high resolution radar sensing via compressive...
TRANSCRIPT
High Resolution Radar Sensing via CompressiveIllumination
Emre ErtinLee Potter, Randy Moses, Phil Schniter, Christian Austin, Jason Parker
The Ohio State University
New Frontiers in Imaging and Sensing WorkshopFebruary 17, 2010
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 1 / 39
RADAR
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 2 / 39
RADAR
Wideband Multichannel Radar is a crucial component of research in:
Emerging Applications in Urban Setting
Collaborative Layered Persistent SensingThru-wall SurveillanceCognitive Radar Networks
Emerging Signal Processing Techniques
Waveform AdaptivityMIMO Radar Systems3D SARRadar Diversity Techniques
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 3 / 39
RADAR
Wideband Multichannel Radar is a crucial component of research in:
Emerging Applications in Urban Setting
Collaborative Layered Persistent SensingThru-wall SurveillanceCognitive Radar Networks
Emerging Signal Processing Techniques
Waveform AdaptivityMIMO Radar Systems3D SARRadar Diversity Techniques
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 3 / 39
Software Defined Radar Sensor
Recent advances in high speed A/D and D/A and fast FPGA structuresfor DSP enabled real time decisions and on the fly waveform adaptation
Next Generation Radar Sensors
Software Configurable for multimode operation: Imaging-TrackingMultiple TX/RX chains to support MIMO RadarIndependent waveforms for TX and coherent processing in RX
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OSU SDR Sensors
1 Tx - 1Rx Software Defined MicroRadar
Software Defined WaveformsFPGA/DSP for online processingSingle Channel125 MHz BW, 5.8 GHz
2 Tx - 4 Rx Software Defined Radar Testbed
UWB 7.5 GHz Tx-Rx Bandwidth (0-26 GHz center)Programmable Software Defined WaveformsFully coherent multichannel operation for MIMOLimited Online Processing, Ideal for Field Measurements
4 Tx - 4 Rx MIMO Software Defined Radar Sensor
Programmable Software Defined WaveformsMultiple FPGA/DSP Chains for online processingFully coherent multichannel operation for MIMO500 MHz BW frequency agile frontend (2-18 GHz)
www.ece.osu.edu/~ertine/RFtestbed
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Wideband Radar Technology
Emerging applications stretch the resolution and bandwidth capabilities ofADC technology
COTS ADCs have limited resolution at high sampling rates
Power consumption quadruples for additional bit of resolution
[R.H. Walden, ”Analog-to-Digital Converter Survey and Analysis”, IEEE JSAS]
Sensing is not just receive processing y = ΦΨs vs y = ΦrΦtΨs
Use transmit diversity to shift burden away from ADC
Transmitter at Radar provides more flexiblity
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 6 / 39
Wideband Radar Technology
Emerging applications stretch the resolution and bandwidth capabilities ofADC technology
COTS ADCs have limited resolution at high sampling rates
Power consumption quadruples for additional bit of resolution
[R.H. Walden, ”Analog-to-Digital Converter Survey and Analysis”, IEEE JSAS]
Sensing is not just receive processing y = ΦΨs vs y = ΦrΦtΨs
Use transmit diversity to shift burden away from ADC
Transmitter at Radar provides more flexiblity
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 6 / 39
Wideband Radar Technology
Emerging applications stretch the resolution and bandwidth capabilities ofADC technology
COTS ADCs have limited resolution at high sampling rates
Power consumption quadruples for additional bit of resolution
[R.H. Walden, ”Analog-to-Digital Converter Survey and Analysis”, IEEE JSAS]
Sensing is not just receive processing y = ΦΨs vs y = ΦrΦtΨs
Use transmit diversity to shift burden away from ADC
Transmitter at Radar provides more flexiblity
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 6 / 39
Radar Estimation Problem
Outline
Radar Estimation Problem
Compressive Sensing
Multifrequency Waveforms for Compressive Radar
Experimental Results
Conclusion and Future Work
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Radar Estimation Problem
Radar as Channel Estimation Problem
System Model
