only be fully explored after the evolution of integrated circuits technology up to being able to support the computational effort required for a practical OFDM implementation. That became possible with the advent of broadband digital applications and very large-scale integrated (VLSI) CMOS chips, in 1990, which brought the technique into the spotlight [38, 39]. Since then, it has been extensively investigated mainly in the context of RF applications. Although its fundamentals remain the same whereas the optical domain is concerned, the translation from an RF OFDM signal, which will propagate through wired or, more typically, wireless channels, into its optical counterpart, which will propagate through an optical fiber, is not straightforward. That is because of intrinsic differences between the communication channels and the linear and nonlinear propagation effects that they induce. For example, in a linear propagation regime, multiple paths undergo a Rayleigh process in a typical wireless media, while in the optical media the phase dispersion caused by the fiber chromatic dispersion affects the propagation of multiple subcarriers in a different way [40, 41]. Although mentioned in this section, these linear effects are not addressed in details in a way to describe how exactly they are dealt with at the transmitter and receiver. Instead, the section will focus on more fundamental concepts and on a simplified mathematical formulation related to the generation and reception of a generic RF OFDM signal. In other words, it focuses on the digital signal processing techniques related to the Fourier transform. In the end, it will illustrate how a transmitter–receiver pairing can be implemented for allowing the propagation of a CO-OFDM signal. OFDM is a special class of parallel transmission scheme, sometimes referred to as multicarrier modulation (MCM) [40, 41]. Conceptually illustrated in Fig. 2a, a generic MCM structure employs a complex multiplier (IQ modulator/demodulator) and requires an optimum detector, for each subcarrier, with a filter that matches the subcarrier waveform or, alternatively, a correlator matched to the subcarrier, as indicated in the figure. A classical MCM uses bandlimited signals that do not overlap and are generated by a large set of oscillators and filters at both ends. The major drawback of this approach is the excessive bandwidth it requires since the channel spacing has to be a multiple of the symbol rate, which reduces the spectral efficiency. OFDM, on the contrary, can be implemented by spectrally overlapping orthogonal signal sets, where the orthogonality originates from a correlation between any two subcarriers [40].

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(a)

(b)

Fig. 2 a Schematic of a generic multicarrier system; b schematic of a generic OFDM transmitter and receiver for a point-to-point transmission (Adapted from [40])

According to the notation in Fig. 2a, for a transmitted signal, s(t), cki is the i-th information symbol at the k-th subcarrier. This way, sk is the waveform corresponding to the k-th subcarrier. Assuming that N sc is the number of subcarriers, f k is the subcarrier frequency, T s is the symbol period, and (t) is the pulse shaping function, it follows that [40]:

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s(t) 

+∞ 

Nsc 

cki sk (t − i Ts )

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(1)

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Ts r (t −

i Ts ) sk∗ dt

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(2)

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In a multicarrier system approach, a high-rate serial data stream is split up into a set of low-rate sub streams, each of which is modulated on a separate subcarrier (SC). In other words, a single data stream is transmitted over a number of lower rates SCs so that the bandwidth of the SCs becomes small compared with the bandwidth of the whole channel. The “key” concept of OFDM is, then, the spectral overlap allowed by selecting a special set of mutually orthogonal subcarrier frequencies, which thus provides the desired high spectral efficiency. The orthogonality originates from a correlation between any two SCs (“k” and “l”) given by [40]: 1 δkl  Ts

Ts 0

sk sl∗ dt

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 exp( j 2π ( f k − fl ))

sin(π ( f k − fl )Ts ) , π ( f k − fl )Ts

(3)

where, for an integer m, the orthogonality condition states that f k − fl  m

1 Ts

(4)

Figure 2b illustrates the implementation of other key concepts behind OFDM. The first states that the banks of I/Q modulators and demodulators, that would otherwise be required, can be replaced by signal processing algorithms. In that case, the inverse discrete Fourier transform (IDFT) and the discrete Fourier transform (DFT) algorithms can be used for, respectively, modulating and demodulating the data transported by the orthogonal SCs. To demonstrate this principle, we replace N sc by N and assume that s(t) is sampled at every interval T s /N. The m-th sample of s(t) may then be written as [40]

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Sm 

N 

ck .e j2π f

(m−1) Ts N

165

where f k 

k1

k−1 Ts

(5)

Using the orthogonality condition (4), in (5), we then obtain [40] sm 

N  k1

ck · e j2π f

(m−1) Ts N



N 

ck · e j2π

(k−1) (m−1) N

 −1 {ck },

(6)

k1

where  refers to the Fourier transform. Similarly, at the receiver, if the received signal r(t) is sampled at every Tx/N interval, we will have [40]: ck  {ck }

(7)

From (6) and (7), we notice that s(t) corresponds to the N-point IDFT of ck , and the received information symbol corresponds to the N-point DFT of the received signal. Note that, for a practical DFT/IDFT implementation, two devices are also essential: a digital-to-analog converter (DAC) that converts the discrete value of sm to the continuous analog value of s(t), and an analog-to-digital converter (ADC), that converts the continuous received signal r(t) to the discrete sample r m . This scheme can be implemented with relative simplicity using the fast Fourier transform (FFT) algorithm. Such simplicity comes from the algorithm’s computational efficiency. In fact, since Cooley and Tukey’s formulation in 1965, the FFT algorithm became a popular computational tool. That is because, as a DFT algorithm, it is able to reduce the complexity of computing a DFT from O (N 2 ) to O (N log N). In this representation, N corresponds to the data size and the big O is a classifying notation of the computational running time and/or space requirements [42]. Another key principle illustrated in Fig. 2b is the introduction, in the time domain, of a cyclic prefix known as Guard Interval (GI), to compensate the effect caused by a dispersive channel. As a consequence of its use, the transmitted signal becomes periodic and a time-dispersive effect (either in the wireless or optical channel) becomes equivalent to a cyclic convolution, discarding the GI at the receiver. A drawback of this technique is the loss of efficiency in transmitted power since the redundant GI must be also transmitted. At the receiver, the equalization (symbol de-mapping) required for detecting the data becomes an element-wise multiplication of the DFT output by the inverse of the estimated channel (channel estimation). For phase modulation schemes, multiplication by the complex conjugate of the channel estimate can do the equalization. Differential detection can also be applied where the symbol of adjacent SCs or subsequent OFDM symbols are compared to recover the data [41]. As a final remark related to the design of an OFDM receiver, time and frequency synchronization are also key issues because they are responsible for, respectively, identifying the start of the OFDM symbol and aligning the local oscillator frequencies at the modulators and demodulators. If any of these synchronization tasks are not performed efficiently and accurately, the orthogonality of the SCs may be lost, or at least partly lost, which will increase the penalties caused by ISI and ICI [41].

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Fig. 3 Block diagram of a generic CO-OFDM transmission system with a direct up-/downconversion architecture (Adapted from [40])

As a summary, Fig. 3 presents a conceptual diagram for implementing a generic CO-OFDM transmission system. It comprises five functional blocks: RF OFDM transmitter, RF-to-optical (RF-O) up-converter, optical link, optical-to-RF (O-RF) down-converter, and RF OFDM receiver [41]. For this basic setup, it is assumed a linear fiber propagation regime as well as a linear operation at the up- and downconversion blocks. As illustrated, the input digital data at the Tx side are first converted from serial to parallel into a block of bits consisting of N sc symbols, where each symbol consists of multiple bits for m-ary coding. These symbols are mapped into a two-dimensional complex signal cki . The RF OFDM signal in the time domain is obtained through the IDFT of cki . Next, a guard interval is inserted to avoid the channel dispersion. The digital signal is then converted to an analog form through a DAC and filtered by a low-pass filter that removes the alias signal. The subsequent RF-O up-converter transfers the baseband signal to the optical domain by using an optical IQ modulator comprising a pair of Mach–Zehnder modulators (MZMs) with a phase offset of 90°. The baseband RF OFDM signal is directly up-converted to the optical domain. After traversing the optical medium, the CO-OFDM signal is then fed into the O-RF down-converter, where it is converted to an RF OFDM signal again. Figure 2b shows the direct down-conversion architecture in which the intermediate frequency (IF) is near-DC. In the RF OFDM receiver, the IF signal is first sampled with an ADC. The signal then undergoes the three levels of synchronization: (i) DFT window synchronization: RF OFDM symbols are properly formatted to avoid ISI; (ii) frequency synchronization: frequency offset is estimated, compen-

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sated, and, if possible, adjusted to a small value at the start; (iii) subcarrier recovery: each subcarrier is estimated and compensated [40].

