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A Subspace Method for MIMO Radar Space-Time Adaptive Processing Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP Lab ICASSP 2007 student paper contest

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Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest Outline Review of the background –MIMO radar –Space-Time Adaptive Processing (STAP) The proposed MIMO-STAP method –Formulation of the MIMO-STAP –Prolate spheroidal representation of the clutter signals –Deriving the proposed method Simulations

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Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest MIMO Radar MIMO radar SIMO radar (Traditional) The radar systems which emits orthogonal (or noncoherent) waveforms in each transmitting antennas are called MIMO radar. w 2 w 1 w 0

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Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest MIMO Radar MIMO radar SIMO radar (Traditional) w 2 w 1 w 0 The radar systems which emits orthogonal (or noncoherent) waveforms in each transmitting antennas are called MIMO radar. [D. J. Rabideau and P. Parker, 03] [D. Bliss and K. Forsythe, 03] [E. Fishler et al. 04] [F. C. Robey, 04] [D. R. Fuhrmann and G. S. Antonio, 05]

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SIMO Radar (Traditional) Transmitter: M antenna elementsReceiver: N antenna elements dTdT e j2 (ft-x/ ) w 2 w 1 w 0 dRdR e j2 (ft-x/ ) Transmitter emits coherent waveforms. Transmitter emits coherent waveforms. Number of received signals: N Number of received signals: N Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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MIMO Radar dTdT e j2 (ft-x/ ) dRdR e j2 (ft-x/ ) MF … … Transmitter emits orthogonal waveforms. Transmitter emits orthogonal waveforms. Matched filters extract the M orthogonal waveforms. Overall number of signals: NM Matched filters extract the M orthogonal waveforms. Overall number of signals: NM Transmitter: M antenna elementsReceiver: N antenna elements Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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MIMO Radar – Virtual Array Transmitter: M antenna elementsReceiver: N antenna elements Virtual array: NM elements d T =Nd R e j2 (ft-x/ ) dRdR e j2 (ft-x/ ) MF … … Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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MIMO Radar – Virtual Array (2) Receiver: N elements Virtual array: NM elements Transmitter: M elements += [D. W. Bliss and K. W. Forsythe, 03] The spatial resolution for clutter is the same as a receiving array with NM physical array elements. NM degrees of freedom can be created using only N+M physical array elements. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Space-Time Adaptive Processing v v sin i airborne radar jammer target i-th clutter vtvt i The adaptive techniques for processing the data from airborne antenna arrays are called space-time adaptive processing (STAP). Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Space-Time Adaptive Processing v v sin i airborne radar jammer target i-th clutter vtvt i The clutter Doppler frequencies depend on angles. So, the problem is non-separable in space-time. The adaptive techniques for processing the data from airborne antenna arrays are called space-time adaptive processing (STAP). Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Space-Time Adaptive Processing (2) Separable : N+L taps Non separable : NL taps Jointly process Doppler frequencies and angles Jointly process Doppler frequencies and angles Independently process Doppler frequencies and angles Independently process Doppler frequencies and angles Angle processing Doppler processing Space-time processing L: # of radar pulses L Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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MIMO Radar STAP STAP MIMO Radar NL signals MIMO STAP M waveforms NML signals N: # of receiving antennas M: # of transmitting antennas L: # of pulses [D. Bliss and K. Forsythe 03] + NM signals Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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MIMO Radar STAP (2) NML signals MVDR (Capon) beamformer: Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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MIMO Radar STAP (2) NML signals MVDR (Capon) beamformer: Very good spatial resolution Pros Cons High complexity Slow convergence NMLxNML Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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The Proposed Method We first observe each of the matrices R c and R J has some special structures. clutterjammernoise We show how to exploit the structures of these matrices to compute R -1 more accurately and efficiently. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Formulation of the Clutter Signals N c : # of clutter points ith clutter signal amplitude Matched filters Pulse 2 Pulse 1 Pulse 0 Matched filters c 002 c 012 c 102 c 001 c 011 c 101 c 000 c 010 c 100 c 112 c 202 c 212 c 111 c 201 c 211 c 110 c 200 c 210 c nml : clutter signals … Clutter points n-th antenna m-th matched filter output l-th radar pulse Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Simplification of the Clutter Expression Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Simplification of the Clutter Expression Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Time-and-Band Limited Signals [0 X] [ ] Time domain Freq. domain The signals are well-localized in a time-frequency region. To concisely represent these signals, we can use a basis which concentrates most of its energy in this time-frequency region. To concisely represent these signals, we can use a basis which concentrates most of its energy in this time-frequency region. