High Resolution Radar Sensing via Compressive Illumination Emre Ertin Lee Potter, Randy Moses, Phil Schniter, Christian Austin, Jason Parker The Ohio State University New Frontiers in Imaging and Sensing Workshop February 17, 2010 E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 1 / 39
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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:
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
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 4 / 39
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
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 5 / 39
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 11 / 39
Compressive Sensing
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 12 / 39
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.
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 13 / 39
Compressive Sensing
Sparsity Regularized Inversion
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 14 / 39
Compressive Sensing
High-frequency scattering center decomposition
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 15 / 39
Compressive Sensing
Sparsity Regularized Inversion
Sparse Signal Recovery Problem
minx‖x‖0 subject to ‖Ax− y‖2
2 6 ε,
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 16 / 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 17 / 39
Compressive Sensing
Geometric Intuition
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 18 / 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)
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.
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 22 / 39
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
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
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 24 / 39
Multifrequency Waveforms for Compressive Radar
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 25 / 39
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
-120
-100
-80
-60
-40
-20
0
20
-1000
0.0
0.5
1.0
1.5
2.0
Freq
uenc
y, G
Hz
dB
100 200 300 400 500 600 700 800 900-1
0
1
Time, ns
Am
pl473.6000 ns1.2451 GHz35.5479 dB
dB
Data=[1x2501], Fs=2.5 GHz
-120
-100
-80
-60
-40
-20
0
20
-1000
0.0
0.5
1.0
1.5
2.0
Fre
quen
cy, G
Hz
dB
100 200 300 400 500 600 700 800 900-5
0
5
Time, ns
Am
pl473.6000 ns
1.2451 GHz
35.5482 dB
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 26 / 39
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.
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 27 / 39
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
−80 −60 −40 −20 0 20 40 60 800
20
40
60
80
100
120
140
range (m) pulse n
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 28 / 39
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
0.5
1
1.5
2
2.5
−80 −60 −40 −20 0 20 40 60 800
20
40
60
80
100
120
140
0 50 100 150 200 2500
0.5
1
1.5
2
2.5
−80 −60 −40 −20 0 20 40 60 800
5
10
15
20
25
30
Range(m)
(a) (b)
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 30 / 39
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
0.05
0.1
0.15
0.2
0.25
Coherence
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.05
0.1
0.15
0.2
0.25
Coherence
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.05
0.1
0.15
0.2
0.25
Coherence
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 31 / 39
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
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Mutual Coherence
CD
F
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Mutual Coherence
CD
F
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Mutual Coherence
CD
F
E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 32 / 39