high resolution radar sensing via compressive...

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


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


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


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


www.ece.osu.edu/~ertine/RFtestbed

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


Radar Estimation Problem

Outline


Compressive Sensing

Multifrequency Waveforms for Compressive Radar

Experimental Results

Conclusion and Future Work



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



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



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



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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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


Compressive Sensing

Outline


Compressive Sensing





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.


Compressive Sensing

Sparsity Regularized Inversion


Compressive Sensing

High-frequency scattering center decomposition


Compressive Sensing


Sparse Signal Recovery Problem

minx‖x‖0 subject to ‖Ax− y‖2

2 6 ε,


Compressive Sensing


Convex Optimization for Sparse Recovery


2 6 ε.

Provides a bounded error solution to the NP-complete sparse recoveryproblem, if δ2K(A) <

√2 − 1)


Compressive Sensing

Geometric Intuition


Compressive Sensing




2 6 ε.


√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.


Compressive Sensing




2 6 ε.


√2 − 1)


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


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.


Compressive Sensing


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


Compressive Sensing


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


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



Outline


Compressive Sensing






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


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Am

pl473.6000 ns1.2451 GHz35.5479 dB

dB


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Am

pl473.6000 ns

1.2451 GHz

35.5482 dB



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.



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

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140

range (m) pulse n



Outline


Compressive Sensing







Basis Pursuit Recovery of Sparse Vector(K=10) with 1/5undersampling at 20dB SNR

0 50 100 150 200 2500

0.5

1

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2

2.5

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30

Range(m)

(a) (b)



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

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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

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0.15

0.2

0.25

Coherence




MSE as a function of SNR and Sparsity and Mutual Coherence

SubCarrier=1 Subcarrier=7 Subcarrier=15

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0.1

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1

Mutual Coherence

CD

F

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Mutual Coherence

CD

F

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1

Mutual Coherence

CD

F




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


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)



Hardware Experiment






Hardware Experiment




0 10 20 30 40 50 60 70 80 90 100−50

0

50

time (nanosec)

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10x 109

range (m)

−80 −60 −40 −20 0 20 40 60 800

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range (m)

Targ

et R

etur

n



Hardware Experiment




−60 −40 −20 0 20 40 600

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Range(m)



Outline


Compressive Sensing







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]


high resolution radar sensing via compressive...

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