ECEN 5254 Remote Sensing Signals and Systems Professor Albin J. Gasiewski Lecture #21 – April 3, 2012 ECOT 246 303-492-9688 (O)
[email protected] Classes: ECCS 1B14 TR 9:30-10:45 AM ECEN 5254 Remote Sensing Signals & Systems
Spring 2012
University of Colorado at Boulder
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Administration • HW4 solutions posted on D2L • HW5 posted on D2L, due April 10 • Reading: – RSSS slides – Skolnik Chapters 10,11 (on D2L) – Additional references on D2L
• Term Paper: – ~10 pages + figures, references – Slide presentations in standard conference format held on Friday, May 4 at end of semester. Schedule to be arranged. – Term paper and slide presentation templates on D2L
• Final Exam: Saturday May 5, 7:30-10:00 PM in ECCS 1B14 2
Last Lecture
• • • •
Sampling, resolution, fringe washing Noise Aperture thinning Intensity correlation (Hanbury-BrownTwiss Experiment)
ECEN 5254 Remote Sensing Signals & Systems
Spring 2012
University of Colorado at Boulder
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Today’s Lecture
• • • • • •
Radar principles Radar cross section Doppler effect Correlation receiver Matched filter Ambiguity
ECEN 5254 Remote Sensing Signals & Systems
Spring 2012
University of Colorado at Boulder
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Radar Principles
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Received Power - Point Scatterer General bistatic radar system:
GT
PT
~
^) σ(k^s ,k i
RT , ^ ki GR
RR ,k^s
PR
Received power in steady state: ^ ) is bistatic σ(k^s ,k i radar scattering cross section: Depends on λ, size, orientation, and polarization 6
Received Power - Point Scatterer Monostatic radar system:
G
PT
~
R,^ ki
^ ,k^ ) σ(-k i i
PR
Received power in steady state:
PR varies as R-4 , G2 :
^ ^ ,k σ(-k i i) is backscattering cross section: Depends on λ, size, orientation, and polarization
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Radar Cross Section
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Radar Cross Section Typical RCS values for λ ~ 3 cm wavelength (X-band):
^ ,k^ ) σ(-k i i
0.01-0.0002
RCS increased by: sharp edges flat and normal surfaces high dielectric contrast and/or low loss materials resonant structures (e.g, λ/2 wires)
RCS ~ f 4D6 for electrically small objects, ~(area) for large objects 9
Scattering Coefficients of Hydrometeors
f 4a6
Liquid
Ice
(parameters are sphere radii a in mm) 10
Doppler Effect
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Doppler Frequency Shift ωo
GT
~ ωo′
Bistatic:
Monostatic:
Assumes non-relativistic velocities (|v| « c) 12
Pulse Modulation Vo
P(t)
~
M
GT
t RT , ^ ki GR
^) σ(k^s ,k i
RR ,k^s
vR(t)
Examples of complex pulse envelopes: P(t)
P(t)
1 T
t
P(t)
1 T
t
T
t
Im{P(t)}
Im{P(t)}
Im{P(t)}
1
t=T Re{P(t)}
Re{P(t)}
Re{P(t)}
t=0
Uniform
Chirp
Phase Coded
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Received Signal (Echo) Waveform P(t) GT
Vo
~
M
t ki RT , ^ GR
RR ,k^s
^) σ(k^s ,k i
vR(t)
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Correlation Receiver
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Estimation of Range Delay Consider correlation receiver for demodulation of received echo signal and range estimation: (v)2
×
vd(tR)
vo(t)
~
^
vR(t)
T
τi
^ Predetected signal vd(tR):
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Detected Signal for Fixed Point Target For fixed target (ωd = 0), monostatic system, and neglecting noise:
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Detected Signal for Fixed Point Target
where ϕP is the pulse autocorrelation function for P(t). The detector output is thus:
… 18
Detected Signal for Fixed Point Target Now, let t = tR+T , and τi « T but τi » 1/ωo:
Terms at 2ωo → filtered out Only spectrum of ϕP2 passes LPF 19
Range Resolution for Uniform Pulse e.g., Uniform pulse envelope: P(t)
T
1
t -T
t
T
~ ~
maximum when tR=2R/c tR
~ ~
T
ϕP(t)
tR 20
Range Resolution for Uniform Pulse e.g., Uniform pulse envelope: P(t)
T
1
t -T
~ ~
T
ϕP(t)
t
T
t
Range estimated by determining peak of vo(t). Accuracy of this estimate is determined by width of ϕP(t), which is ~T. Thus, ΔR ~ cT/2 is a fundamental limit.
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Matched Filter
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Optimal Estimation of Range Delay Optimal demodulator for estimating range delay is the matched filter receiver : (v)2
h(t)
^
vR(t)
vd(t)
τi vo(t)
MF impulse response is reversed, time-shifted copy of transmitted waveform. Predetected signal vd(t):
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Optimal Estimation of Range Delay Again, for monostatic system, fixed target, and neglecting noise :
which (aside from a time offset) is identical to the predetected signal for the correlation receiver. 24
MF Range-Doppler Estimation Consider bank of MFs for combined range delay and Doppler shift estimation : h1(t)
fd2
h2(t)
(v)2
fdN
hN(t)
(v)2
τi
vo(t, fd1)
τi
vo(t, fd2)
← Range bins
^
vR(t)
fd1
(v)2
← Doppler bins
Ts ~ τi
Δfd
…
…
…
τi
vo(t, fdN)
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MF Bank Response to Target in Motion ~ ~
t
~ ~
vo(t, fd1)
t
vo(t, fd2)
Strongest response for MF with closest fdi ~ ~ ~ ~
vo(t, fdN)
t
t
~ ~
vo(t, fd3)
t 26
Ambiguity
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MF Response to Point Target in Motion Received signal with ωd shift MF impulse response
Matched filter bank output is Fourier transform (wrt τ) of P(τ)P*(t-2R/c-T+τ) as a function of ωd = Doppler shift 28
MF Receiver Response to Target in Motion
Ambiguity function χ(t,ωd) is defined as the Fourier transform (wrt τ) of P(τ)P*(t+τ) as a function of ωd : Interpret as time-Doppler point target response of system
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Ambiguity Function for Uniform Pulse P(t)
Uniform pulse envelope:
1 T
t
P*(t+τ) P(τ) 1
T
τ
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Ambiguity Function for Uniform Pulse P(t)
Uniform pulse envelope:
1 T
t
contours
fd
t → to be compared to system noise… 31
Range-Doppler Ambiguity P(t)
Uniform pulse envelope:
1 T
t
Fundamental tradeoff between range and Doppler resolution for simple pulse envelopes
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Next Lecture
• • • • •
Radar resolution (Doppler, range) Pulse compression (chirp) Pulse coding & Barker Sequences Noise in Radar Systems Matched Filter NEB
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