Signal Processing Algorithms for MIMO Radar Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP Lab Candidacy

Outline Review of the background The proposed MIMO-STAP method 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 Conclusion and future work. Chun-Yang Chen, Caltech DSP Lab | Candidacy

MIMO Radar and Beamforming 1 MIMO Radar and Beamforming

SIMO radar (Traditional) MIMO Radar The radar systems which emits orthogonal (or noncoherent) waveforms in each transmitting antennas are called MIMO radar. MIMO radar SIMO radar (Traditional) f2(t) w2f(t) f1(t) w1f(t) f0(t) w0f(t) Chun-Yang Chen, Caltech DSP Lab | Candidacy

SIMO radar (Traditional) MIMO Radar The radar systems which emits orthogonal (or noncoherent) waveforms in each transmitting antennas are called MIMO radar. MIMO radar SIMO radar (Traditional) f2(t) w2f(t) f1(t) w1f(t) f0(t) w0f(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 | Candidacy

Radar was an acronym for Radio Detection and Ranging. Radar Systems Radar was an acronym for Radio Detection and Ranging. Radar target R Received Signal Detection Time Matched filter output Ranging threshold R=ct/2 t Chun-Yang Chen, Caltech DSP Lab | Candidacy

Beampattern of Antennas Beampattern is the antenna gain as a function of angle of arrival. target Chun-Yang Chen, Caltech DSP Lab | Candidacy

Beampattern of Antennas Beampattern is the antenna gain as a function of angle of arrival. d/2 Plane wave-front q target -d/2 Chun-Yang Chen, Caltech DSP Lab | Candidacy

Beampattern of Antennas Beampattern is the antenna gain as a function of angle of arrival. d/2 Plane wave-front q target -d/2 Chun-Yang Chen, Caltech DSP Lab | Candidacy

Beampattern of Antennas Beampattern is the antenna gain as a function of angle of arrival. d/2 Plane wave-front q target -d/2 Fourier transform Chun-Yang Chen, Caltech DSP Lab | Candidacy

Antenna Array By linearly combining the output of a group of antennas, we can control the beampattern digitally. N-1 1 … I/Q Down-Convert and ADC I/Q Down-Convert and ADC I/Q Down-Convert and ADC w*N-1 w*1 w*0 + Chun-Yang Chen, Caltech DSP Lab | Candidacy

Antenna Array By linearly combining the output of a group of antennas, we can control the beampattern digitally. Plane wave-front q N-1 1 … I/Q Down-Convert and ADC I/Q Down-Convert and ADC I/Q Down-Convert and ADC w*N-1 w*1 w*0 + Chun-Yang Chen, Caltech DSP Lab | Candidacy

Antenna Array … q + Discrete time Fourier transform By linearly combining the output of a group of antennas, we can control the beampattern digitally. Plane wave-front q N-1 1 … I/Q Down-Convert and ADC I/Q Down-Convert and ADC I/Q Down-Convert and ADC w*N-1 w*1 w*0 + Discrete time Fourier transform Chun-Yang Chen, Caltech DSP Lab | Candidacy

Antenna Array (2) … Advantages of antenna array: Beampattern can be steered digitally. target … Chun-Yang Chen, Caltech DSP Lab | Candidacy

Antenna Array (2) … Advantages of antenna array: Beampattern can be steered digitally. Beampattern can be adapted to the interferences. target interferences … Chun-Yang Chen, Caltech DSP Lab | Candidacy

The signal processing techniques to control the beampattern Antenna Array (2) Advantages of antenna array: Beampattern can be steered digitally. Beampattern can be adapted to the interferences. target interferences … The signal processing techniques to control the beampattern is called beamforming. Chun-Yang Chen, Caltech DSP Lab | Candidacy

Phased Array Beamforming The response of a desired angle of arrival q can be maximized by adjust wi. Plane wave-front q N-1 1 … I/Q Down-Convert and ADC I/Q Down-Convert and ADC I/Q Down-Convert and ADC w*N-1 w*1 w*0 + Chun-Yang Chen, Caltech DSP Lab | Candidacy

