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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 on theme: "Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP."— Presentation transcript:

1 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

2 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

3 1 Problem Formulation 3

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

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

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

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

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

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

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

11 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)

12 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)

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

14 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

15 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

16 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

17 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

18 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

19 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

20 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

21 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

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

23 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]

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

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

26 2 Proposed Algorithm 26

27 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

28 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

29 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

30 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.

31 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

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

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

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

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

36 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

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

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

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

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

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

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

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

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

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

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

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

48 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

49 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

50 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

51 Numerical Examples 51Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 05101520253035404550 20 22 24 26 28 30 32 34 36 38 40 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

52 Numerical Examples 52Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009 -10-50510152025303540 -50 -40 -30 -20 -10 0 10 20 30 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)

53 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]

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

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