3 O-OFDM Generation The possibility of operating with only one optical source for generating multiple carriers represents a paramount issue for the O-OFDM technique and may favor it over N-WDM, where the operation of multiple laser sources is mandatory. In this context, a challenge for the O-OFDM design is to build up an optical multicarrier source where the orthogonality condition is always guaranteed. One way to assure the orthogonality relies upon the use of a single laser seed for generating phase-coherent frequency-locked subcarriers that will be synchronously modulated. As a bonus, the mechanism should also be able to guarantee the desired high aggregate capacity by exploiting parallel processing techniques, moderate modulation rate per subcarrier and high spectral efficiency. A signal generated from such an arrangement is usually referred to as optical superchannel [12, 43]. Since the subcarriers are overlapped, the interference between them can be eliminated by avoiding frequency shifts of adjacent channels and that imposes another challenge, which is to adequately separate the subcarriers for individual processing. Therefore, a correct processing of one subcarrier out of several others requires that, at least, the following three conditions are met [43]: 1. The subcarrier separation must be equal to the symbol rate of each modulated subcarrier (that assures the orthogonality condition); 2. The symbols, in modulated subcarriers, must be aligned in time (thus fulfilling the synchronism requirement); 3. The transmitter bandwidth must be large enough to accommodate all subcarriers, provided that an appropriate sample rate and anti-aliasing filtering are applied (which satisfies the requirements for operation in an elastic optical networking context). From the above conditions, it follows that for a given total symbol rate, the bigger the number of subcarriers the smaller the difference between their frequency separation and, consequently, the smaller the symbol rate that modulates each one of them. Although a complete O-OFDM generation process undergoes two basic steps: generation of an optical comb and adequate modulation of subcarriers, this section is more concentrated on the optical comb generation stage. In previous works, we have experimental and theoretically investigated this subject in more details [43–46] but for the present scope it is enough to highlight that, from a number of optical comb generation techniques, proposed in the literature for this application, three have stood out as a promising base for more practical implementations: 1. Cascade of Mach–Zehnder/Phase modulators (MZM/PM), seen in Fig. 4a: commonly used to generate signals with two to around eleven subcarriers—this

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Fig. 4 Schematics of optical comb generators with their respective simulated spectrum: a cascade of Mach–Zehnder modulators; b recirculating frequency shifting (RFS); c laser gain switching (Adapted from [43])

limitation is determined by the MZMs/PMs electro-optic bandwidth and by the maximum amplitude of the driver signal. In this approach, two or more cascaded modulators are driven by phase-controlled sinusoidal electrical waves (tuned into the same RF frequencies). It is important to notice that not just MZ modulators may be cascaded, the setup may comprise a cascade of phase modulators (PM), or a combination of PMs and MZs. The important point here is that each modulator will produce a set of sidebands shifted by the RF frequency applied on the modulators. Another important aspect is that, in order to keep the overall optical to signal to noise ratio (OSNR) equalized, the amplitude of each subcarrier will have to be individually controlled [43, 47, 48]. 2. Recirculating Frequency Shifting, RFS, Fig. 4b: based on the frequency conversion produced by single sideband modulation, allows the generation of a great number of stable subcarriers. In the RFS technique, a continuous wave (cw) laser signal is shifted, in frequency, within a recirculation loop due to an analog phase modulation process. In a basic configuration, the OCG consists of a seed laser, a 2 × 2 optical coupler, a double MZ modulator, an Erbium-doped fiber amplifier

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(EDFA), to compensate for the loop losses, and an optical filter, for limiting the number of generated subcarriers and the level of amplified spontaneous emission noise (ASE) within the loop. The cw optical signal is continuously injected into the loop through one of the coupler input ports. After each round trip, part of the signal exits the loop and part returns to it. In the loop, the modulator is electrically driven by two mutually orthogonal RF sine waves. Its biasing points are adjusted in such a way to generate a single sideband suppressed carrier (SSB-SC) signal, which is then amplified and filtered. Note that the filter output is recombined with the signal seed laser signal, at the coupler input, so that, at each round trip, new comb lines may be continuously generated while the modulator output is continuously shifted by the RF frequency applied to the modulator. After many round trips, the initial comb lines are totally shifted to outside of the filter band; however, the process assures that new comb lines will be continuously generated inside the filter band. In the RFS spectrum, an excessive noise level is usually present, due to the use of optical amplifiers (EDFAs) required for the technique implementation [43, 49, 50]. 3. Discrete mode laser (DM) driven by a sine wave, Fig. 4c: similar to gain switching in semiconductor lasers, results in phase locking at the comb output. Compared to the previous approaches, this one is relatively simpler and, consequently, of lower cost. In this implementation, a sinusoidal RF signal is amplified and directly applied into a laser designed for direct modulation applications. Its amplitude is adjusted for the desired optical to signal to noise ratio (OSNR) [43, 51–55]. The spectra seen in Fig. 4 were obtained from simulation pallets configured to equalize the comb lines by using a set of variable attenuators (VOAs) placed in between a DEMUX/MUX (WSS), as illustrated in Fig. 5. A generic O-OFDM generator thus comprises two basic stages: a seed-laser-based OCG and a modulation stage, consisting of a WSS (DEMUX/MUX) and modulation modules (MOD). If subcarriers’ power equalization is necessary, VOAs may be included. The two experimental spectra illustrated in Fig. 5 were obtained with the RFS technique, taken at the DEMUX and MUX input and output, respectively [45].

4 Optical FFT/IFFT Events in the time domain can be related to events in the frequency domain via the Fourier transform: going from time to frequency requires the Fourier transform itself, whereas the reverse process requires the inverse Fourier transform. This procedure can be implemented in several versions and the choice of which to use depends on the intended application. One of these applications is the signal processing performed with a sampled signal. At the limit, for a large spectrum tending to infinite, the sampling process causes different signals to become indistinguishable, an effect known as aliasing. On the other hand, at the time domain side, signals not limited

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ModulaƟon Stage

DATA Wavelength (nm)

OpƟcal OFDM stream

OpƟcal Power (dBm)

OpƟcal Power (dBm)

Comb GeneraƟon Stage

Wavelength (nm)

Fig. 5 Basic diagram of an O-OFDM superchannel generator comprising a seed-laser-based OCG and a modulation stage: WSS (DEMUX/MUX) plus modulation modules (MOD) (ECL: External Cavity Laser) (Adapted from [45])

in time lead to a processing that requires an infinite storage space [42]. Such a dual problem can be avoided by using the discrete Fourier transform (DFT), in which the signals are sampled in both time and frequency domains [42]. The fast Fourier transform (FFT) is merely a rapid mathematical method for computational applications of DFT. In this context, RF OFDM has become a prominence due to the ability of modern integrated circuits to generate this multicarrier signal by using IFFT and to reverse the process, in the receiver, by using FFT [42]. In a similar but not straightforward way, the O-OFDM approach depends on the maturity of a technology that will allow it to become as popular as RF OFDM. That, by inference, should be related to the optical counterpart of the (I)FFT algorithm implemented by an optical integrated circuit. The use of integrated optics (IO) for implementing the FFT algorithm in the optical domain was first suggested by Marhic et al. in 1987 [56], although at the time the IO technology was not mature enough for practical demonstrations. Later, in 2001, Siegman et al. proposed a more achievable solution for obtaining the DFT of a sampled optical array that traversed a combination of optical 3-dB couplers and optical phase shifters [57]. Despite the difficulty to be implemented and stabilized in discrete assemblies, these interferometric types of structure have been studied for the processing of O-OFDM signals since then [58–65]. As they may suffer from complexity increase in their design as the number of subcarriers increase, in 2010 Hillerkuss et al. proposed a simplification in the interferometric method that could form a basis for the design of reliable and less complex schemes aiming at more cost-effective solutions [21]. In this same line of application, in 2011 Wang et al. proposed the use of conventional arrayed waveguide gratings (AWG) as integrated spectral filters to perform the optical FFT/IFFT functions [25]. Wang’s proposal is

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promising because, compared with other FFT/IFFT optical circuits, AWGs are less complex structures, especially for a large number of inputs and outputs [25].

