Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP.

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Presentation transcript:

Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP Lab ICASSP 2009

Outline  Problem Formulation –Extended target and clutter –Detection –MIMO radar  Proposed Algorithm –Iterative algorithm –Receiver –Waveforms  Numerical Examples  Conclusions 2Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009

1 Problem Formulation 3

Extended Target vs. Point Target 4Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 Point Target

Extended Target vs. Point Target 5Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 Point Target : radar cross section : delay

Extended Target vs. Point Target 6Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 Point Target

Extended Target vs. Point Target 7Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 Point Target Extended Target

Extended Target and Clutter 8Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 Extended Target Extended Clutter

Extended Target and Clutter 9Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 Extended Target Extended Clutter

Extended Target and Clutter 10Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 Extended Target R(s) C(s) v(t) f(t) Extended Clutter

Baseband Equivalent Model 11Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 Modu lation R(s) C(s) Demod ulation v (t) f(n) D/A A/D r(n)

Baseband Equivalent Model 12Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 Modu lation R(s) C(s) Demod ulation v (t) f(n) D/A A/D r(n) R(z) C(z) v (n) f(n)

Detection Problem 13Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 H0H0 H1H1 Target Clutter

Detection Problem 14Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 H0H0 H1H1 Target Clutter R(z) C(z) v (n) f(n) H(z)LRT Receiving filter H 0 or H 1 Likelihood ratio test [Delong & Hofstetter 67] [Pillai et al. 03] Transmitted waveform

Detection Problem 15Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 H0H0 H1H1 Target Clutter R(z) C(z) v (n) f(n) H(z)LRT Receiving filter H 0 or H 1 Likelihood ratio test [Delong & Hofstetter 67] [Pillai et al. 03] Transmitted waveform

SINR Maximization 16Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 R(z) C(z) v (n) f(n) H(z)LRT Receiving filter H 0 or H 1 Likelihood ratio test Transmitted waveform [Delong & Hofstetter 67] [Pillai et al. 03] u

SINR Maximization 17Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 R(z) C(z) v (n) f(n) H(z)LRT Receiving filter H 0 or H 1 Likelihood ratio test Transmitted waveform [Delong & Hofstetter 67] [Pillai et al. 03] u

SINR Maximization 18Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 R(z) C(z) v (n) f(n) H(z)LRT Receiving filter H 0 or H 1 Likelihood ratio test Transmitted waveform [Delong & Hofstetter 67] [Pillai et al. 03] u Signal

SINR Maximization 19Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 R(z) C(z) v (n) f(n) H(z)LRT Receiving filter H 0 or H 1 Likelihood ratio test Transmitted waveform [Delong & Hofstetter 67] [Pillai et al. 03] u Clutter

SINR Maximization 20Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 R(z) C(z) v (n) f(n) H(z)LRT Receiving filter H 0 or H 1 Likelihood ratio test Transmitted waveform [Delong & Hofstetter 67] [Pillai et al. 03] u Noise

SINR Maximization 21Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 R(z) C(z) v (n) f(n) H(z)LRT Receiving filter H 0 or H 1 Likelihood ratio test Transmitted waveform [Delong & Hofstetter 67] [Pillai et al. 03] u Power constraint

The MIMO Case 22Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 [Friedlander 07]

The MIMO Case 23Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 R(z) C(z) v (n) f(n) H(z)LRT Receiving filter H 0 or H 1 Likelihood ratio test Transmitted waveform u [Friedlander 07]

Prior Information 24Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 Assumptions: Target impulse responseis known

Prior Information 25Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 Assumptions: Target impulse responseis known 2 nd order statistics of clutteris known

2 Proposed Algorithm 26

Iterative Algorithm 27Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 R(z) C(z) v (n) f(n) H(z)LRT Receiving filter H 0 or H 1 Likelihood ratio test Transmitted waveform u 1. Fixed f, solve for h

Iterative Algorithm 28Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 R(z) C(z) v (n) f(n) H(z)LRT Receiving filter H 0 or H 1 Likelihood ratio test Transmitted waveform u 1. Fixed f, solve for h 2. Fixed h, solve for f

Iterative Algorithm 29Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 R(z) C(z) v (n) f(n) H(z)LRT Receiving filter H 0 or H 1 Likelihood ratio test Transmitted waveform u 1. Fixed f, solve for h 2. Fixed h, solve for f 3. Fixed f, solve for h

Iterative Algorithm 30Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 R(z) C(z) v (n) f(n) H(z)LRT Receiving filter H 0 or H 1 Likelihood ratio test Transmitted waveform u 1. Fixed f, solve for h 2. Fixed h, solve for f 3. Fixed f, solve for h SINR is guaranteed to be non-decreasing in each iterative step.

Solving for the Receiver 31Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 R(z) C(z) v (n) f(n) H(z)LRT Receiving filter H 0 or H 1 Likelihood ratio test Transmitted waveform u

Solving for the Receiver 32Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009

Solving for the Receiver 33Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009

Solving for the Receiver 34Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 MVDR (Minimum Variance Distortionless)

Solving for the Receiver 35Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 MVDR (Minimum Variance Distortionless)

Solving for the Waveforms 36Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 R(z) C(z) v (n) f(n) H(z)LRT Receiving filter H 0 or H 1 Likelihood ratio test Transmitted waveform u

Solving for the Waveforms 37Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009

Solving for the Waveforms 38Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 Cannot be solved using MVDR

Solving for the Waveforms 39Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 Try Lagrange Method:

Solving for the Waveforms 40Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 cannot be solved easily Try Lagrange Method:

Recasting the Waveform Optimization Problem 41Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009

Recasting the Waveform Optimization Problem 42Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009

Recasting the Waveform Optimization Problem 43Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009

Recasting the Waveform Optimization Problem 44Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009

Recasting the Waveform Optimization Problem 45Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009

Recasting the Waveform Optimization Problem 46Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 MVDR (Minimum Variance Distortionless)

Recasting the Waveform Optimization Problem 47Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 MVDR (Minimum Variance Distortionless)

Proposed Algorithm 48Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 R(z) C(z) v (n) f(n) H(z) Receiving filter Transmitted waveform Initialize: Choose a start point for f

Proposed Algorithm 49Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 R(z) C(z) v (n) f(n) H(z) Receiving filter Transmitted waveform Initialize: Choose a start point for f

Proposed Algorithm 50Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 Repeat R(z) C(z) v (n) f(n) H(z) Receiving filter Transmitted waveform Initialize: Choose a start point for f

Numerical Examples 51Chun-Yang Chen, Caltech DSP Lab | ICASSP SINR (dB) # of iterations Proposed Method in [Pillai et al. 03] LFM (Linear Frequency Modulation) Matched Filter Bound Parameters # of transmitters: 2 # of receivers: 2 Randomly generated impulse response

Numerical Examples 52Chun-Yang Chen, Caltech DSP Lab | ICASSP CNR (dB) SNR (dB) Proposed Method in [Pillai et al. 03] Matched Filter Bound Parameters # of transmitters: 2 # of receivers: 2 Averaging 1000 randomly generated examples LFM (Linear Frequency Modulation)

Conclusions  Detection of Extended Target in Clutter –Prior information Target impulse response Clutter statistics  Iterative Algorithm –Recast the problem –MVDR solution  More General Target Impulse Response are considered in the Journal Version –Uncertainty Set (Worst case optimization) –Random 53Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 [Chen & Vaidyanathan, TSP under review]

Q&A Thank You! Any questions? 54Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009