A Subspace Method for MIMO Radar SpaceTime Adaptive

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

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 Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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

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

SIMO Radar (Traditional) Transmitter: M antenna elements ej 2 p(ft-x/l) d. T w 2 f(t) w 1 f(t) w 0 f(t) Transmitter emits coherent waveforms. Receiver: N antenna elements ej 2 p(ft-x/l) d. R Number of received signals: N Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

MIMO Radar Transmitter: M antenna elements ej 2 p(ft-x/l) f 2(t) f 1(t) d. T Receiver: N antenna elements ej 2 p(ft-x/l) d. R f 0(t) Transmitter emits orthogonal waveforms. MF … Matched filters extract the M orthogonal waveforms. Overall number of signals: NM Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

MIMO Radar – Virtual Array ej 2 p(ft-x/l) q q d. R f 2(t) d. T=Nd. R f 1(t) MF … f 0(t) Transmitter: M antenna elements Receiver: N antenna elements q Virtual array: NM elements Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

MIMO Radar – Virtual Array (2) [D. W. Bliss and K. W. Forsythe, 03] + Transmitter: M elements = Receiver: N elements Virtual array: NM elements 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

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

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

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

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

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

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

The Proposed Method clutter jammer noise We first observe each of the matrices Rc and RJ has some special structures. We show 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

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

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

Simplification of the Clutter Expression Re{c(x; fs, i)} Re{c(n+gm+bl; fs, i)} 1. 5 1 0. 5 0 -0. 5 -1 -1. 5 -2 0 2 4 6 x Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest 8 10 12

“Time-and-Band” Limited Signals The signals are well-localized in a time-frequency region. Time domain [0 X] Freq. domain [-0. 5] 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

Prolate Spheroidal Wave Functions (PSWF) is called PSWF. 0 X Time window -0. 5 Frequency window Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest in [0, X]

Prolate Spheroidal Wave Functions (PSWF) is called PSWF. 0 X Time window -0. 5 in [0, X] Frequency window [D. Slepian, 62] Only X+1 basis functions are required to well represent the “time-and-band limited” signal Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The Zero-Forcing Method § Typically we can assume that the clutter is very strong and all eigenvalues of Rx 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

Simulations Parameters: N=10, M=5, L=16 CNR=50 d. B 2 jammers, JNR=40 d. B SINR of a target at angle zero and Doppler frequencies [-0. 5, 0. 5] 0 MVDR known R (unrealizable) -2 Sample matrix inversion K=1000 SINR (d. B) -4 -6 -8 -10 Diagonal loading K=300 Principal component K=300 Proposed method K=300, Kv=20 Proposed ZF method -12 -14 -16 -0. 5 -0. 4 -0. 3 -0. 2 -0. 1 0. 2 0. 3 Normalized Doppler frequency 0. 4 0. 5 Kv=20 K: number of samples Kv: number of clutter free samples collected in passive mode Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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

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