yp = RpXptp + np p = 1 . . .P
yp : radar returnXp : convolution matrix of the channel responsetp : transmit waveformRp : receive processing filternp : system noise
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Radar Estimation Problem
Radar Sensing Model
System Model
yp = RpTpxp + np p = 1 . . .P
= A(rp, tp)xp + np
yp : radar returnTp : convolution matrix of the transmit waveformxp : unknown target responseRp : receive processing filternp : system noise
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 9 / 39
Radar Estimation Problem
Radar Sensing Model
System Model
yp = RpTpxp + np p = 1 . . .P
= A(rp, tp)xp + np
yp : radar returnTp : convolution matrix of the transmit waveformxp : unknown target responseRp : receive processing filternp : system noise
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Radar Estimation Problem
Radar Sensing Model
Radar Imaging Problem
Estimate unknown target range profile x from the sampled radar returnsyp
yp = A(rp, tp)x+ np
x is sampled at the transmit bandwidth (or higher)
yp sampling rate determines ADC requirements
Use prior knowledge about the scene for design of (rp, tp) to reduce ADCrate
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 10 / 39
Radar Estimation Problem
Radar Sensing Model
Radar Imaging Problem
Estimate unknown target range profile x from the sampled radar returnsyp
yp = A(rp, tp)x+ np
x is sampled at the transmit bandwidth (or higher)
yp sampling rate determines ADC requirements
Use prior knowledge about the scene for design of (rp, tp) to reduce ADCrate
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Radar Estimation Problem
Example: Stretch Processing
Traditional LFM chirp signals can provide 2-10x sub-Nyquist sampling
Analog dechirp processingfollowed by low rate ADCs
Sample uniformly in frequency;alias to exploit limited swath inrange
Stretch gives compression versustransmit bandwidth
Bτ
Tpvs B
swath τ = 2R/c sec; pulse duration Tp
sec
dB
Data=[1x2501], Fs=2.5 GHz
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Time, ns
Am
pl473.6000 ns1.2451 GHz35.5479 dB
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Compressive Sensing
Outline
Radar Estimation Problem
Compressive Sensing
Multifrequency Waveforms for Compressive Radar
Experimental Results
Conclusion and Future Work
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Compressive Sensing
Signal recovery from projections
Signal Recovery
Inverse problem of recovering a signal x ∈ CN from noisy measurements ofits linear projections
y = Ax+ n ∈ CM. (1)
Focus: A ∈ CMxN forms a non-complete basis with M << N.Ill posed recovery problem is reqularized:
1 the unknown signal x has at most K non-zero entries
2 the noise process is bounded by ‖n‖2 < ε.
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Compressive Sensing
Sparsity Regularized Inversion
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Compressive Sensing
High-frequency scattering center decomposition
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Compressive Sensing
Sparsity Regularized Inversion
Sparse Signal Recovery Problem
minx‖x‖0 subject to ‖Ax− y‖2
2 6 ε,
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Compressive Sensing
Sparsity Regularized Inversion
Convex Optimization for Sparse Recovery
minx‖x‖1 subject to ‖Ax− y‖2
2 6 ε.
Provides a bounded error solution to the NP-complete sparse recoveryproblem, if δ2K(A) <
√2 − 1)
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Compressive Sensing
Geometric Intuition
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Compressive Sensing
Sparsity Regularized Inversion
Convex Optimization for Sparse Recovery
minx‖x‖1 subject to ‖Ax− y‖2
2 6 ε.
Provides a bounded error solution to the NP-complete sparse recoveryproblem, if δ2K(A) <
√2 − 1)
Restricted Isometry Constant
RIC (δs) for forward operator A is defined as the smallest δ ∈ (0, 1) suchthat:
(1 − δs)‖x‖22 6 ‖Ax‖2
2 6 (1 + δs)‖x‖22
holds for all vectors x with at most s non-zero entries.
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 19 / 39
Compressive Sensing
Sparsity Regularized Inversion
Convex Optimization for Sparse Recovery
minx‖x‖1 subject to ‖Ax− y‖2
2 6 ε.
