High Resolution Radar Sensing via Compressive Illumination

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

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 Sensing Thru-wall Surveillance Cognitive Radar Networks 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 Sensing Thru-wall Surveillance Cognitive Radar Networks Emerging Signal Processing Techniques Waveform Adaptivity MIMO Radar Systems 3D SAR Radar 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 structures for DSP enabled real time decisions and on the fly waveform adaptation Next Generation Radar Sensors Software Configurable for multimode operation: Imaging-Tracking Multiple TX/RX chains to support MIMO Radar Independent 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 Waveforms FPGA/DSP for online processing Single Channel 125 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 Waveforms Fully coherent multichannel operation for MIMO Limited Online Processing, Ideal for Field Measurements 4 Tx - 4 Rx MIMO Software Defined Radar Sensor Programmable Software Defined Waveforms Multiple FPGA/DSP Chains for online processing Fully coherent multichannel operation for MIMO 500 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

Wideband Radar Technology Emerging applications stretch the resolution and bandwidth capabilities of ADC 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 = Φ r Φ t Ψs E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 6 / 39

Wideband Radar Technology Emerging applications stretch the resolution and bandwidth capabilities of ADC 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 = Φ r Φ t Ψs 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

Outline Radar Estimation Problem 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 7 / 39

Radar Estimation Problem Radar as Channel Estimation Problem System Model y p = R p X p t p + n p p = 1... P y p : radar return X p : convolution matrix of the channel response t p : transmit waveform R p : receive processing filter n p : system noise E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 8 / 39

Radar Sensing Model Radar Estimation Problem System Model y p = R p T p x p + n p p = 1... P y p : radar return T p : convolution matrix of the transmit waveform x p : unknown target response R p : receive processing filter n p : system noise E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 9 / 39

Radar Estimation Problem Radar Sensing Model System Model y p = R p T p x p + n p p = 1... P = A(r p, t p )x p + n p y p : radar return T p : convolution matrix of the transmit waveform x p : unknown target response R p : receive processing filter n p : system noise E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 9 / 39

Radar Estimation Problem Radar Sensing Model Radar Imaging Problem Estimate unknown target range profile x from the sampled radar returns y p y p = A(r p, t p )x + n p x is sampled at the transmit bandwidth (or higher) y p sampling rate determines ADC requirements 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 returns y p y p = A(r p, t p )x + n p x is sampled at the transmit bandwidth (or higher) y p sampling rate determines ADC requirements Use prior knowledge about the scene for design of (r p, t p ) to reduce ADC rate E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 10 / 39

Radar Estimation Problem Example: Stretch Processing Traditional LFM chirp signals can provide 2-10x sub-nyquist sampling Analog dechirp processing followed by low rate ADCs Sample uniformly in frequency; alias to exploit limited swath in range Stretch gives compression versus transmit bandwidth B τ T p vs B db 0-100 2.0 1.5 1.0 0.5 0.0 473.6000 ns 1.2451 GHz 35.5479 db Frequency, GHz Data=[1x2501], Fs=2.5 GHz 1 0-1 100 200 300 400 500 600 700 800 900 Time, ns db Ampl 20 0-20 -40-60 -80-100 -120 swath τ = 2R/c sec; pulse duration T p sec E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 11 / 39

Outline Compressive Sensing 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 C N from noisy measurements of its linear projections y = Ax + n C M. (1) Focus: A C MxN 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 < ɛ. 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 min x x 0 subject to Ax y 2 2 ɛ, E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 16 / 39

Geometric Intuition Compressive Sensing E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 18 / 39

Compressive Sensing Sparsity Regularized Inversion Convex Optimization for Sparse Recovery min x x 1 subject to Ax y 2 2 ɛ. Provides a bounded error solution to the NP-complete sparse recovery problem, if δ 2K (A) < 2 1) Restricted Isometry Constant RIC (δ s ) for forward operator A is defined as the smallest δ (0, 1) such that: (1 δ s ) x 2 2 Ax 2 2 (1 + δ s ) x 2 2 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 Compressive Sensing in Radar Imaging To ccount for anisotropic scattering, complex-valued data, sparsity in various domains, use penalty terms adopted in image processing in complex data setting [Cetin, Karl, others 2001] min y Ax 2 2 + λ 1 x p p + λ 2 D x p p E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 21 / 39

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-plane height in L2 reconstruction L. C. Potter, E. Ertin, J. T. Parker, and M. Cetin, Sparsity and compressed sensing 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: RIC is bounded by δ s < (s 1)µ µ(a) = max i j AH i A j. (2) Design Transmit Waveforms and Receive Processing to minimize mutual coherence of the forward operator A(r p, t p ) 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: RIC is bounded by δ s < (s 1)µ µ(a) = max i j AH i A j. (2) Design Transmit Waveforms and Receive Processing to minimize mutual coherence of the forward operator A(r p, t p ) Random waveforms sacrifice stretch processing gain We 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 funtion yields mutual coherence, µ RIP constant: δ s < (s 1)µ Past history of randomization in radar array geometries pulse repetition jitter noise waveforms E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 24 / 39

