joint mimo radar waveform and receiving filter optimization chun-yang chen and p. p. vaidyanathan...
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![Page 1: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/1.jpg)
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
![Page 2: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/2.jpg)
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
![Page 3: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/3.jpg)
1Problem Formulation
3
![Page 4: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/4.jpg)
Extended Target vs. Point Target
4Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
)(tfPoint Target
![Page 5: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/5.jpg)
Extended Target vs. Point Target
5Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
)(tf )( trfPoint Target
r : radar cross section : delay
![Page 6: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/6.jpg)
Extended Target vs. Point Target
6Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
)(tf
)(tf )( ii tfr
)( trfPoint Target
![Page 7: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/7.jpg)
Extended Target vs. Point Target
7Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
dtfr )()(
)(tf
)(tf
)(tf
)( ii tfr
)( trfPoint Target
Extended Target
![Page 8: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/8.jpg)
Extended Target and Clutter
8Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
)(tf
Extended Target Extended Clutter
![Page 9: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/9.jpg)
Extended Target and Clutter
9Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
dtfc
dtfr
)()(
)()(
)(tf
Extended Target Extended Clutter
![Page 10: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/10.jpg)
Extended Target and Clutter
10Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
dtfc
dtfr
)()(
)()(
)(tf
Extended Target
R(s)
C(s)
v(t)f(t)
Extended Clutter
![Page 11: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/11.jpg)
Baseband Equivalent Model
11Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
Modulation R(s)
C(s)
Demodulation
v (t)
f(n) D/A A/D r(n)
![Page 12: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/12.jpg)
Baseband Equivalent Model
12Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
Modulation R(s)
C(s)
Demodulation
v (t)
f(n) D/A A/D r(n)
R(z)
C(z)
v (n)
f(n)
)()(
)()(
mnfmc
mnfmr
![Page 13: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/13.jpg)
Detection Problem
13Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
H0
H1 Target
Clutter
![Page 14: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/14.jpg)
Detection Problem
14Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
H0
H1 Target
Clutter
R(z)
C(z)
v (n)
f(n) H(z) LRT
Receiving filter
H0 or H1
Likelihood ratio test
[Delong & Hofstetter 67] [Pillai et al. 03]
Transmittedwaveform
![Page 15: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/15.jpg)
Detection Problem
15Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
H0
H1 Target
Clutter
R(z)
C(z)
v (n)
f(n) H(z) LRT
Receiving filter
H0 or H1
Likelihood ratio test
[Delong & Hofstetter 67] [Pillai et al. 03]
Transmittedwaveform
![Page 16: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/16.jpg)
SINR Maximization
16Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
R(z)
C(z)
v (n)
f(n) H(z) LRT
Receiving filter
H0 or H1
Likelihood ratio test
Transmittedwaveform
[Delong & Hofstetter 67] [Pillai et al. 03]
u
)( vCfRfh Hu vhCfhRfh HHH
![Page 17: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/17.jpg)
vhCfhRfh HHH
SINR Maximization
17Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
R(z)
C(z)
v (n)
f(n) H(z) LRT
Receiving filter
H0 or H1
Likelihood ratio test
Transmittedwaveform
[Delong & Hofstetter 67] [Pillai et al. 03]
u
)( vCfRfh Hu
1 subject to
max22
2
,
f
vhCfh
Rfhfh
HH
H
EE
![Page 18: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/18.jpg)
vhCfhRfh HHH
SINR Maximization
18Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
R(z)
C(z)
v (n)
f(n) H(z) LRT
Receiving filter
H0 or H1
Likelihood ratio test
Transmittedwaveform
[Delong & Hofstetter 67] [Pillai et al. 03]
u
)( vCfRfh HuSignal
1 subject to
max22
2
,
f
vhCfh
Rfhfh
HH
H
EE
![Page 19: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/19.jpg)
vhCfhRfh HHH
SINR Maximization
19Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
R(z)
C(z)
v (n)
f(n) H(z) LRT
Receiving filter
H0 or H1
Likelihood ratio test
Transmittedwaveform
[Delong & Hofstetter 67] [Pillai et al. 03]
u
)( vCfRfh HuClutter
1 subject to
max22
2
,
f
vhCfh
Rfhfh
HH
H
EE
![Page 20: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/20.jpg)
vhCfhRfh HHH
SINR Maximization
20Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