4.1 Interferometric Technique Consider a system with n inputs, m outputs and N time samples, where N  2p and p is an integer. Furthermore, consider that x n represents the time-series sample of a signal x(t), taken over a period T , and X m is the correspondent complex spectral components repeated with a period T . The N-point DFT transforming the N inputs x n into N outputs X m is then given by [21]: Xm 

 mn  xn , exp − j2π N n0

N −1 

m  0, . . . , N − 1

(8)

The FFT operates in such a way that it splits a DFT of size N into two interleaved DFTs of size N/2 after a number of recursive stages. That originates ‘E m ’ and ‘Om ’, the even and odd DFT of size N/2, for even and odd inputs x 2l and x 2l+1 (l  0, 1, 2,…N/2 − 1), respectively. Mathematically, that can be expressed as [21] ⎧  ⎨ E m + exp − j2π mn Om if m < N2 N Xm  (9)  

⎩ E m−N 2 − exp − j2π m − N Om−N 2 if m > N / / 2 2 In independent proposals, Marhic [56] and Siegman [57] demonstrated that, in order to obtain the spectral components of a time series, the N samples, taken at an interval T , must be fed simultaneously into an optical circuitry comprising a set of optical time delays acting as a serial-to-parallel (S/P) converter. This type of optical FFT (sometimes referred to as OFFT, or O-FFT) differs from the electronic implementation because it operates in a continuous mode and, to function correctly, the sampling must be performed in synchronization with the symbol over duration of T /N. This condition imposes a severe stability restriction and requires an extra care in maintaining equal delays and proper phase relations within waveguides that interconnect the optical couplers, thus configuring an interferometric structure. Despite these challenges, it is important to note that the optical FFT approach requires, mostly, passive devices with low power consumption in comparison with components of the electronic FFT approach. Furthermore, the fact that the optical sampling window sizes can be shorter than the electronic sampling windows (at the ADCs) gives to the optical FFT approach another important advantage. This chapter focuses on Hillerkuss’ proposal [21] because, besides the possibility of leading to simpler integrated devices, it may lead to a simpler experiment using discrete components. In fact, by working on both Marhic and Siegman’s ideas, Hillerkuss et al. demonstrated that by reordering optical delays lines and relabeling

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(a)

(b)

Fig. 6 a Four-point optical FFT in a low-complexity interferometric scheme; b complete interferometric method followed by the simplified version for N  2, 4 and 8 (Adapted from [21])

outputs accordingly it is possible to simplify the overall structure of the optical FFT. Based on their development, Fig. 6a illustrates a setup for N  4 [21]. Taking the initial approaches as a reference, this configuration was achieved after relocating the sampling gates to the end of the circuit, a step that does not change the overall operation. Furthermore, the delays in the S/P conversion stage were reordered and the outputs were relabeled accordingly in a way that the OFFT input could comprise two parallel delay interferometers (DIs). The simplification rules as proposed by Hillerkuss can be applied to any size (N) of FFT. Figure 6b illustrates the simplification process applied for N  8, going from Marhic’s scheme (top of Fig. 6b to the Hillerkuss’ simplified version (bottom of Figure(b)) [21]. For applications that require add and drop functionalities, Hillerkuss’ proposal offers an important advantage for the extraction of a single subcarrier. For that, once the subcarrier to be extracted has been selected, it is possible to remove all delay interferometers (DIs) that are not on the optical path that corresponds to the selected output port that leaves only one DI per stage, which leads to a number of DIs equal to log2 N. To select the subcarrier, it is only necessary to tune the phases in each DI, and that can be accomplished without changing the setup design, as illustrated in Fig. 7 [21]. Another important simplification proposed by Hillerkuss’ aims at reducing one or more stages of DI by replacing them with standard optical filters [21]. The idea is

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OPTICAL COUPLER

T/2

φ1

OPTICAL COUPLER

OPTICAL COUPLER

T/8

φ3

OPTICAL COUPLER

OPTICAL COUPLER

173 φ2

T/4

OPTICAL COUPLER

GATE

Xn Fig. 7 Simplification principle: within a delay interferometer (DI), all delay lines (DL) that are not on the optical path correspondent to the selected output are removed (Adapted from [21])

based on the fact that the DFT acts as a periodic filter in the frequency domain with a free spectral range (FSR) equal to NΔω. Furthermore, each DI can be seen as a periodic filter with FSR NΔω/2p where p is the index of the FFT stage and N is the order of the FFT. As a rule of thumb, the stages with a higher subscript (those being traversed last) have the largest FSR and should be replaced first. Figure 8 illustrates the technique for N  8 [21].

4.2 AWG Technique To further Hillerkuss’ approach toward a popular device used as WDM MUX and DEMUX, Wang et al. proposed and demonstrated an all-optical FFT/IFFT scheme based on conventional arrayed waveguide gratings (AWGs) [25]. For this purpose, they showed, through simulated results, that it is possible to employ AWGs performing both functionalities, i.e., MUX/DEMUX and optical FFT/IFFT. That may be an important feature for an optical OFDM transmission that involves a large number of inputs and outputs. Wang’s demonstration is based on a few additional conditions imposed onto the design parameters of a conventional AWG that operates as a WDM filter. Figure 9a illustrates a typical AWG with input/output waveguides, two focusing slab regions and one arrayed multichannel waveguide between two slab regions, with constant path increment ΔL between the channels. Usually, the two slab regions are identical with the details shown in Fig. 9b [25]. The basic design of such structure may be altered to include the optical FFT/IFFT functionalities in such a way to control the time difference of light traveling, τ , between adjacent channels in the arrayed waveguide, where 1/τ defines the FSR in the frequency domain. The AWG can perform both optical FFT and IFFT operations by introducing a selection condition so that the AWG transmission spectrum repeats itself after every NΔ periods. In other words, the FSR of the AWG, 1/τ matches exactly the spacing between different frequency bands, each band containing N channels. Such structures are named cyclic AWGs where the N arrayed waveguides provide temporal delays and the input/output slab regions produce phase shifts. The operation is only valid when all N copies of the signal, s(t), overlap with

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(a)

(b)

(c)

(d)

Fig. 8 a Optical FFT (OFFT) scheme for N  4 points combining passive splitters and optical time delays for serial-to-parallel conversion. The optical gates sample the optical signal and the OFFT is obtained using 2 × 2 couplers and phase shifts; b after simplifications that eliminate redundancies and relocate the gates, a simpler scheme may be obtained; c technique for replacing parts of the DI by a first-order passband Gaussian filter wide enough to extract one subcarrier; d to replace more DI stages a narrower filter may be used but crosstalk and ISI may occur (Adapted from [21])

different time delay, i.e., there is only a time window with width τ , during which the FFT is realized. In this structure, a time gating device may be required to sample the signal at that window (as indicated in Fig. 10a). In the optical IFFT configuration (Fig. 10b), the input signal must be discrete at each subcarrier frequency, or at least have time interval less than τ . Otherwise, there will be ISI at some of the N samples caused by the time delay in the arrayed waveguide [25].

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j-1

Array waveguide

(a)

(b) L + jΔL

d

N-1

f f + d sin θ/2 = f + dx/2f

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j

0

j

L

x = fθ x

Slab region

f - d sin θ/2 = f - dx/2f

D

N-1

Input waveguide

k

i 0

Output waveguide

0

k

Output waveguide

Fig. 9 a Typical AWG structure; b detail of its design where D is the AWG’s input/output waveguide separation, the arrayed waveguide separation is d (for input) and d 1 (for output), and the radius of the curvatures is f (for input) and f 1 (for output). Here d  d 1 , and f  f 1 (Adapted from [25])

(a)

(b) τ

T=Nτ

AWG

AWG

T=Nτ

T=Nτ

t

Input i

O-FFT

t Output k

t

Input i

O-IFFT

Output k

t

Fig. 10 Configuration of an AWG to operate as an optical. a FFT and b IFFT subsystem (adapted from [25])

4.3 Optical FFT Experimental Demonstration In this section, we present the results obtained from a setup assembled for evaluating experimentally the drop stage of an optical FFT based on a discrete-component implementation, as illustrated in Fig. 11 [26]. The demonstration of an all-optical node that includes the add stage was simulated and will be presented in the next section. Despite having already investigated the OCG techniques based on a cascade of Mach–Zehnder and/or phase-modulators and also on the recirculating frequency shifter (rfs) techniques, for this proof of concept we used an OCG based on the gain switching of a semiconductor laser because of its simplicity and energy-saving potentiality. The generated comb lines can be seen in Fig. 11a, where the frequency spacing between the optical carriers, Δf , 12.5 GHz, imposes a bit rate equal to 12.5 GBd to satisfy the orthogonality condition. Due to its laboratorial availability, the modulation format used was quadrature shift phase keying (QPSK), which thus resulted in a bit rate of 25 Gb/s/subcarrier. Figure 11c illustrates the eye diagram

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Fig. 11 OFFT experimental demonstration by dropping one subcarrier out of a three-subcarrier O-OFDM signal. The OFFT comprises a two-stage DI where the second one is replaced by a tunable bandpass filter wavelength shaper (WSS) (Adapted from [26])

of the modulating data at the PRBS generator output. Furthermore, as the need of using discrete components that are insensitive to polarization fluctuations limited the number of available couplers, the demonstration was performed with only three subcarriers (Fig. 11b), thus resulting in a gross rate of 75 Gb/s. The optical OFFT demonstration was based on the scheme seen in Fig. 11, where the second DI stage was replaced by an optical bandpass filter. The assembling of the first DI required the use of an optical bench because the nonintegrated interferometric subsystem operated without a stabilization circuitry. For dropping one carrier out of the three-subcarrier signal, we used one delay line (DL), one splitter and one 2 × 2 coupler with polarization maintaining (PM) fibers, followed by a WSS replacing the second DI. Figure 11d–f show the spectra at the first DI input, second DI input (after the EDFA) and output, respectively. To evaluate the influence of crosstalk and ISI in the BER performance, caused by replacing the second DI by the filter, the WSS was set to two band values, 15 and 25 GHz so that we could select the best performance passband [26].