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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is called PSWF. Prolate Spheroidal Wave Functions (PSWF) Time window Frequency window X in [0,X] Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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is called PSWF. Prolate Spheroidal Wave Functions (PSWF) [D. Slepian, 62] in [0,X] Only X+1 basis functions are required to well represent the time-and-band limited signal Only X+1 basis functions are required to well represent the time-and-band limited signal Time window Frequency window X Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Clutter Representation by PSWF consists of NML N+ (M-1)+ (L-1) Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Clutter Representation by PSWF consists of can be obtained by sampling from. The PSWF can be computed off-line can be obtained by sampling from. The PSWF can be computed off-line NML N+ (M-1)+ (L-1) Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Clutter Representation by PSWF consists of can be obtained by sampling from. The PSWF can be computed off-line can be obtained by sampling from. The PSWF can be computed off-line NML N+ (M-1)+ (L-1) The NMLxNML clutter covariance matrix has only N+ (M-1)+ (L-1) significant eigenvalues. This is the MIMO extension of Brennans rule (1994). Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Jammer Covariance Matrix Matched filters jammer Pulse 2 Pulse 1 Pulse 0 Matched filters j 002 j 012 j 102 j 001 j 011 j 101 j 000 j 010 j 100 j 112 j 202 j 212 j 111 j 201 j 211 j 110 j 200 j 210 j nml : jammer signals Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Jammer Covariance Matrix Matched filters jammer Pulse 2 Pulse 1 Pulse 0 Jammer signals in different pulses are independent. Matched filters j 002 j 012 j 102 j 001 j 011 j 101 j 000 j 010 j 100 j 112 j 202 j 212 j 111 j 201 j 211 j 110 j 200 j 210 j nml : jammer signals Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Jammer Covariance Matrix Matched filters jammer Pulse 2 Pulse 1 Pulse 0 Jammer signals in different pulses are independent. Jammer signals in different matched filter outputs are independent. Matched filters j 002 j 012 j 102 j 001 j 011 j 101 j 000 j 010 j 100 j 112 j 202 j 212 j 111 j 201 j 211 j 110 j 200 j 210 j nml : jammer signals Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Jammer Covariance Matrix Matched filters jammer Pulse 2 Pulse 1 Pulse 0 Jammer signals in different pulses are independent. Jammer signals in different matched filter outputs are independent. Matched filters Block diagonal j 002 j 012 j 102 j 001 j 011 j 101 j 000 j 010 j 100 j 112 j 202 j 212 j 111 j 201 j 211 j 110 j 200 j 210 j nml : jammer signals Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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The Proposed Method low rank block diagonal Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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The Proposed Method low rank block diagonal By Matrix Inversion Lemma Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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The Proposed Method low rank block diagonal The proposed method –Compute by sampling the prolate spheroidal wave functions. By Matrix Inversion Lemma Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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The Proposed Method low rank block diagonal The proposed method –Compute by sampling the prolate spheroidal wave functions. –Instead of estimating R, we estimate R v and R. The matrix R v can be estimated using a small number of clutter free samples. By Matrix Inversion Lemma Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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The Proposed Method low rank block diagonal The proposed method –Compute by sampling the prolate spheroidal wave functions. –Instead of estimating R, we estimate R v and R. The matrix R v can be estimated using a small number of clutter free samples. –Use the above equation to compute R -1. By Matrix Inversion Lemma Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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The Proposed Method – Advantages :block diagonal :small size Inversions are easy to compute Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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The Proposed Method – Advantages :block diagonal :small size Inversions are easy to compute Low complexity Low complexity Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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The Proposed Method – Advantages :block diagonal :small size Inversions are easy to compute Fewer parameters need to be estimated Low complexity Low complexity Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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The Proposed Method – Advantages :block diagonal :small size Inversions are easy to compute Fewer parameters need to be estimated Low complexity Low complexity Fast convergence Fast convergence Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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The Proposed Method – Complexity Complexity: Direct methodThe proposed method Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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The Zero-Forcing Method Typically we can assume that the clutter is very strong and all eigenvalues of R are very large. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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The Zero-Forcing Method Typically we can assume that the clutter is very strong and all eigenvalues of R are very large. Zero-forcing method –The entire clutter space is nulled out without estimation Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Proposed method K=300,K v =20 Simulations MVDR known R (unrealizable) Proposed ZF method K v =20 Sample matrix inversion K=1000 Diagonal loading K=300 Principal component K=300 SINR of a target at angle zero and Doppler frequencies [-0.5, 0.5] Parameters: N=10, M=5, L=16 CNR=50dB 2 jammers, JNR=40dB K: number of samples K v : number of clutter free samples collected in passive mode Normalized Doppler frequency SINR (dB) Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Conclusion and Future Work Conclusion –The clutter subspace is derived using the geometry of the problem. (data independent) –A new STAP method for MIMO radar is developed. –The new method is both efficient and accurate. Future work –This method is entirely based on the ideal model. –Find algorithms which are robust against model mismatch. –Develop clutter subspace estimation methods using a combination of both the geometry and the received data. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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Q&A Thank You! Any questions? Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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