Phased Array Beamforming The response of a desired angle of arrival q can be maximized by adjust wi. Plane wave-front q N-1 1 … I/Q Down-Convert and ADC I/Q Down-Convert and ADC I/Q Down-Convert and ADC w*N-1 w*1 w*0 + Chun-Yang Chen, Caltech DSP Lab | Candidacy

Phased Array Beamforming The response of a desired angle of arrival q can be maximized by adjust wi. Plane wave-front q N-1 1 … I/Q Down-Convert and ADC I/Q Down-Convert and ADC I/Q Down-Convert and ADC w*N-1 w*1 w*0 + Chun-Yang Chen, Caltech DSP Lab | Candidacy

Adaptive Beamforming The beamformer can be further designed to maximize the SINR using second order statistics of received signals. Chun-Yang Chen, Caltech DSP Lab | Candidacy

Adaptive Beamforming The beamformer can be further designed to maximize the SINR using second order statistics of received signals. The SINR can be maximized by minimizing the total variance while maintaining unity signal response. Chun-Yang Chen, Caltech DSP Lab | Candidacy

Adaptive Beamforming [Capon 1969] The beamformer can be further designed to maximize the SINR using second order statistics of received signals. The SINR can be maximized by minimizing the total variance while maintaining unity signal response. [Capon 1969] MVDR beamformer (Minimum Variance Distortionless Response) Chun-Yang Chen, Caltech DSP Lab | Candidacy

An Example of Adaptive Beamforming Parameters Noise: 0dB Signal: 10dB, 43 degree Jammer1: 40dB, 30 degree Jammer2: 20dB, 75 degree 10 20 30 40 50 60 70 80 90 -60 -50 -40 -30 -20 -10 Angle Beam pattern (dB) However, the MVDR beamformer is very sensitive to target DoA (Direction of Arrival) mismatch. SINR Phased array: -20.13dB Adaptive: 9.70dB Adaptive beamforming can be very effective when there exists strong interferences. Chun-Yang Chen, Caltech DSP Lab | Candidacy

Beamforming under Direction-of-Arrival Mismatch Parameters Noise: 0dB Signal: 10dB, 43 degree Jammer1: 40dB, 30 degree Jammer2: 20dB, 75 degree 20 10 -10 Beam pattern (dB) -20 SINR Matched DoA: 9.70dB Mismatched DoA: -8.80dB -30 -40 -50 -60 10 20 30 40 50 60 70 80 90 Angle [2] Chun-Yang Chen and P. P. Vaidyanathan, “Quadratically Constrained Beamforming Robust Against Direction-of-Arrival Mismatch,” IEEE Trans. on Signal Processing, July 2007.  Chun-Yang Chen, Caltech DSP Lab | Candidacy

Transmit Beamforming … By weighting the input of a group of antennas, we can also control the transmit beampattern digitally. N-1 1 … I/Q Down-Convert and ADC I/Q Down-Convert and ADC I/Q Down-Convert and ADC w*N-1 w*1 w*0 transmitted waveform Chun-Yang Chen, Caltech DSP Lab | Candidacy

Transmit Beamforming … q By weighting the input of a group of antennas, we can also control the transmit beampattern digitally. Plane wave-front q N-1 1 … I/Q Down-Convert and ADC I/Q Down-Convert and ADC I/Q Down-Convert and ADC w*N-1 w*1 w*0 transmitted waveform Chun-Yang Chen, Caltech DSP Lab | Candidacy

Transmit Beamforming … q Discrete time Fourier transform By weighting the input of a group of antennas, we can also control the transmit beampattern digitally. Plane wave-front q N-1 1 … I/Q Down-Convert and ADC I/Q Down-Convert and ADC I/Q Down-Convert and ADC w*N-1 w*1 w*0 Discrete time Fourier transform transmitted waveform Chun-Yang Chen, Caltech DSP Lab | Candidacy

SIMO Radar (Traditional) Transmitter: M antenna elements Receiver: N antenna elements dR ej2p(ft-x/l) Number of received signals: N ej2p(ft-x/l) dT w2f(t) w1f(t) w0f(t) Transmitter emits coherent waveforms. (transmit beamforming) The traditional radar use a coherent waveforms in the transmitter. The coherent waveforms can form focused transmit beam. The total output in the receiver is the same as the number of the receiver antenna elements N. Chun-Yang Chen, Caltech DSP Lab | Candidacy