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OFFT λ2

OFFT λ3

25 GHz

15 GHz

OFFT λ1

FEC limit

Fig. 12 (a) Experimental results (BER vs. OSNR) for each carrier dropped by the OFFT where one DI stage was replaced by a band pass filter (BPF) tuned to 15 and 25 GHz. Inset: constellation of the three dropped carriers (Adapted from [26])

To complete the setup, there was a coherent receiver together with an arrangement comprising an EDFA, a VOA followed by an optical coupler, a splitter and a polarization controller (not shown but necessary for accessing the received signal before its processing at the DSP [26]). The receiver was a commercial integrated coherent receiver (ICR) used for the reception of 28 GBd-QPSK signals. The two electrical ICR output signals were sampled at 50 GSa/s by a two-channel real-time scope (20 GHz band) for offline DSP. As an optical local oscillator, we used a tunable external cavity laser (ECL) with 100 kHz linewidth. The DSP subsystem included anti-aliasing filtering, ortho-normalization, resampling to two samples/symbol, time recovery, constant modulus algorithm (CMA)-based equalization (with 60 taps), and carrier/phase recovery. For taking into account the measurement fluctuations and for providing a better assessment of the system behavior, each measurement was repeated sixty times. From these data, we selected the five with best performance and averaged them. The results thus obtained are summarized in Fig. 12. Figure 12 shows the BER versus OSNR for each carrier dropped by the OFFT using the BPFs configured to 15 and 25 GHz, as well as the constellation diagrams after the OFFT operation. The performance with the narrower band (15 GHz) was worse for the three carriers in comparison to their behavior with the wider band (25 GHz). That happened because the narrower band cut the high-frequency components of the signal, thus distorting its eye diagram. Note that for both pass bands, the central carrier (λ2 ) presented a better performance than the side carriers (λ1 and λ3 ). One possible explanation for that behavior is the lack of symmetry, caused by

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Fig. 13 Scheme for the all-optical FFT/IFFT/FFT processing of a four-subcarrier O-OFDM, as configured in a simulation pallet (Adapted from [26])

the absence of the fourth subcarrier, in the four-order OFFT implemented. Figure 12 also illustrates the constellation diagrams of the received carriers for the OSNR equal to 6 dB. Again, we can note the degradation of the dropped carriers when using the narrower filtering (15 GHz) [26].

4.4 Optical FFT/IFFT Simulated Demonstration To validate the simulated results, a setup (Fig. 13) similar to the experiment was configured in a simulator (Optisystem 13.2). As the optical devices used in the experiment present a higher insertion loss, they required the use of optical amplifiers that could be avoided in the simulation but special care was taken to control the OSNR level. For the calibration, we used only one stage of DI and replaced the second stage by a Gaussian OBPF with (25 and 15 GHz). As in the experiment, the best results were obtained for Δf  25 GHz. Therefore, the results presented are all related to this bandwidth. We used a standard QPSK coherent receiver and DSP. At the receiver input, a block called “OSNR controller” was implemented to keep the OSNR at the same level of the experiment. However,

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Fig. 14 a Simulated and experimental results (log BER vs. OSNR) for each subcarrier dropped by the OFFT and b a complete O-OFDM signal processing (dropping and adding) using the proposed all-optical FFT/IFFT interferometric technique in the simulation setup (Adapted from [26])

as expected, simulated results showed best performance and they did not take into account the unstable behavior of the experimental interferometers. All considered a comparison between experiment and simulation for the OFFT functionality shows a reasonable agreement for BER values up to ~10−12 (Fig. 14) [26]. Once validated, the pallet was adapted to include all DI stages, i.e., three stages wherein the first the delay is T /2. At one of its two outputs, a delay of T /4 was applied and combined with a phase shift of π /2, as indicated in Fig. 13. The N  4 OFFT was then able to separate four subcarriers: X 0 and X 2 (the even subcarriers) and X 1 and X 3 (the odd ones). After the second DI stage, the four subcarriers were finally separated. For the next processing step (gate), we used electro-absorber modulators to sample each carrier. After that, the optical IFFT (similar to the optical FFT but with a reversed order of processing) was implemented. This whole procedure corresponds to the dropping and adding functionalities as it happens in an add/drop node. At the receiver, another optical IFFT was used for subcarrier selection, also tuned by the local oscillator laser. To complete the data assessment, a DSP analyzed the constellations and calculated the BER. The OSNR controller comprises an optical amplifier (to add noise) and an optical coupler. The results for the four carriers, after being dropped, reinserted and received, are shown in Fig. 14 and their good BER versus OSNR behavior in a back-to-back configuration demonstrate the feasibility of the proposed technique applied to the O-OFDM signal processing [26].

5 Synchronization and Clock Recovery Clock synchronization is another key step for implementing the O-OFDM technique and that can, in principle, be accomplished in two ways: asynchronously or syn-

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chronously [66]. In the first, a received signal is used as a reference for detecting an offset between the clocks at the transmitter and receiver. The offset is then processed for further compensation, usually in a DSP. In a synchronous operation, the clock signal is extracted from the received signal, being, therefore, synchronized with it. Whenever coherent detection occurs, it is possible to use digital signal processing for performing the clock-related operation but, more generically, wherever synchronization is required, it may be more practical and costly if achieved in the optical domain [66–68]. For the O-OFDM approach, a challenge to be pointed out is that no matter the chosen clock recovery method, it should also satisfy the requirements of being simple, compact, easily integrated and low power consumer—that is not an easy task. The all-optical process that takes place at a node or at the receiver of an O-OFDM superchannel system can be divided into steps. At first, the OFDM signal is demultiplexed by an optical IFFT module and, after that, a bank of optical gates (electroabsorption modulators, EAM) performs the time sampling of those subcarriers that will be dropped or rerouted. The optical gates are synchronized to a common clock, extracted from the superchannel. The availability of an analog clock is an important resource for enabling functionalities such as synchronization, phase tracking, and regeneration. One of the challenges in this particular part of the O-OFDM operation is to provide the desired clock signal disregarding the modulation format being used. In particular, for phase-modulated formats, recovering the clock from a signal is tricky. Aiming at that goal, there have been many proposals in the literature, among them, this section describes a method that exploits the all-optical signal processing based on the nonlinear effect of four-wave mixing (FWM) [27, 28]. To illustrate the technique, Fig. 15 shows a scheme where the O-OFDM subcarriers are spaced by Δf and modulated with a QPSK data [27]. Initially, Δf is filtered by a narrow filter that selects two adjacent channels. Note that only two subcarriers are necessary to recover the clock but, for simplicity, the entire superchannel could be used. As the FWM will result after beating the signal and a pump, the use of only two subcarriers minimizes the distance between the pump and signal. The filtered signals and a continuous wave (cw) pump are then combined and injected into the first stage of a SOA. As it takes place, the FWM gives rise to idlers, whose frequency and phase are governed by [27] fI  2 fS − fp φI  2φS − φp

(10)

where f I and φ I are the frequency and phase of the idler, f s and φ s are the frequency and phase of the signal, and f p and φ p are the frequency and phase of the pump. The two idlers have double frequency spacing, 2Δf , and double phase modulation and are, by the process, converted into BPSK signals. These two generated BPSK signals are selected by another filtering and injected into a second SOA, together with a second pump. This second stage is equivalent to the first one, and hence the phase information on the generated idlers is doubled again, converting the signals into nonmodulated carriers spaced by 4Δf . Finally, these two idlers are filtered and

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Fig. 15 All-optical clock recovery for an optical OFDM QPSK-modulated technique (Adapted from [27])

launched into a photodiode, where they beat with each other to produce a clock at a frequency of 4Δf . In the electrical domain, this clock is down-converted, thus resulting in the original clock with frequency Δf [27].