Provides a bounded error solution to the NP-complete sparse recoveryproblem, if δ2K(A) <
√2 − 1)
Restricted Isometry Constant
RIC (δs) for forward operator A is defined as the smallest δ ∈ (0, 1) suchthat:
(1 − δs)‖x‖22 6 ‖Ax‖2
2 6 (1 + δs)‖x‖22
holds for all vectors x with at most s non-zero entries.
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 19 / 39
Compressive Sensing
Sparsity Regularized Inversion
Convex Optimization for Sparse Recovery
minx‖x‖1 subject to ‖Ax− y‖2
2 6 ε.
Provides a bounded error solution to the NP-complete sparse recoveryproblem, if δ2K(A) <
√2 − 1)
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 20 / 39
Compressive Sensing
Compressive Sensing in Radar Imaging
To ccount for anisotropic scattering, complex-valued data, sparsity invarious domains, use penalty terms adopted in image processing incomplex data setting [Cetin, Karl, others 2001]
min ‖y−Ax‖22 + λ1‖x‖pp + λ2‖D|x|‖pp
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Compressive Sensing
Compressive Sensing in Radar Imaging
3D Imaging: Combine 2D data from few passes to form 3D Imagery.Sparse sampling in elevation leads to high sidelobes in slant-planeheight in L2 reconstruction
L. C. Potter, E. Ertin, J. T. Parker, and M. Cetin, Sparsity and compressedsensing in radar imaging, Proceedings of the IEEE, 2010.
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Compressive Sensing
Sparsity Regularized Inversion
Mutual Coherence
Mutual coherence of the forward operator A:
µ(A) = maxi 6=j
|AHi Aj|. (2)
RIC is bounded by δs < (s− 1)µ
Design Transmit Waveforms and Receive Processing to minimize mutualcoherence of the forward operator A(rp, tp)
Random waveforms sacrifice stretch processing gainWe consider multifrequency chirp signals
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Compressive Sensing
Sparsity Regularized Inversion
Mutual Coherence
Mutual coherence of the forward operator A:
µ(A) = maxi 6=j
|AHi Aj|. (2)
RIC is bounded by δs < (s− 1)µ
Design Transmit Waveforms and Receive Processing to minimize mutualcoherence of the forward operator A(rp, tp)Random waveforms sacrifice stretch processing gainWe consider multifrequency chirp signals
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 23 / 39
Compressive Sensing
Measurement Kernels in Radar
Classical radar ambiguity funtionyields mutual coherence, µ
RIP constant: δs < (s− 1)µ
Past history of randomization in radar
array geometriespulse repetition jitternoise waveforms
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Multifrequency Waveforms for Compressive Radar
Outline
Radar Estimation Problem
Compressive Sensing
Multifrequency Waveforms for Compressive Radar
Experimental Results
Conclusion and Future Work
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Multifrequency Waveforms for Compressive Radar
Multi-frequency Chirp Waveforms
Multi-frequency chirp, K sub-carriers
fp(t) =
K∑k=1
ejφpkrec(
t
τ) exp
(j2π(fkpt+
α
2t2)
)Received signal for target at distanced (td = 2d
c )
sp(t) = c
K∑k=1
ejφ(fpk ,td,φpk)rec(t
τ− td)
× exp(j2π((fkp − f0 − αtd)t)
)φ(fpk, td,φpk) = φ
pk − 2πfpktd
dB
Data=[1x2501], Fs=2.5 GHz
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pl473.6000 ns1.2451 GHz35.5479 dB
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Multifrequency Waveforms for Compressive Radar
Receive Processing
Transmit: Illuminate scene with sum of multi-frequency chirps;randomize subcarrier frequencies and phases.Receive:
Analog: Mix with a single chirp and sample with a slow A/D with wideanalog bandwidth to obtain randomized projections.Software: Use compressive sensing recovery algorithm with provableperformance guarantees.