(No transmit beamforming) MIMO Radar Transmitter: M antenna elements dR ej2p(ft-x/l) MF … Matched filters extract the M orthogonal waveforms. Overall number of signals: NM Receiver: N antenna elements ej2p(ft-x/l) dT f2(t) f1(t) f0(t) Transmitter emits orthogonal waveforms. (No transmit beamforming) Chun-Yang Chen, Caltech DSP Lab | Candidacy

MIMO Radar – Virtual Array Receiver: N antenna elements dR ej2p(ft-x/l) MF … q ej2p(ft-x/l) f2(t) q dT=NdR f1(t) f0(t) Transmitter: M antenna elements q Virtual array: NM elements Chun-Yang Chen, Caltech DSP Lab | Candidacy

MIMO Radar – Virtual Array (2) [D. W. Bliss and K. W. Forsythe, 03] + = Virtual array: NM elements Transmitter: M elements Receiver: N 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. However, a processing gain of M is lost because of the broad transmitting beam. Chun-Yang Chen, Caltech DSP Lab | Candidacy

MIMO Transmitter vs. SIMO Transmitter … dT dT=NdR w2f(t) w1f(t) w0f(t) f2(t) f1(t) f0(t) In the application of scanning or imaging, global illumination is required. In this case the SIMO system needs to steer the transmit beam. This cancels the processing gain obtained by the focused beam in SIMO system. Chun-Yang Chen, Caltech DSP Lab | Candidacy

Space-Time Adaptive Processing 2 Space-Time Adaptive Processing

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 The goal in STAP is to detect the moving target on the ground and estimate its position and velocity. qi jammer target vt i-th clutter Chun-Yang Chen, Caltech DSP Lab | Candidacy 34

Doppler Processing v target Radar Chun-Yang Chen, Caltech DSP Lab | Candidacy

Doppler Processing v v target Radar target Radar Doppler effect: The phenomenon can be used to estimate velocity. Chun-Yang Chen, Caltech DSP Lab | Candidacy

Adaptive Temporal Processing The same idea in adaptive beamforming can be applied in Doppler processing. I/Q Down-Convert and ADC w*0 w*1 w*L-1 T … + Chun-Yang Chen, Caltech DSP Lab | Candidacy

Adaptive Temporal Processing The same idea in adaptive beamforming can be applied in Doppler processing. I/Q Down-Convert and ADC w*0 w*1 w*L-1 T … + Chun-Yang Chen, Caltech DSP Lab | Candidacy

Separable Space-Time Processing When the Doppler frequencies and looking-directions are independent, the spatial and temporal filtering can be implemented separately. N-1 1 … I/Q Down-Convert and ADC I/Q Down-Convert and ADC I/Q Down-Convert and ADC w*N-1 w*1 w*0 Filtered out the unwanted angles + T T … w*0 w*1 w*L-1 Filtered out the unwanted frequencies + Chun-Yang Chen, Caltech DSP Lab | Candidacy

Example of Separable Space-Time Processing Space-time beampattern is the antenna gain as a function of angle of arrival and Doppler frequency. Parameters Noise: 0dB Signal: 10dB, (0.11, 0.15) Jammer1: 40dB, (-0.22, x ) Jammer2: 20dB, (0.33, x ) Clutter: 40dB, (x , 0 ) However, the beampattern is not always separable. Chun-Yang Chen, Caltech DSP Lab | Candidacy

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 jammer target vt i-th clutter Chun-Yang Chen, Caltech DSP Lab | Candidacy 41

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 The clutter Doppler frequencies depend on angles. So, the problem is non-separable in space-time. jammer target vt i-th clutter Chun-Yang Chen, Caltech DSP Lab | Candidacy 42

Example of a Non-Separable Beampattern In airborne radar, clutter Doppler frequency is proportional to the angle of arrival. Consequently, the beampattern becomes non-separable. In a stationary radar, clutter Doppler frequency is zero for all angle of arrival. Chun-Yang Chen, Caltech DSP Lab | Candidacy