6 Final Discussion To conclude, this section presents a schematic view that integrates the parts described in the previous sections. In this way, it becomes possible to glimpse the transmission and reception structures as well as a node architecture, which can serve as a reference for an integrated photonic design aiming at overcoming the challenges for making O-OFDM an economical and technically feasible alternative.

6.1 O-OFDM Node Architecture Figure 16 shows a proposal for combining the OCG-, clock recovery-, gating-, and optical FFT/IFFT- subsystems in a way to assemble an O-OFDM transmitter, an OOFDM Intermediate node (ROADM) and an O-OFDM receiver. These diagrams give a better idea of how the subsystems can be integrated. Provided that it is guaranteed, the integrated structure design must be driven by requirements of operation stability, number of interconnections reduction and energy consumption optimization.

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Fig. 16 Proposed architecture for assembling an O-OFDM transmitter, receiver and intermediated ROADM O-OFDM node

As illustrated in Fig. 16, the transmitter module comprises an OCG stage, one WSS, a modulation stage, and an OIFFT module (OIFFT 1). The WSS is used to separate the comb lines before their individual equalization and modulation. After that, the OIFFT module combines the mutually orthogonal subcarriers in order to generate the O-OFDM stream (A). At the intermediate node input, an optical switch may connect the arriving superchannel to a WSS, for a sub-band selection, prior to the O-OFDM processing (B), or directly to the O-OFDM node, for local processing of as many subcarriers as required (D), or to bypass the intermediate node (O-OFDM node) by routing the whole data

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stream to a next node or to a receiver (E) in a way that the ROADM O-OFDM node becomes transparent to the superchannel propagation. The receiver stage comprises an OFFT module (OFFT-1) and individual coherent receiver setups (Rx), synchronized by the clock recovery module, where the local oscillator is provided by an OCG module. If the O-OFDM stream is to be processed partially (C) or totally (D) at the intermediate node, the function of local extraction (dropping of subcarriers) and insertion (adding of subcarriers), controlled by a bank optical switches, may be performed as indicated by the green arrows. For that operation, after the subcarriers’ separation, performed by the OFFT-2 module, a clock recovery module provides synchronism to gates, modulators of locally generated subcarriers and receivers. Usually, electro-absorption modulators perform the sampling operation (gates), necessary for extraction of subcarriers. The OIFFT module (OIFFT 2) combines the subcarriers, generated at the local OCG, which will be modulated and inserted into the traversing O-OFDM superchannel. Note that the local OCG must be phase locked with the O-OFDM entering the node and, for that, a phase reference may be used as indicated. Alternatively, and for routing purposes, the optical switches may include more WSS’s for band selection (at the input) and band recombination (at the output) for dropping/adding or routing of subcarriers in a passband, while the remaining subcarriers just traverse the node. As it can be inferred from the proposed architecture and the description of its modules presented in previous sections, there is still a long road in integrated photonics’ design to be crossed before reaching the cost-effective target. However, the path is relatively clear and recent advances, especially in the design of waveguide structures such as modulators, delay lines, and phase shifters, when integrated with optoelectronic devices, point toward a promising near future for O-OFDM [63, 69].

6.2 A Few Remarks on Technical and Energy-Saving Feasibility No matter, if applied to O-OFDM or N-WDM, it will be always convenient to replace high power consumption technologies (based, for instance, on high-speed digital signal processing) by all-optical signal processing techniques that represents a potentially energy-efficient alternative to their electronic counterpart either for N-WDM of O-OFDM. For this reason only, the research on all-optical signal processing is justifiable, especially when applied for also enhancing the spectral efficiency. That is the context for developing all-optical OFDM technology because it employs a great number of passive devices, such as optical delay lines, optical phase shifters, optical filters, and optical couplers, usually connected in interferometric configurations. The research on this area has been carried out by many groups that report different designs including such elements. Usually, the designs are based on silica planer light-

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(a)

(b)

Fig. 17 Example of an equivalent circuit for an electro-optical modulator combined with a resistive load and b capacitive load (Adapted from [75])

wave circuit (PLC) and must fulfil requirements that go beyond the device operation [31–35, 69]. Particularly, for photonic modulators, which seem to be the core devices for the optical OFDM implementation, the electrical energy consumption to operate the modulator is a critical issue. As related in [70], the power required to operate the device increases with the modulation frequency, and can be measured by the ratio of the operating power per bandwidth unit. Usually, this figure of merit is expressed in watts per hertz [70] or in joule per bit [71]. Energy efficiency has been emphasized in recent years as one of the most important metrics of interfaces involving photonic circuits and electronic circuits. By verifying the state of the art in photonic devices, studies show that the best alternative for energy consumption is focused on electrooptic (EO) modulators, as can be seen in [72–74]. The energy consumption of an EO modulator depends on the physical properties of the phase shifters and the electronic design of the driving circuits. Figure 17 shows two examples of equivalent circuits used to measure the power consumption in electro-optical modulators. Conventionally, some modulators are designed as traveling wave devices, which have 50 input impedance (r i ) combined with 50 impedance of the transmission line and RF cables (Z L ), in order to achieve maximum power transfer to the transmission line (see Fig. 17a). In this case, the driving voltage (V D ) is only half the voltage of the open circuit source (V 0 ). Therefore, for a simple OOK modulation format, for example, the energy consumption per bit (E bit, R ) in the modulator can be estimated by considering the energy dissipation in the load resistor (RL ) during a bit duration slot (T bit ) [75]. E bit,R 

VD2 × Tbit 4RL

(11)

Thus, if we consider V D  1 V, RL  50 , a bit rate of 10 Gb/s and a bit duration equal to 100 ps, for example, the energy consumption per bit will be 500 fJ/bit [75]. On the other hand, according to Koos et al. [75], this energy consumption can be reduced by using silicon–organic hybrid (SOH) modulators, since the phase shifters of these structures can be manufactured in much smaller dimensions than devices based on the free-carriers dispersion. As a consequence, the length of the SOH modulators phase shifters can be short compared to the RF wavelength of the modulation

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signal, so that the device does not need to be designed in a traveling wave configuration combined with impedance. Assuming that the electronic driver circuits can be integrated in close proximity so that the circuit power lines can be kept short and the impedance is not required, these modulators (SOH) can be operated by purely capacitive loads, as shown by Fig. 17b. Considering a SOH modulator operating below its cutoff frequency (f c  1/2πr i C), the driving voltage reaches a permanent state value equivalent to V D  V 0 . Thus, the energy consumption will be related to the energy dissipation in the resistor r i during the charging and the discharge of the capacitor (C). For a NRZOOK modulation format, for example, the power consumption per bit (E bit, C ) in this modulators class is given by [75] E bit,C 

VD2 × C 4

(12)

Considering V D  1 V and a phase shifter of 500 μm, which has capacitance of 200 fF, for example, the energy consumption per bit (E bit, C ) can be estimated at 50 fJ/bit. Note that, when compared to the value of the previous traveling wave example, this value is 10 times lower in magnitude [75]. To illustrate a design of integrated photonics applied to the optical OFDM operation, Fig. 18 shows an all-optical eight-channel OFDM demultiplexer (O-FFT) based on an integrated silicon-on-insulator (SOI) technique using PLC implemented by Hai Yu et al. [76]. Basically, the structure combines three-stage cascaded MZIs, and adjacent stages of the MZIs are connected by a directional coupler. The differential path length of each stage MZI is designed in a way that the first stage has the longest length, the second stage has a length half of that of the first stage and the third stage has a length half of that of the second stage. On one arm of each stage MZI, there is a phase shifter, which is used to tune the phase difference between the two arms. With the specific phase difference on each stage MZIs as shown, the eight channel outputs would be the demultiplexed OFDM signal in eight different subcarriers. More details on the design, fabrication and performance of the device may be found at [76]. In summary, we started the chapter with the premise that it should be possible to relate O-OFDM and N-WDM in a fairer comparison basis that assumes that both techniques can be implemented with similar technologies that would allow an evaluation of circuitry complexity and its associated energy consumption for both cases. Before this accurate comparison becomes possible, however, some challenges have yet to be overcome and we believe that the evolution of PLC design to integrate passive optical components and optoelectronic devices will soon allow surpassing most of these obstacles. Furthermore, regardless the integration challenging aspect, some subsystems still require a conceptual improvement in the sense of reducing complexity (that will also lead to reduced energy consumption). In this sense, an example of a technique that still requires improvement is the clock recovery. In some approaches, it may demand the use of one or two pumping lasers (and, in some cases, additional EDFAs) associated with SOAs to guarantee the power levels necessary for providing an efficient FWM process.