R(z)
C(z)
v (n)
f(n) H(z) LRT
Receiving filter
H0 or H1
Likelihood ratio test
Transmittedwaveform
[Delong & Hofstetter 67] [Pillai et al. 03]
u
)( vCfRfh HuNoise
1 subject to
max22
2
,
f
vhCfh
Rfhfh
HH
H
EE
![Page 21: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/21.jpg)
vhCfhRfh HHH
SINR Maximization
21Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
R(z)
C(z)
v (n)
f(n) H(z) LRT
Receiving filter
H0 or H1
Likelihood ratio test
Transmittedwaveform
[Delong & Hofstetter 67] [Pillai et al. 03]
u
)( vCfRfh Hu
Power constraint1 subject to
max22
2
,
f
vhCfh
Rfhfh
HH
H
EE
![Page 22: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/22.jpg)
The MIMO Case
22Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
[Friedlander 07]
![Page 23: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/23.jpg)
The MIMO Case
23Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
R(z)
C(z)
v (n)
f(n) H(z) LRT
Receiving filter
H0 or H1
Likelihood ratio test
Transmittedwaveform
u
)( vCfRfh Hu vhCfhRfh HHH
[Friedlander 07]
![Page 24: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/24.jpg)
Prior Information
24Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
1 subject to
max22
2
f
vhCfh
Rfhfh
HH
H
,
EE
Assumptions:
RTarget impulse response is known
![Page 25: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/25.jpg)
Prior Information
25Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
Assumptions:
RTarget impulse response is known
''*jiijCCE2nd order statistics of clutter is known
1 subject to
max22
2
f
vhCfh
Rfhfh
HH
H
,
EE
![Page 26: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/26.jpg)
2 Proposed Algorithm
26
![Page 27: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/27.jpg)
Iterative Algorithm
27Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
R(z)
C(z)
v (n)
f(n) H(z) LRT
Receiving filter
H0 or H1
Likelihood ratio test
Transmittedwaveform
u
1. Fixed f, solve for h
22
2
maxvhCfh
Rfhh
HH
H
EE
![Page 28: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/28.jpg)
Iterative Algorithm
28Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
R(z)
C(z)
v (n)
f(n) H(z) LRT
Receiving filter
H0 or H1
Likelihood ratio test
Transmittedwaveform
u
1. Fixed f, solve for h
2. Fixed h, solve for f
1 subject to
max22
2
f
vhCfh
Rfhf
HH
H
EE
![Page 29: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/29.jpg)
Iterative Algorithm
29Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
R(z)
C(z)
v (n)
f(n) H(z) LRT
Receiving filter
H0 or H1
Likelihood ratio test
Transmittedwaveform
u
1. Fixed f, solve for h
2. Fixed h, solve for f
3. Fixed f, solve for h
22
2
maxvhCfh
Rfhh
HH
H
EE
![Page 30: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/30.jpg)
Iterative Algorithm
30Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
R(z)
C(z)
v (n)
f(n) H(z) LRT
Receiving filter
H0 or H1
Likelihood ratio test
Transmittedwaveform
u
1. Fixed f, solve for h
2. Fixed h, solve for f
3. Fixed f, solve for h
22
2
maxvhCfh
Rfhh
HH
H
EE
SINR is guaranteed to be non-decreasing in each iterative step.
![Page 31: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/31.jpg)
Solving for the Receiver
31Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
22
2
maxvhCfh
Rfhh
HH
H
EE
R(z)
C(z)
v (n)
f(n) H(z) LRT
Receiving filter
H0 or H1
Likelihood ratio test
Transmittedwaveform
u
![Page 32: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/32.jpg)
Solving for the Receiver
32Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
22
2
maxvhCfh
Rfhh
HH
H
EE
hvvhhCCffh
Rfhh
max
2
HHHHH
H
EE
![Page 33: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/33.jpg)
Solving for the Receiver
33Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
hvvhhCCffh
Rfhh
max
2
HHHHH
H
EE
![Page 34: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/34.jpg)
Solving for the Receiver
34Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
hvvhhCCffh
Rfhh
max
2
HHHHH
H
EE
1 subject to
min
Rfh
hvvCCffhhH
HHHH EE MVDR (Minimum Variance Distortionless)
![Page 35: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/35.jpg)
Solving for the Receiver
35Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
hvvhhCCffh
Rfhh
max
2
HHHHH
H
EE
1 subject to
min
Rfh
hvvCCffhhH
HHHH EE MVDR (Minimum Variance Distortionless)
RfvvCCffh-1 HHH EE
![Page 36: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/36.jpg)
Solving for the Waveforms
36Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
1 subject to
max22
2
f
vhCfh
Rfhf
HH
H
EE
R(z)
C(z)
v (n)
f(n) H(z) LRT
Receiving filter
H0 or H1
Likelihood ratio test
Transmittedwaveform
u
![Page 37: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/37.jpg)
Solving for the Waveforms
37Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
1 subject to
max22
2
f
vhCfh
Rfhf
HH
H