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

Optimal Space-Time Adaptive Processing As in beamforming and Doppler processing, the maximum SINR can be obtained by minimizing the total variance while maintaining unity signal response. NL signals Chun-Yang Chen, Caltech DSP Lab | Candidacy

Optimal Space-Time Adaptive Processing As in beamforming and Doppler processing, the maximum SINR can be obtained by minimizing the total variance while maintaining unity signal response. NL signals Chun-Yang Chen, Caltech DSP Lab | Candidacy

Optimal Space-Time Adaptive Processing As in beamforming and Doppler processing, the maximum SINR can be obtained by minimizing the total variance while maintaining unity signal response. NL signals Chun-Yang Chen, Caltech DSP Lab | Candidacy

An Efficient Space-Time Adaptive Processing Algorithm for MIMO Radar 3 An Efficient Space-Time Adaptive Processing Algorithm for MIMO Radar

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

MIMO Radar STAP (2) MVDR (Capon) beamformer: NML signals Chun-Yang Chen, Caltech DSP Lab | Candidacy

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

The Proposed Method [Chun-Yang Chen and P. P. Vaidyanathan, ICASSP 07] clutter jammer noise We first observe each of the matrices Rc and RJ has some special structures. We show how to exploit the structures of these matrices to compute R-1 more accurately and efficiently. Chun-Yang Chen, Caltech DSP Lab | Candidacy

The MIMO STAP Signals Received signal: yn,m,l n: receiving antenna index m: transmitting antenna index l: pulse trains index The signals contain four components: Target Noise Jammer Clutter airborne radar v vsinqi qi jammer target vt i-th clutter Target Noise Jammer Clutter Chun-Yang Chen, Caltech DSP Lab | Candidacy

Formulation of the Clutter Signals points … n-th antenna m-th matched filter output l-th radar pulse Matched filters Matched filters Matched filters Pulse 2 c002 c012 c102 c112 c202 c212 Pulse 1 c001 c011 c101 c111 c201 c211 Pulse 0 c000 c010 c100 c110 c200 c210 cnml: clutter signals Chun-Yang Chen, Caltech DSP Lab | Candidacy

Formulation of the Clutter Signals points … n-th antenna m-th matched filter output l-th radar pulse Matched filters Matched filters Matched filters Pulse 2 c002 c012 c102 c112 c202 c212 Nc: # of clutter points ri: i-th clutter signal amplitude Receiving antenna Transmitting antenna Doppler effect Pulse 1 c001 c011 c101 c111 c201 c211 Pulse 0 c000 c010 c100 c110 c200 c210 cnml: clutter signals Chun-Yang Chen, Caltech DSP Lab | Candidacy

Simplification of the Clutter Expression Chun-Yang Chen, Caltech DSP Lab | Candidacy

Simplification of the Clutter Expression Chun-Yang Chen, Caltech DSP Lab | Candidacy

Simplification of the Clutter Expression Chun-Yang Chen, Caltech DSP Lab | Candidacy

Simplification of the Clutter Expression Trick: We can view the three dimensional signal as non-uniformly sampled one dimensional signal. Chun-Yang Chen, Caltech DSP Lab | Candidacy

Simplification of the Clutter Expression (2) -2 2 4 6 8 10 12 -1.5 -1 -0.5 0.5 1 1.5 x Re{c(x;fs,i)} Re{c(n+gm+bl;fs,i)} Chun-Yang Chen, Caltech DSP Lab | Candidacy

“Time-and-Band” Limited Signals The signals are well-localized in a time-frequency region. Time domain [0 X] To concisely represent these signals, we can use a basis which concentrates most of its energy in this time-frequency region. Freq. domain [-0.5 0.5] Chun-Yang Chen, Caltech DSP Lab | Candidacy

Prolate Spheroidal Wave Functions (PSWF) is called PSWF. Frequency window -0.5 0.5 Time window X in [0,X] Chun-Yang Chen, Caltech DSP Lab | Candidacy

Prolate Spheroidal Wave Functions (PSWF) is called PSWF. Frequency window -0.5 0.5 Time window X in [0,X] [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 | Candidacy

Concise Representation of the Clutter Signals [D. Slepian, 62] Chun-Yang Chen, Caltech DSP Lab | Candidacy