Outline Multifrequency Waveforms for Compressive Radar 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 Data=[1x2501], Fs=2.5 GHz Multi-frequency chirp, K sub-carriers f p (t) = K k=1 t ( e jφp k rec( τ ) exp j2π(f k pt + α ) 2 t2 ) db 0-100 2.0 1.5 1.0 0.5 0.0 473.6000 ns 1.2451 GHz 35.5479 db Frequency, GHz -1 100 200 300 400 500 600 700 800 900 Time, ns db 20 0-20 -40-60 -80-100 -120 1 0 Ampl Received signal for target at distance d (t d = 2d c ) 0 db -100 Data=[1x2501], Fs=2.5 GHz db 20 K s p (t) = c e jφ(fp k,t d,φ p k ) rec( t τ t d) k=1 exp ( j2π((f k p f 0 αt d )t) ) 2.0 1.5 1.0 0.5 0.0 473.6000 ns 1.2451 GHz 35.5482 db Frequency, GHz 5 0-5 100 200 300 400 500 600 700 800 900 Time, ns Ampl 0-20 -40-60 -80-100 -120 φ(f p k, t d, φ p k ) = φp k 2πfp k t d 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 wide analog bandwidth to obtain randomized projections. Software: Use compressive sensing recovery algorithm with provable performance guarantees. Measurement Kernel Design Direct Digital Systhesis Power Combiner FPGA Real Time Processor Low Speed A/D Dechirp LNA Digital Backend RF Frontend 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

140 120 100 80 60 40 20 0 80 60 40 20 0 20 40 60 80 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 range (m) pulse n E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 28 / 39

Outline Experimental Results 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 1/5 undersampling at 20dB SNR 140 120 100 80 60 40 20 0 80 60 40 20 0 20 40 60 80 30 25 20 15 10 5 0 80 60 40 20 0 20 40 60 80 Range(m) 2.5 2.5 2 2 1.5 1.5 1 1 0.5 0.5 0 0 50 100 150 200 250 (a) 0 0 50 100 150 200 250 (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) 0.25 1 Chirp 7 Chirps 15 Chirps 0.25 0.25 0.2 0.2 0.2 0.15 0.15 0.15 0.1 0.1 0.1 0.05 0.05 0.05 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Coherence 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Coherence 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 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 1 1 1 0.9 0.9 0.9 0.8 0.8 0.8 0.7 0.7 0.7 0.6 0.6 0.6 CDF 0.5 CDF 0.5 CDF 0.5 0.4 0.4 0.4 0.3 0.3 0.3 0.2 0.2 0.2 0.1 0.1 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mutual Coherence 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mutual Coherence 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mutual Coherence E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 32 / 39

Channels=3 Channels =4 E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 33 / 39 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

Experimental Results Hardware Experiment Transmit waveform consists of 11 non-overlapping 50 MHz bandwidth chirps of total approximate bandwidth of 550 MHz. Single Pulse of 10 µseconds Single stretch processor sampling at a rate of 5 Msample/sec (I/Q) E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 34 / 39

Hardware Experiment Experimental Results Transmit waveform consists of 11 non-overlapping 50 MHz bandwidth chirps of total approximate bandwidth of 550 MHz. Single Pulse of 10 µseconds Single stretch processor sampling at a rate of 5 Msample/sec (I/Q) Target Return 50 0 50 0 10 20 30 40 50 60 70 80 90 100 time (nanosec) 200 150 100 50 0 80 60 40 20 0 20 40 60 80 range (m) 10 x 109 5 0 80 60 40 20 0 20 40 60 80 range (m) E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 36 / 39

Hardware Experiment Experimental Results Transmit waveform consists of 11 non-overlapping 50 MHz bandwidth chirps of total approximate bandwidth of 550 MHz. Single Pulse of 10 µseconds Single stretch processor sampling at a rate of 5 Msample/sec (I/Q) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 60 40 20 0 20 40 60 0.8 0.6 0.4 0.2 0 4.6 4.8 5 5.2 5.4 5.6 Range(m) E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 37 / 39

Outline Conclusion and Future Work 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 compressive radar sensor based on multifrequency FM waveforms Shift the complexity from the receiver to transmitter Future work in characterizing coherence of the resulting forward operator and sparse construction performance Extend compressive sampling on the other dimensions of the radar data cube Angle of Arrival [Phase Center] Doppler [Slow Time] Range [Fast Time] E. Ertin (OSU) Compressive Illumination New Frontiers in I & S 39 / 39