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Fig. 18 Optical FFT structure (DEMUX) based on a three-stage MZI implemented on integrated SOI by Yu et al. (Adapted from [76])

In spite of challenges yet to be faced, the spectral efficiency, the potentiality for reducing the energy consumption and for tolerating linear fiber impairments, such as those induced by chromatic dispersion (CD) and polarization mode dispersion (PMD), continue to guarantee to O-OFDM a place of relevance in the group of technologies for very high capacity systems.

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Narrow Linewidth and Compact External-Cavity Lasers for Coherent Optical Communications Giovanni B. de Farias, Leandro T. Zanvettor, Hening A. de Andrade, João C. S. S. Januário, Mayara E. Bonani, Maria Chiara Ubaldi , Aldo Righetti, Fausto Meli, Giorgio Grasso and Luis H. H. de Carvalho

Abstract In this chapter, the activities related to external-cavity laser development executed in CPqD will be presented in detail. The target application is high-speed and high-order modulation formats optical systems for telecom. Using cavity design techniques, a narrow linewidth and high output power laser suitable for manufacturing is presented. It is presented the operation principle of the tunable mirror which is used as channel selector for the external cavity. Experimental results of a fixedwavelength prototype are presented, showing optical output power above 16 dBm, Side-mode Suppression Ratio (SMSR) of 60 dB, and linewidth around 75 kHz. The cavity shows good stability for long-term high-temperature storage.

1 Introduction Lasers are fundamental building blocks of any optical communications systems. They are responsible for generating the light (optical source) for the optical transmission and reception. There are a variety of technologies that can be used for building lasers [1]. For telecommunication applications, in order to achieve a reach of hundreds or even thousands of kilometers, it is necessary to have a coherent optical source that can emit in a single longitudinal mode. In literature, such a class of lasers is called single-mode lasers. They typically use semiconductor technology in order to achieve coherent emission through stimulated emission process. To target coherent transmission systems, several features are mandatory for the optical laser sources: G. B. de Farias (B) · L. T. Zanvettor · H. A. de Andrade · J. C. S. S. Januário · C. S. S. Bonani Optical Technologies Division, CPqD, Campinas, SP 13086-902, Brazil e-mail: [email protected] M. E. Ubaldi · M. C. Righetti · A. Meli · F. Grasso Fondazione CIFE, 81, Via Giuseppe Colombo, 20133 Milano, Italy e-mail: [email protected] G. Carvalho BrPhotonics, Campinas, SP 13086-902, Brazil © Springer Nature Switzerland AG 2019 A. Paradisi et al. (eds.), Optical Communications, Telecommunications and Information Technology, https://doi.org/10.1007/978-3-319-97187-2_9

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High optical output power (>15.5 dBm), Wide tuning range (40nm), Narrow linewidth (typically TE TE −> TE

−2.5 1520 1530 1540 1550 1560 1570 λ (nm)

0

0

−10 −20 −30 −40

TM −> TE TE −> TE

−50 1520 1530 1540 1550 1560 1570 λ (nm)

Fig. 4 Simulation results: distributions of the electric field through the PSR when inserted of mode a TE0 and b TM0 . Experimental results: c measured spectra of the PSR with input and output grating loss normalized showing IL and PCL and d crosstalk. Adapted from [7]

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figures detail the electric field propagation distribution at the mode converter and the MMI, corresponding to the first and fourth parts of the PSR. Then, this same PSR was fabricated in standard SOI process in a multi-project wafer (MPW) run at IME. Figure 4c shows measured insertion loss (IL) - TE->TE, and polarization conversion loss (PCL) - TM->TE, over a wavelength range of 50 nm. Figure 4d shows the respective cross talk. The proposed PSR was first presented in [7], experimentally demonstrating an IL of 1.2 dB, a PCL lower than 1.8 dB and a cross talk below −5 dB. The wavelengthdependent crosstalk is under investigation and it will be solved in the next runs.

2.1.2

PSRs Based on Polarization Cross-Coupling

It is known that two waveguides relatively close to each other exchange energy due to the evanescent coupling effect. After a certain length, the energy can be totally transferred from one waveguide to the other if the phase-matching condition is achieved (same propagation constant in both waveguides). Moreover, in a birefringent medium such as a silicon rectangle waveguide, the orthogonal modes TE0 and TM0 have different propagation constants. With the correct waveguide engineering, it is possible to design a device that, after a certain length, all TM energy can be transferred to the cross waveguide, while the TE0 mode energy remains on the through waveguide. Some PSRs are proposed based on this mechanism, which is called mode coupling or polarization cross-coupling and occurs between two waveguides in a simple directional coupler (DC). In this approach, the polarization rotation phenomenon is achieved by phase-matching conditions between the TE0 and TM0 modes on both waveguides and assuming some structure asymmetry on the waveguide cross section. Mode coupling PSR has become a popular option due to its simpler structure, resulting in small devices, with a typical footprint of 1.9 µm × 3.7 µm [8]. Moreover, devices with low PCL, achieving a peak of around 0.1 dB [9–11]; low ILs at a broad bandwidth (less than 0.1 dB over 120 nm) [8, 12]; and improved fabrication tolerance with tapered waveguides [12, 13] have been recently demonstrated. However, the main drawbacks of mode coupling PSRs are the low fabrication tolerance when compared to PSRs based on mode evolution [14]. We have recently proposed a PSRs based on mode coupling [7]. It is depicted in Fig. 5a, and it is composed of an asymmetric directional coupler (ADC), in which the through waveguide is connected to the input, receiving both TM0 and TE0 signals and transferring only the TE0 mode to its output. The cross waveguide has no input access, and it is responsible to transfer the TM0 mode converted into TE0 to its output. As already mentioned, to achieve the cross-coupling between the TM0 input and the TE0 cross output two conditions must be satisfied. The first one is related to the waveguide cross section asymmetry. In our case, it is achieved by distributing the cross and through waveguides in different y levels, as illustrated in Fig. 5b. Moreover, the proposed design makes use of a poly-silicon (Poly-Si) cross waveguide, which is available in standard SOI processes. The second condition for cross-coupling refers

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Cross (PSi)

(a) hb

TM0 TE0

TE0

Through (Si)

(b)

x Lb

z y

hSi

WSi g

Lc

y WPSi

hPSi x

Lb

TE0 SiO2

Fig. 5 Basic structure of the proposed PSR based on mode coupling: a top view; b cross section view. Adapted from [7]

to the phase match between the TM0 in Si (through) waveguide, and the TE0 in the Poly-Si (cross) waveguide. Insets in Fig. 5a present the mode evolution of the transverse electric field intensity for some sections along the central coupling region for TM0 input (through) and TE0 output (cross). It is possible to observe the energy transmission from one waveguide to the other, along the device. Finally, as the input and output access ports are standard SOI waveguides (500-nm width and 220-nm height), a taper, not illustrated in Fig. 5a, is necessary at the PSR input/outputs [7]. Figure 6 presents the main results for the PSR proposed in [7]. Figure 6a, b shows the electric field intensities along the PSR structure at 1550 nm for TE and TM input modes, respectively. Figure 6c shows the simulated performance analysis in FDTD in terms of IL for the TE mode transmission: TE - TE (out through), and the PCL for the TM conversion: TM - TE (out-cross), both in dB and as a function of the wavelength. These results show a PCL smaller than 0.42 dB for a bandwidth of 40 nm (from 1530 to 1570 nm), achieving a peak 0.35 dB near 1550 nm. On the other hand, the insertion loss for the TE mode is up to 0.026 dB. Figure 6d shows the crosstalk for both outputs, which is always below −26 dB. In summary, our recently proposed PSR based on mode coupling is very compact (30 µm × 10 µm) and have a high polarization conversion efficiency in the C-band. This PSR was sent to fabrication at IMEC, and it is expected to be received soon for experimental validation.