Concise Representation of the Clutter Signals [D. Slepian, 62] Chun-Yang Chen, Caltech DSP Lab | Candidacy

Concise Representation of the Clutter Signals [D. Slepian, 62] consists of NML X+1 Chun-Yang Chen, Caltech DSP Lab | Candidacy

Concise Representation of the Clutter Signals (2) consists of NML N+g(M-1)+b(L-1) Chun-Yang Chen, Caltech DSP Lab | Candidacy

Concise Representation of the Clutter Signals (2) consists of NML N+g(M-1)+b(L-1) can be obtained by sampling from . The PSWF can be computed off-line Chun-Yang Chen, Caltech DSP Lab | Candidacy

[Chun-Yang Chen and P. P. Vaidyanathan, IEEE Trans SP, to appear] Concise Representation of the Clutter Signals (2) consists of NML N+g(M-1)+b(L-1) can be obtained by sampling from . The PSWF can be computed off-line The NMLxNML 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 and P. P. Vaidyanathan, IEEE Trans SP, to appear] Chun-Yang Chen, Caltech DSP Lab | Candidacy

Jammer Covariance Matrix Matched filters Matched filters Matched filters Pulse 2 j002 j012 j102 j112 j202 j212 Pulse 1 j001 j011 j101 j111 j201 j211 Pulse 0 j000 j010 j100 j110 j200 j210 jnml: jammer signals Chun-Yang Chen, Caltech DSP Lab | Candidacy

Jammer Covariance Matrix Jammer signals in different pulses are independent. Matched filters Matched filters Matched filters Pulse 2 j002 j012 j102 j112 j202 j212 Pulse 1 j001 j011 j101 j111 j201 j211 Pulse 0 j000 j010 j100 j110 j200 j210 jnml: jammer signals Chun-Yang Chen, Caltech DSP Lab | Candidacy

Jammer Covariance Matrix Jammer signals in different pulses are independent. Jammer signals in different matched filter outputs are independent. Matched filters Matched filters Matched filters Pulse 2 j002 j012 j102 j112 j202 j212 Pulse 1 j001 j011 j101 j111 j201 j211 Pulse 0 j000 j010 j100 j110 j200 j210 jnml: jammer signals Chun-Yang Chen, Caltech DSP Lab | Candidacy

Jammer Covariance Matrix Jammer signals in different pulses are independent. Jammer signals in different matched filter outputs are independent. Matched filters Matched filters Matched filters Pulse 2 j002 j012 j102 j112 j202 j212 Pulse 1 j001 j011 j101 j111 j201 j211 Pulse 0 j000 j010 j100 j110 j200 j210 jnml: jammer signals Block diagonal Chun-Yang Chen, Caltech DSP Lab | Candidacy

The Proposed Method low rank block diagonal Chun-Yang Chen, Caltech DSP Lab | Candidacy

By Matrix Inversion Lemma The Proposed Method low rank block diagonal By Matrix Inversion Lemma Chun-Yang Chen, Caltech DSP Lab | Candidacy

By Matrix Inversion Lemma 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 | Candidacy

By Matrix Inversion Lemma 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.k Chun-Yang Chen, Caltech DSP Lab | Candidacy

By Matrix Inversion Lemma 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 | Candidacy

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

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

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

The Proposed Method – Advantages Low complexity Inversions are easy to compute :block diagonal :small size Fast convergence Fewer parameters need to be estimated To summarize it, we can compute Psi by sampling the prolate spheroidal wave functions which can be computed off-line. Instead of estimate R, we estimate Rv and Rx. Use the above equation to compute R-1. Chun-Yang Chen, Caltech DSP Lab | Candidacy

The Proposed Method – Complexity Chun-Yang Chen, Caltech DSP Lab | Candidacy

The Proposed Method – Complexity Direct method The proposed method Chun-Yang Chen, Caltech DSP Lab | Candidacy

The Proposed Method – Complexity Direct method The proposed method Chun-Yang Chen, Caltech DSP Lab | Candidacy