Measurement Kernel Design
FPGAReal Time Processor
Direct Digital
Systhesis
Low Speed
A/D
Power Combiner
Digital Backend RF Frontend
Dechirp LNA
For multiple pulses, dual of Xampling [Mishali & Eldar] which uses fixed bank of hardware
mixers on receive to alias wideband signal to baseband.
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Multifrequency Waveforms for Compressive Radar
Receive Processing
For multiple pulses:
target at 5 m
500 MHz bandwidth transmission; 5 Msps ADC
Observe:
low-rate ADC aliases wide-band returns to common baseband
Subcarrier phases and frequencies yield randomized projections
pulse 1
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40
60
80
100
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140
range (m) pulse n
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Experimental Results
Outline
Radar Estimation Problem
Compressive Sensing
Multifrequency Waveforms for Compressive Radar
Experimental Results
Conclusion and Future Work
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 29 / 39
Experimental Results
Experimental Results
Basis Pursuit Recovery of Sparse Vector(K=10) with 1/5undersampling at 20dB SNR
0 50 100 150 200 2500
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Range(m)
(a) (b)
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Experimental Results
Experimental Results: Single Pulse
Top row: MSE as a function of SNR & sparsity; bottom row:histogram of A ′ ∗A magnitudes (coherence)
1 Chirp 7 Chirps 15 Chirps
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
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Coherence
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.05
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0.15
0.2
0.25
Coherence
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Experimental Results
Experimental Results
MSE as a function of SNR and Sparsity and Mutual Coherence
SubCarrier=1 Subcarrier=7 Subcarrier=15
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
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1
Mutual Coherence
CD
F
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Mutual Coherence
CD
F
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Mutual Coherence
CD
F
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Experimental Results
Experimental Results
Multiple Channels: Multiple Pulses, Orthogonal Waveforms, Polarization
MSE as a function of SNR and Sparsity for 15 Subcarriers
Channels=1 Channels=2
Channels=3 Channels =4E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 33 / 39
Experimental Results
Hardware Experiment
Transmit waveform consists of 11non-overlapping 50 MHz bandwidthchirps of total approximate bandwidthof 550 MHz.
Single Pulse of 10 µseconds
Single stretch processor sampling at arate of 5 Msample/sec (I/Q)
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Experimental Results
Hardware Experiment
Transmit waveform consists of 11non-overlapping 50 MHz bandwidthchirps of total approximate bandwidthof 550 MHz.
Single Pulse of 10 µseconds
Single stretch processor sampling at arate of 5 Msample/sec (I/Q)
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 35 / 39
Experimental Results
Hardware Experiment
Transmit waveform consists of 11non-overlapping 50 MHz bandwidthchirps of total approximate bandwidthof 550 MHz.
Single Pulse of 10 µseconds
Single stretch processor sampling at arate of 5 Msample/sec (I/Q)
0 10 20 30 40 50 60 70 80 90 100−50
0
50
time (nanosec)
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5
10x 109
range (m)
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50
100
150
200
range (m)
Targ
et R
etur
n
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 36 / 39
Experimental Results
Hardware Experiment
Transmit waveform consists of 11non-overlapping 50 MHz bandwidthchirps of total approximate bandwidthof 550 MHz.
Single Pulse of 10 µseconds
Single stretch processor sampling at arate of 5 Msample/sec (I/Q)
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4.6 4.8 5 5.2 5.4 5.6
0
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Range(m)
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Conclusion and Future Work
Outline
Radar Estimation Problem
Compressive Sensing
Multifrequency Waveforms for Compressive Radar
Experimental Results
Conclusion and Future Work
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 38 / 39
Conclusion and Future Work
Conclusion and Future Work
We presented wideband compressiveradar sensor based on multifrequencyFM waveforms
Shift the complexity from the receiverto transmitter
Future work in characterizing coherenceof the resulting forward operator andsparse construction performance
Extend compressive sampling on theother dimensions of the radar data cube
Range[Fast Time]
Doppler[Slow Time]
Angle of Arrival[Phase Center]
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