2.2 90◦ Hybrid One important component for the design of coherent receivers is the 90◦ hybrid. This component provides a linear combination of two input fields at its four outputs, enabling the detection of the real and imaginary parts of the signal [15, 16]. The

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(a)

1

0

z

(d)

−0.1

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TM −> TE through TE −> TE cross 1540

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Fig. 6 Simulated performance of the PSR over the C-band: electric field propagation considering as an input signal: the a TE and the b TM modes, c IL and PCL, and d crosstalks. Adapted from [7]

PIC platforms considered for coherent receivers’ implementation are silicon-based and InP-based. Coherent receivers with silicon photonics have a great potential due to the high refractive index contrast that allows ultra-compact devices [17]. Different implementations for the 90◦ hybrids are discussed in detail in the following subsections.

2.2.1

90◦ Hybrid with Single MMI

A possible configuration for the 90◦ hybrid consists in a single 4 × 4 MMI, as depicted in Fig. 7. The MMI input ports 1 and 3 carry the signal and LO, respectively. The output ports 1 and 4 are subtracted by the balanced photodiodes (PDs) to obtain the in-phase component, while ports 2 and 3 are also subtracted to obtain the quadrature component of the signal, as also illustrated in Fig. 7 [15]. The transfer matrix for this configuration is represented by the following equation: ⎤ ⎡ 1 E1 ⎢ E 2 ⎥ ⎢ e j (3π/4) ⎢ ⎥ = k44 ⎢ − j (π/4) ⎣e ⎣ E3⎦ E4 1    ⎡

Eout

0 e− j (π/4) 0 1 0 1 0 e j (3π/4)

TMMI4×4

⎤ ⎤ ⎡ 0 Es ⎥ ⎢ 0⎥ ⎥ . ⎢ 0 ⎥, 0⎦ ⎣ E L O ⎦ 0 0    Ein

(1)

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Fig. 7 Schematic diagram of a coherent detection consisting 90◦ hybrid based on general interference and balanced PDs. Adapted from [15]

(b)

1.5 5 1

4 3

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70 ch14 − in1 ch14 − in3 ch23 − in1 ch23 − in3

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2

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(a)

50 40 30

1 0

1530

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0

20

1530

λ (nm)

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1550

1560

λ [nm]

Fig. 8 90◦ Hybrid based on general interference a IL and phase error, and b CMRR

where k44 specific power splitting coefficient of the 4 × 4. The 90◦ hybrid based on general interference results is presented in Fig. 8, showing IL and phase error (Fig. 8a) and common mode rejection ratio (CMRR) (Fig. 8b) as a function of the wavelength (in C-band). The results were calculated using FDTD using Lumerical© software. It is possible to observe that all the results satisfy the target values mentioned in Optical Internetworking Forum (OIF) [18].

2.2.2

90◦ Hybrid Based on Paired Interference

The 90◦ hybrid can also be realized using a configuration based on paired interference which consists of a 2 × 4 MMI, a phase shifter, and a 2 × 2 MMI, as depicted in Fig. 9. This configuration does not require any optical crossing between the 90◦ hybrid output and balanced PDs because the components of phase and quadrature are obtained from output ports 1-2 and 3-4, respectively [15]. The transfer function for this device is given by

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Fig. 9 Schematic diagram of a coherent detection consisting hybrid 90◦ based on paired interference and balanced PDs. Adapted from [15]

⎡

⎤ ⎡ ⎤ E1 Es ⎢ E2 ⎥ ⎢ ⎥ ⎢ ⎥ = [TM M I 2×2 ][TP S ][TM M I 2×4 ] ⎢ E L O ⎥, ⎣ E3⎦ ⎣ 0 ⎦ E4 0     Eout

Ein

with

⎡

TM M I 2×2

1 ⎢0 =⎢ ⎣0 0

0 1 0 0 ⎡

TP S

0 0

⎤

0 0

⎥

⎥ √1 √1 e− j (π/2) ⎦ 2 2 √1 e− j (π/2) √1 2 2

1 ⎢0 =⎢ ⎣0 0 ⎡

TM M I 2×4

(2)

⎤ 0 0 0 1 0 0 ⎥ ⎥ 0 e− jθ1 0 ⎦ 0 0 e− jθ2

e j (7π/16) √ ⎢ e j (3π/16) = k24 ⎢ ⎣ e j (3π/16) e− j (9π/16)

e− j (9π/16) e j (3π/16) e− j (29π/16) e− j (25π/16)

(3)

(4)

0 0 0 0

⎤ 0 0⎥ ⎥, 0⎦ 0

(5)

where k24 is the power splitting coefficient of the 2 × 4 coupler, θ1 = π/4, and θ2 = 0. The paired interference-based 90◦ hybrid simulation results such as IL, CMRR, and phase error as function of wavelength (C-band) are shown in Fig. 10. It was also calculated using FDTD method in Lumerical© software. These results show an IL of up to 1 dB, a CMRR higher than 20 dB, and phase error between I and Q components lower than 2.5◦ . These values satisfy OIF specifications [18] for coherent receiver modules.

Optical Devices in Silicon Photonics 5 4

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(a)

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50 40 30 20

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Fig. 10 Hybrid 90◦ based on paired interference a IL and phase, error and b CMRR

3 Active Components This chapter describes fundamental active components for silicon photonic integrated circuits. Specifically, it describes modulator and laser, as depicted in Fig. 1.

3.1 Modulator In recent years, one of the major challenges of integrated silicon photonics is the construction of optical modulators that have high efficiency and high electro-optical (EO) bandwidth. In this context, silicon Mach–Zehnder modulator (MZM) based on reverse polarization PN junctions with the traveling wave electrode (TWE) has demonstrated results with good modulation efficiency, high EO bandwidth, and good thermal stability [19–21]. However, as its main drawback, TWE-based MZM presents a large device length, typically ∼3 mm [21]. This type of modulator, the TWE, should be designed to have impedance match and low loss to offer a large EO bandwidth. The most commonly used electrodes for designing high-velocity modulators are the coplanar waveguides (CPW) and coplanar stripline (CPS) [21]. These transmission lines TLs, depicted in Fig. 11, have attracted great attention due to their capacity of integration with optical devices and compatibility with the standard CMOS technology [22]. In another hand, the PN junction is established in the optical waveguide, and the efficient interaction with the waveguide mode must be optimized to ensure a low optical loss. The physical phenomena occurring in optical modulators using silicon is the plasma dispersion effect. They are responsible to change refractive index: the real part (n) is changed by the free-carrier dispersion effect while the imaginary part (α), related to optical losses, is changed by the free-carrier absorption. The relations between carrier concentration in silicon and the variations in the refractive index obey the adapted Soref’s equations [23, 24]:

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(a)

GND Signal

(b)

GND

Signal

GND

Fig. 11 Illustration of a a coplanar waveguide and a b coplanar stripline transmission lines. Adapted from [25]

Δn = −5.4 × 10−22 ΔN 1.011 − 1.53 × 10−18 ΔP 0.838 , Δα = 8.88 × 10

−21

ΔN

1.167

+ 5.84 × 10

−20

ΔP

1.109

,

(6) (7)

where Δn and Δα are the changes in refractive index and absorption coefficient, respectively. ΔN and ΔP are the concentrations of electrons and holes in cm−3 , respectively. In a typical configuration, silicon modulators embed a PN junction in the optical waveguide. The variation in concentration of the free carriers can be achieved by applying a reverse voltage at the PN junction [26]. The DC modulation efficiency in the depletion region is determined by the depletion width and its overlap with optical mode [20]. The depletion width is defined as

W = W p + Wn =

20  Si O2 q



NA + ND NA ND

 (V j − VBias ),

(8)

where W p,n is the depletion widths in the P and N sides, q is the fundamental electron charge, N A,D is the impurity densities, VBias is the applied voltage, V j = k B T /q ln(N D N A /n i2 ) is the built-in voltage of the depletion region, k B is the Boltzmann constant, T is the ambient temperature, and n i is the intrinsic carrier density. According to [21, 27], the capacitance depletion Cdep can be written as a sum of two capacitances: the ideal depletion capacitance of the PN diode C and the fringe capacitance C f in a simplified version: Cdep = C + C f .