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 | Candidacy

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 | Candidacy

Simulations – SINR K: number of samples Parameters: N=10, M=5, L=16 CNR=50dB 2 jammers, JNR=40dB SINR of a target at angle zero and Doppler frequencies [-0.5, 0.5] MVDR known R (unrealizable) -2 Sample matrix inversion K=1000 -4 Diagonal loading K=300 -6 Principal component K=300 SINR (dB) -8 Proposed method K=300,Kv=20 -10 Proposed ZF method Kv=20 -12 -14 K: number of samples Kv: number of clutter free samples collected in passive mode -16 -0.5 -0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5 Normalized Doppler frequency Chun-Yang Chen, Caltech DSP Lab | Candidacy

Simulations – Beampattern Parameters: N=10, M=5, L=16, CNR=50dB 2 jammers, JNR=40dB Target: (0,0.25) Proposed ZF Method Chun-Yang Chen, Caltech DSP Lab | Candidacy

Conclusion and Future Work 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 clutter subspace mismatch. Develop clutter subspace estimation methods using a combination of both the geometry and the received data. Chun-Yang Chen, Caltech DSP Lab | Candidacy

4 Research Topics Chun-Yang Chen, Caltech DSP Lab | Candidacy

Beamforming techniques for Radar systems Research Topics Beamforming techniques for Radar systems Robust Beamforming Algorithm against DoA Mismatch [2] An Efficient STAP Algorithm for MIMO Radar [3] An Efficient STAP Algorithm for MIMO Radar [3] Precoded V-BLAST Transceiver for MIMO Communication [1] Chun-Yang Chen, Caltech DSP Lab | Candidacy

Publications Journal Papers Book Chapter [1] Chun-Yang Chen and P. P. Vaidyanathan, “Precoded FIR and Redundant V-BLAST Systems for Frequency-Selective MIMO Channels,” IEEE Trans. on Signal Processing, July, 2007.  [2] Chun-Yang Chen and P. P. Vaidyanathan, “Quadratically Constrained Beamforming Robust Against Direction-of-Arrival Mismatch,” IEEE Trans. on Signal Processing, Aug., 2007.   [3] Chun-Yang Chen and P. P. Vaidyanathan, “MIMO Radar Space-Time Adaptive Processing Using Prolate Spheroidal Wave Functions,” accepted to IEEE Trans. on Signal Processing. Book Chapter [4] Chun-Yang Chen and P. P. Vaidyanathan, “MIMO Radar Space-Time Adaptive Processing and Signal Design,” invited chapter in MIMO Radar Signal Processing, J. Li and P. Stoica, Wiley, to be published. Chun-Yang Chen, Caltech DSP Lab | Candidacy

Publications Conference Papers [5] Chun-Yang Chen and P. P. Vaidyanathan, “A Subspace Method for MIMO Radar Space-Time Processing,” IEEE International Conference on Acoustics, Speech, and Signal Processing Honolulu, Hi, April 2007. [6] Chun-Yang Chen and P. P. Vaidyanathan, “Beamforming issues in modern MIMO Radars with Doppler,” Proc. 40th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov. 2006.   [7] Chun-Yang Chen and P. P. Vaidyanathan, “A Novel Beamformer Robust to Steering Vector Mismatch,” Proc. 40th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov. 2006. [8] Chun-Yang Chen and P. P. Vaidyanathan, “Precoded V-BLAST for ISI MIMO channels,” IEEE International Symposium on Circuit and System Kos, Greece, May 2006, [9] Chun-Yang Chen and P. P. Vaidyanathan, “IIR Ultra-Wideband Pulse Shaper Design,” Proc. 39th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, Nov. 2005.   Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

Future Topic – Waveform Design in MIMO Radar In SIMO radar, chirp waveform is often used in the transmitter to increase the range resolution. This technique is called pulse compression. target Radar R Received Signal Matched filter output Time Range resolution Chun-Yang Chen, Caltech DSP Lab | Candidacy

Future Topic – Waveform Design in MIMO Radar In MIMO radar, multiple orthogonal waveforms are transmitted. These waveforms affects not only the range resolution but also angle and Doppler resolution. It is not clear how to design multiple waveforms which provide good range, angle and Doppler resolution. Range resolution Angle resolution Doppler f2(t) f1(t) f0(t) Chun-Yang Chen, Caltech DSP Lab | Candidacy