EE
1 subject to
max
2
2
f
vhfChhCf
Rfhf
HHHH
H
EE
![Page 38: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/38.jpg)
Solving for the Waveforms
38Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
1 subject to
max22
2
f
vhCfh
Rfhf
HH
H
EE
1 subject to
max
2
2
f
vhfChhCf
Rfhf
HHHH
H
EE
Cannot be solved using MVDR
![Page 39: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/39.jpg)
Solving for the Waveforms
39Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
1 subject to
max22
2
f
vhCfh
Rfhf
HH
H
EE 1 subject to
max
2
2
f
vhfChhCf
Rfhf
HHHH
H
EE
Try Lagrange Method:
![Page 40: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/40.jpg)
Solving for the Waveforms
40Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
1 subject to
max22
2
f
vhCfh
Rfhf
HH
H
EE 1 subject to
max
2
2
f
vhfChhCf
Rfhf
HHHH
H
EE
0
22
22
f
vhfChhCf
fChhCRfhvhfChhCfRfhhRλ
EE
EEE
HHHH
HHHHHHHHH
cannot be solved easily
Try Lagrange Method:
![Page 41: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/41.jpg)
Recasting the Waveform Optimization Problem
41Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
1 subject to
max
2
2
f
vhfChhCf
Rfhf
HHHH
H
EE
![Page 42: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/42.jpg)
1 subject to
max
2
2
f
vhfChhCf
Rfhf
HHHH
H
EE
Recasting the Waveform Optimization Problem
42Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
1 f
![Page 43: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/43.jpg)
Recasting the Waveform Optimization Problem
43Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
1 f
1 subject to
max
2
2
f
vhfChhCf
Rfhf
HHHH
H
EE
1 subject to
max
22
2
f
fvhfChhCf
Rfhf
HHHH
H
EE
![Page 44: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/44.jpg)
Recasting the Waveform Optimization Problem
44Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
1 subject to
max
2
2
f
vhfChhCf
Rfhf
HHHH
H
EE
1 f
1 subject to
max
22
2
f
fvhfChhCf
Rfhf
HHHH
H
EE
![Page 45: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/45.jpg)
Recasting the Waveform Optimization Problem
45Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
22
2
max
fvhfChhCf
Rfhf
HHHH
H
EE
![Page 46: Joint MIMO Radar Waveform and Receiving Filter Optimization Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d2c5503460f94a02166/html5/thumbnails/46.jpg)
Recasting the Waveform Optimization Problem
46Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
22
2
max
fvhfChhCf
Rfhf
HHHH
H
EE
MVDR (Minimum Variance Distortionless)
1 subject to
min2
Rfh
fIvhChhCff
H
HHHH EE
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Recasting the Waveform Optimization Problem
47Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
22
2
max
fvhfChhCf
Rfhf
HHHH
H
EE
MVDR (Minimum Variance Distortionless)
1 subject to
min2
Rfh
fIvhChhCff
H
HHHH EE
hRIvhChhCf H-1
2
HHH EE
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Proposed Algorithm
48Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
R(z)
C(z)
v (n)
f(n) H(z)
Receiving filterTransmittedwaveform
HHE CCffR f Compute .1
RfvvRh 1f ])[( .2 HE
Initialize: Choose a start point for f
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Proposed Algorithm
49Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
R(z)
C(z)
v (n)
f(n) H(z)
Receiving filterTransmittedwaveform
HHE CCffR f Compute .1
RfvvRh 1f ])[( .2 HE
ChhCR HHEh Compute .3
hRIhvvhRf HHHE 1h )][( .4
Initialize: Choose a start point for f
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Proposed Algorithm
50Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
HHE CCffR f Compute .1
RfvvRh 1f ])[( .2 HE
ChhCR HHEh Compute .3
hRIhvvhRf HHHE 1h )][( .4
f
ff .5
Repeat
R(z)
C(z)
v (n)
f(n) H(z)
Receiving filterTransmittedwaveform
Initialize: Choose a start point for f
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Numerical Examples
51Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
0 5 10 15 20 25 30 35 40 45 50
20
22
24
26
28
30
32
34
36
38
40
SIN
R (
dB)
# of iterations
Proposed
Method in [Pillai et al. 03]
LFM (Linear Frequency Modulation)
Matched Filter Bound
Parameters# of transmitters: 2# of receivers: 2Randomly generated impulse response
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Numerical Examples
52Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009
-10 -5 0 5 10 15 20 25 30 35 40-50
-40
-30
-20
-10
0
10
20
30
CNR (dB)
SN
R (
dB)
Proposed
Method in [Pillai et al. 03]
Matched Filter Bound
Parameters# of transmitters: 2# of receivers: 2Averaging 1000randomly generated examples
LFM (Linear Frequency Modulation)
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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]
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Q&AThank You!
Any questions?
54Chun-Yang Chen, Caltech DSP Lab | ICASSP 2009