(9)

These capacitances are expressed as  C = 0  Si

H W

 ,

(10)

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where H is the height of the silicon waveguide, W is the depletion width, 0 is the vacuum permittivity, and  Si is the silicon relative permittivity   2π H 0  Si O2 ln , Cf = π W

(11)

where  Si O2 is the silicon dioxide relative permittivity. In order to compare the efficiency of silicon modulators, a generally used figure of merit is the Vπ L π for a given bias voltage. The Vπ can be obtained using the following equation [28]: Vπ ·

2π dn e f f |V =Vd = π, λ dV

(12)

where V = Vd is the bias voltage. Vπ L π is Vπ times the modulator active length. Section 3.1.1 shows the calculation of the electro-optical bandwidth of a carrierdepletion-based modulator considering parameters the PN junction and the transmission line. Sections 3.1.2 and 3.1.3 show our new designs of modulator with a high bandwidth and low driving voltage using TWE on CPW and on CPS-Slow, respectively.

3.1.1

Electro-Optical Bandwidth

To determine the modulator EO response, it is considered the driving signal with a voltage amplitude Vg and a frequency ωg . The average voltage experienced by a photon traveling through the optical waveguide can be calculated using the following expression [19]: Vavg (ω) =

Vg (1 + ρ1 )(V+ + ρ2 V− ) exp ( jβo ) , 2 [exp(γ ) + ρ1 ρ2 exp(−γ )]

(13)

with sin φ± , φ±  = −( jγ ± βo ) , 2 Z0 − Zs = , Z0 + Zs Zt − Z0 = , Z0 + Zt ω = ng, c

V± = exp(± jφ± )

(14)

φ±

(15)

ρ1 ρ2 βo

(16) (17) (18)

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where Z s , Z t , and Z 0 are the impedances of the source, the termination of the TL, and the characteristic impedance of the electrode, respectively;  is the TWE length, n g is the group refractive index of the optical mode, β0 is the optical propagation constant (waveguide), c is the light speed, and γ is the electrical propagation constant (TL). Considering a small driving voltage, the modulation depth is proportional to the effective voltage applied to the depletion region of the device. This effective voltage is simply the voltage over the RC series equivalent circuit, where the resistance is the R pn and the capacitance is the depletion capacitance is Cdep . By normalizing the voltage at a certain frequency ω by the low-frequency response at ω0 , the EO bandwidth (m) of the device can be calculated as [19]    (1 + jω0 Cdep R pn )Vavg (ω)  . (19) m(ω) =  (1 + jωCdep R pn )Vavg (ω0 )  In conclusion, the EO bandwidth is limited by: 1. The transmission line attenuation; 2. The impedance mismatch between the line loaded with the termination line; 3. The velocity of the group mismatch between the optical and electrical signal.

3.1.2

Single-Drive Push–Pull Silicon Modulator with a CPW TL

Figure 12 depicts the cross section of a typical carrier-depletion-based silicon TWEMZM in SOI based on CPWs. This structure can be modeled using the analytical equivalent circuit model proposed in [19, 28]. We consider a single-drive series push– pull (SPP) configuration [29]. We have recently designed a PN junction configuration illustrated in Fig. 13a, in order to maximize the optical efficiency and loss tradeoff. The propagation loss and modulation efficiency results obtained with this new configuration are shown in Fig. 13b for bias voltages between −10 and 0 V. The capacitance calculated C pn = 231 pF/m and contact resistance R pn = 0.43  cm for a bias voltage V = −2.5 V [30]. The RC constant of the junction does not limit the device bandwidth. Each component in Fig. 12b is associated with its physical structure, while inset depicts the distributed equivalent circuit model, with the four distributed elements (R, L, C, and G) defined per length [31]. The components in Fig. 12b are calculated according to the equations given in [19]. This equivalent circuit results in a total shunt admittance Y = G + jωC for an unloaded condition (without the optical waveguide) and a total series impedance Z = R + jωL. R and L are obtained using the quasi-TEM model for coplanar structures presented in [31]. With the values of Z and Y , it is possible to find the electrical propagation constant γ and the characteristic impedance Z 0 by using (considered the loaded condition):

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(a)

(b)

Cair Cclad 0.5Cmetal

0.5Cmetal CPMD_r

Cvia 0.5Cdep

Csslab

0.5Cdep Rpn

Cssub Cbox

Cslab Cslab1

Gslab

Csub1

Csub

Gsub

Fig. 12 TW-MZM based on CPW: a top schematic of the capacitively loaded coplanar waveguide electrode, and b equivalent electrical circuit associating each component to its physical structure (inset: the equivalent circuit for the transmission line). Adapted from [19]

 Z0 = γ =

√

Z , Y

(20)

Z · Y.

(21)

Then, the microwave effective index n e f f is obtained by

ne f f =

img(γ ) · c . (2 · π · f )2

The microwave attenuation is the real part of the propagation constant.

(22)

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(b)

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Vπ Lπ (V.cm)

(a)

1 0

Fig. 13 a Cross section of the PN junction and b propagation loss and modulation efficiency of the PN junction. © 2017 IEEE. Reprinted with permission from [30]

The simulation results for the CPW using the analytical model is presented in Fig. 14. The results show the real part of the characteristic impedance (real(Z 0 ), Fig. 14a), the microwave effective index (n e f f , Fig. 14b) and the microwave attenuation (Fig. 14c), considering loaded and unloaded TL conditions. Unloaded TL results are obtained removing the elements associated with the optical waveguide, highlighted in Fig. 12b, while the loaded condition considers Cdep = 231 pF/m and R pn = 1.28  cm. Observe that the loaded result for the characteristic impedance (Fig. 14a) is near 50 , especially for frequencies higher than 20 GHz. In Fig. 14b, it is possible to observe a mismatch between the optical and electrical effective index for frequencies considering loaded conditions. Finally, Fig. 14d presents the EO bandwidth for different termination loads, using the modeling given in Sect. 3.1.1. Observe that the EO bandwidth is very sensitive to the termination load, varying from 23 to 35 GHz when decreasing the load from 50 to 30 . By decreasing the termination resistance, with respect to the line impedance, the reflected wave adds constructively with the forward wave, and EO bandwidth is enhanced. The drawback is the higher reflection (S11 ), which, for most commercial devices, should be below −10 dB inside the band of interest ( 2 dB -5

-10

-15

Wavelength

Wavelength

Fig. 21 Design criteria: a Ring resonances are suppressed by the lattice filter response. b The filter should be sharp enough so that side modes whose wavelengths are Δλ apart from the resonance are suppressed by more than 2 dB. © 2017 IEEE. Adapted with permission from [39]

tion ratio at FSR should guarantee a stable operation, considering the superimposed lattice filter spectral answer. This means that if the resonance peak of the ring-based filter falls inside the C-band, the adjacent peaks should be suppressed by the lattice filter response as shown in Fig. 21a. Moreover, the FWHM should guarantee suppression of the side modes of the cavity in order to obtain stable operation, as portrayed in Fig. 21b. Δλ is the wavelength separation of side modes.

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Cavity Simulation

In order to predict the general behavior of the laser, a numerical model for the Si was built in [39]. This is based on a time-domain propagation of a sampled signal through the different sections of the device: gain medium, Si optical filters, mirrors, etc. The gain chip model is a simplified model calibrated to the available experimental characterization of commercial gain chips, considering frequency-selective gain, saturation, and noise. The simulation block diagram is shown in Fig. 22. A sweep is performed on the output mirror reflectivity to determine the optimal point in terms of output power and SMSR. These results are shown in Fig. 23a, as well as the spectra of some possible channels in the optimal conditions in Fig. 23b. Simulation exhibits an output power of around 55 mW and SMSR higher than 45 dB for the optimal reflectivity value. The device concept presented here will be improved to minimize output power difference of the channels and to handle nonlinear effects due to high emission powers. Eventually, it will be fabricated and measured.

Mirror (HR)

Gain Chip

Ring 1

...

Coupling Loss

Ring 2

...

C/L Band Duplexer

Propagation Loss

Output Mirror

50 40

40 30

20 20 0

10 0

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Optical Power (dBm)

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60

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Fig. 22 Block diagram of the cavity simulation. A sampled signal propagates in the time domain through the blocks as it keeps bouncing between the mirrors. HR stands for high reflectivity. © 2017 IEEE. Adapted with permission from [39] 20 0 -20 -40 1500

1550

1600

1650

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Fig. 23 Cavity simulation results. a The reflectivity sweep to find the optimal point for the output mirror. b The spectra of some of the possible channels. © 2017 IEEE. Reprinted with permission from [39]

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4 Conclusion In this chapter, the principle of operation, modeling, and results are shown of the following silicon photonics components: PSR, hybrid, modulator, and laser. These devices are designed to be compatible with the standard fabrication processes that allow monolithic integration. Acknowledgements The authors thank Stenio M. Ranzini for reviewing a draft of this chapter and also acknowledge FAPESP under grant 2016/20615-8 for funding this project.

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