Q&A Thank You! Any questions? Chun-Yang Chen, Caltech DSP Lab | Candidacy

Simulations – Beampattern -0.4 Clutter -0.3 -0.2 Jammer 2 Jammer 1 -0.1 Normalized Doppler Frequency Target 0.1 0.2 0.3 0.4 0.5 -0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5 Normalized Spatial Frequency Parameters: N=10, M=5, L=16, CNR=50dB 2 jammers, JNR=40dB Target: (0,0.25) Proposed ZF Method Chun-Yang Chen, Caltech DSP Lab | Candidacy

Space-Time Beam Pattern Normalized Doppler Freq. Normalized Spatial Freq. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

Space-Time Beam Pattern Velocity mismatch Normalized Doppler Freq. Normalized Spatial Freq. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

Space-Time Beam Pattern Velocity misalignment Normalized Doppler Freq. Normalized Spatial Freq. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

Space-Time Beam Pattern Internal clutter motion (ICM) Normalized Doppler Freq. Normalized Spatial Freq. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

MIMO vs. SIMO Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

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

Clutter Power in PSWF Vector Basis Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

Simulations K: number of samples Kv: number of clutter free samples Parameters: N=10, M=5, L=16 CNR=50dB 2 jammers, JNR=40dB SINR of a target at angle zero and Doppler frequencies [-0.5, 0.5] MVDR perfect R -2 Sample matrix inversion K=2000 -4 Proposed method K=300,Kv=20 -6 SINR (dB) Proposed ZF method Kv=20 -8 Diagonal loading K=300 -10 Principal component K=300 -12 -14 This is a example of the SINR of a target at angle zero and Doppler frequencies from -0.5 to 0.5. The y-axis is the SINR and the x-axis is the Doppler frequency. This is the SINR for the sample matrix inversion with 2000 samples. These are the SINR for the proposed methods. We can see that the number of samples are much smaller than the direct method. These are the SINR of diagonal loading and the principle component methods. With the same number of samples, the proposed methods has better performance. This is because the methods fully utilize the structure of the matrix and use a concise way to represent the signals. Therefore the STAP method converges faster. K: number of samples Kv: number of clutter free samples collected in passive mode -16 -0.5 -0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5 Normalized Doppler frequency Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

MIMO Radar – Virtual Array (2) [D. W. Bliss and K. W. Forsythe, 03] + = Virtual array: NM elements Transmitter: M elements Receiver: N 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. Using this idea, we can create the spatial resolution like a receiver array with NM elements. NM degrees of freedom can be created using only N+M physical array elements. However, because there is no focused beam in MIMO radar a processing gain of M is lost. But for some application that dose not require focused beam such as imaging or scanning. This is not a problem. A processing gain of M is lost because of the broad transmitting beam. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

Efficient Representation for the Clutter [D. Slepian, 62] We can stack the clutter signals into a vector c. Then it can be represented by a smaller vector xi. The matrix Psi contains the vectors obtained samples from these prolate spheroidal functions. So, we have this concise basis to represent the clutter signal. The corresponding covariance matrix can be expressed as this form. The inner covariance matrix R_xi is X+1 by X+1. It is much smaller than the covariance matrix R_c. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

Efficient Representation for the Clutter [D. Slepian, 62] consists of We can stack the clutter signals into a vector c. Then it can be represented by a smaller vector xi. The matrix Psi contains the vectors obtained samples from these prolate spheroidal functions. So, we have this concise basis to represent the clutter signal. The corresponding covariance matrix can be expressed as this form. The inner covariance matrix R_xi is X+1 by X+1. It is much smaller than the covariance matrix R_c. NML X+1 Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

Simplification of the Clutter Expression Receiver Transmitter Doppler -2 2 4 6 8 10 12 -1.5 -1 -0.5 0.5 1 1.5 x Re{c(x;fs,i)} Re{c(n+gm+bl;fs,i)} So, we can view the clutter signals as linear combination of some non-uniformly sampled version of the truncated sinusoidal signals. This figure shows the real part of such a signal. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

… T T T T T T … T T … … … T … T T T

X -W W in [0,X] Time window Frequency window