1. Minimum Redundancy MIMO Radar Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP Lab ISCAS 2008

2. Outline  Review of the background –MIMO radar and virtual array –Minimum redundancy linear array  Minimum redundancy MIMO radar –Extension of the minimum redundancy idea –Examples and simulations  Conclusion 2Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008

3. 1 Review: MIMO Radar and Virtual Array 3

4. AAdvantages –B–Better spatial resolution [Bliss & Forsythe 03] –F–Flexible transmit beampattern design [Fuhrmann & San Antonio 04] –I–Improved parameter identifiability [Li et al. 07] 4Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 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 

5. 5Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 SIMO Radar (Traditional) Transmitter: M antenna elements e j2  (ft-x/ ) w 2  w 1  w 0  Transmitter emits coherent waveforms. Transmitter emits coherent waveforms. Receiver: N antenna elements e j2  (ft-x/ ) Number of received signals: N Number of received signals: N

6. 6Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 MIMO Radar e j2  (ft-x/ )         Transmitter emits orthogonal waveforms. Transmitter emits orthogonal waveforms. Transmitter: M antenna elements e j2  (ft-x/ ) MF … … Matched filters extract the M orthogonal waveforms. Overall number of signals: NM Matched filters extract the M orthogonal waveforms. Overall number of signals: NM Receiver: N antenna elements

7. Virtual Array Concept 7Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 e j2  (ft-x/ )  x T,0 =0x T,1 x T,2 Receiver: N antenna elements e j2  (ft-x/ )  x R,0 =0x R,2 Transmitter: M antenna elements x R,3 x R,1

8. Virtual Array Concept 8Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 e j2  (ft-x/ )  Receiver: N antenna elements e j2  (ft-x/ )  Transmitter: M antenna elements x T,0 =0x T,1 x T,2 x R,0 =0x R,2 x R,3 x R,1

9. Virtual Array Concept 9Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 e j2  (ft-x/ )  Receiver: N antenna elements e j2  (ft-x/ )  Transmitter: M antenna elements x T,0 =0x T,1 x T,2 x R,0 =0x R,2 x R,3 x R,1

10. Virtual Array Concept 10Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 e j2  (ft-x/ )  Receiver: N antenna elements e j2  (ft-x/ )  Transmitter: M antenna elements x T,0 =0x T,1 x T,2 x R,0 =0x R,2 x R,3 x R,1

11. 11Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 MIMO Radar – Virtual Array Transmitter: M antenna elementsReceiver: N antenna elements Virtual array: NM elements  e j2  (ft-x/ )   x T,0 =0x T,1 x T,2 x R,0 =0x R,2 x R,3 x R,1

12. 12Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 MIMO Radar – Virtual Array Receiver: N elements Virtual array: NM elements Transmitter: M elements += [D. W. Bliss and K. W. Forsythe, 03] The spatial resolution 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.

13. 2 Review: Minimum Redundancy Linear Array 13

14. Spacings in Linear Array 14Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008   Spacing=1: 4  Spacing=2: 3  Spacing=3: 2  Spacing=4: 1 The beamformer resolves the DoA by observing the phase differences of the antenna elements. Different phase differences can be observed by different spacings.

15. Minimum Redundancy Linear Array 15Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 [Moffet 1968] Minimize the number of array elements by reducing the redundancy of the spacing.

16. Minimum Redundancy Linear Array 16Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 [Moffet 1968] Minimize the number of array elements by reducing the redundancy of the spacing.  Spacing=1: 2  Spacing=2: 1  Spacing=3: 1  Spacing=4: 1  Spacing=5: 1  Spacing=6: 1  Spacing=7: 1  Spacing=8: 1  Spacing=9: 1

17. Minimum Redundancy Linear Array  Given the desired aperture L, the minimum redundancy array can be found by the following optimization problem: 17Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008

18. 18Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 3 Minimum Redundancy MIMO Radar

19.  Recall the virtual array element locations are 19Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 NM elements

20. Minimum Redundancy MIMO Radar  Recall the virtual array element locations are  The spacings between the virtual array elements are 20Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 NM elements N 2 M 2 spacings

21. Minimum Redundancy MIMO Radar  The minimum redundancy MIMO Radar can be found by solving the following optimization problem: 21Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008

22. Example of the minimum redundancy MIMO Radar 22Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 0102030405060 Receiver 3 elements

23. Example of the minimum redundancy MIMO Radar 23Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 01020304050600102030405060 Receiver 3 elements Transmitter 5 elements

24. Example of the minimum redundancy MIMO Radar 24Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 01020304050600102030405060 Receiver 3 elements Transmitter 5 elements Virtual array 15 elements

25. Example of the minimum redundancy MIMO Radar 25Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 01020304050600102030405060 Receiver 3 elements Transmitter 5 elements Virtual array 15 elements 0102030405060 0 5 10 Histogram of Spacings

26. 0204060 0204060 0204060 Example of the minimum redundancy MIMO Radar 26Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 Receiver Transmitter Virtual array Histogram of Spacings Minimum RedundancyUniform 0102030405060 0 5 10 0 2030405060 0 5 10 15

27. Simulations: MVDR beamformer 27Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 -80-60-40-20020406080 -60 -50 -40 -30 -20 -10 0 10 20 30 40 Angle (degree) Beampattern (dB) Target: 0°, 0dB Interference: [2°, 15°, -60°] [10, 10, 20] dB Minimum Redundancy SINR= 9.74 dB Uniform SINR= 4.70 dB Mainlobe interference Mainlobe interference White noise: 0dB The minimum redundancy MIMO structure improves the rejection of mainlobe interferences.

28. Simulations: MVDR beamformer 28Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 -80-60-40-20020406080 -60 -50 -40 -30 -20 -10 0 10 20 30 40 Angle (degree) Beampattern (dB) Target: 0°, 0dB Interference: [2°, 15°, -60°] [10, 10, 20] dB -20° White noise: 0dB No Mainlobe interference No Mainlobe interference

29. Simulations: MVDR beamformer 29Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 -80-60-40-20020406080 -60 -50 -40 -30 -20 -10 0 10 20 30 40 Angle (degree) Beampattern (dB) Target: 0°, 0dB Interference: [-20°, 15°, -60°] [10, 10, 20] dB Minimum Redundancy SINR= 11.19 dB Uniform SINR= 11.70 dB White noise: 0dB When there is no mainlobe interference, the minimum redundancy and uniform MIMO structure have about the same SINR.

30. Conclusion & Future work  We have extended the minimum redundancy idea to the MIMO radar. –Reducing multiple occurrence of identical spacings in the virtual array –Larger aperture can be obtained with fewer elements –The simulation shows that the proposed structure improves rejection of mainlobe interference.  Future work –Design the nonuniform MIMO array structure with more sophisticated optimization criteria. 30Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008

31. Q&A Thank You! Any questions? 31Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008

32. Simulations: MVDR beamformer 32Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 N-1 I/Q Down- Convert and ADC w * N-1 1 I/Q Down- Convert and ADC w*1w*1 0 w*0w*0 + … Plane wave-front 

33. Simulations: MVDR beamformer 33Chun-Yang Chen, Caltech DSP Lab | ISCAS 2008 N-1 I/Q Down- Convert and ADC w * N-1 1 I/Q Down- Convert and ADC w*1w*1 0 w*0w*0 + … Plane wave-front  MVDR beamformer (Minimum Variance Distortionless Response)