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

Minimum Redundancy MIMO Radar

Chun-Yang Chen and P. P. Vaidyanathan

California Institute of Technology

Electrical Engineering/DSP Lab

ISCAS 2008

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

1Review: MIMO Radar and Virtual Array

3

Advantages– Better spatial resolution [Bliss & Forsythe 03]– Flexible transmit beampattern design [Fuhrmann & San Antonio 04]– Improved parameter identifiability [Li et al. 07]


MIMO Radar

MIMO radar

f2( )tf1( )t

f0( )t

SIMO radar (Traditional)

The radar systems which emits orthogonal (or noncoherent) waveforms in each transmitting antennas are called MIMO radar.

w2 ( )f tw1 ( )f t

w0 ( )f t


SIMO Radar (Traditional)

Transmitter: M antenna elements

ej2p(ft-x/l)

w2 ( )f t w1 ( )f t w0 ( )f t

Transmitter emits

coherent waveforms.

Transmitter emits

coherent waveforms.

Receiver: N antenna elements

ej2p(ft-x/l)

Number of received signals: N

Number of received signals: N


MIMO Radar

ej2p(ft-x/l)

f2( )t f1( )t f0( )t

Transmitter emits

orthogonal waveforms.

Transmitter emits

orthogonal waveforms.


ej2p(ft-x/l)

MF 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


Virtual Array Concept


ej2p(ft-x/l)

q

xT,0=0xT,1xT,2


ej2p(ft-x/l)

q

xR,0=0xR,2


xR,3 xR,1



ej2p(ft-x/l)

q


ej2p(ft-x/l)

q


xT,0=0xT,1xT,2 xR,0=0xR,2xR,3 xR,1

))(sin2

exp( ,,, nRmTmn xxjs



ej2p(ft-x/l)

q


ej2p(ft-x/l)

q



))(sin2

exp( ,,, nRmTmn xxjs



ej2p(ft-x/l)

q


ej2p(ft-x/l)

q




MIMO Radar – Virtual Array

Transmitter: M antenna elements Receiver: N antenna elements

Virtual array: NM elements

q

))(sin2

exp( ,,

,

nRmT

mn

xxj

s

ej2p(ft-x/l)

q

ej2p(ft-x/l)

q



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.

2Review: Minimum Redundancy Linear Array

13

Spacings in Linear Array


q

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.

The beamformer resolves the DoA by observing the phase differences of the antenna elements.

Different phase differences can be observed by different spacings.

Different phase differences can be observed by different spacings.

Minimum Redundancy Linear Array


[Moffet 1968] Minimize the number of array elements by reducing the redundancy of the spacing.


Minimum Redundancy Linear Array




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

Minimum Redundancy Linear Array Given the desired aperture L, the minimum

redundancy array can be found by the following optimization problem:


2/321

subject to

min

'

L},,,{}x{x

N}||{x

N

kk

k

}{xk

2/L


3Minimum Redundancy MIMO Radar

Minimum Redundancy MIMO Radar Recall the virtual array element locations are


locations antenna receiving :

locations antenna ing transmitt:

,

,

nR

mT

x

x

NM elements

}{ ,, nRmT xx

Minimum Redundancy MIMO Radar Recall the virtual array element locations are

The spacings between the virtual array elements are


}{ ,, nRmT xx locations antenna receiving :

locations antenna ing transmitt:

,

,

nR

mT

x

x

}{ ',',,, nRmTnRmT xxxx

NM elements

N2M2 spacings

Minimum Redundancy MIMO Radar The minimum redundancy MIMO Radar can be found by

solving the following optimization problem:


2/21

subject to

min

',',,,

,

,

, ,,

L},,{}xxx{x

M}||{x

N}||{x

MN

nRmTnRmT

nR

mT

}{x}{x nRmT

Example of the minimum redundancy MIMO Radar


0 10 20 30 40 50 60

Receiver3 elements

}{ ,nRx



0 10 20 30 40 50 60

0 10 20 30 40 50 60

Receiver3 elements

Transmitter5 elements

}{ ,mTx

}{ ,nRx



0 10 20 30 40 50 60

0 10 20 30 40 50 60

0 10 20 30 40 50 60

Receiver3 elements


Virtual array15 elements

}{ ,, nRmT xx

}{ ,mTx

}{ ,nRx



0 10 20 30 40 50 60

0 10 20 30 40 50 60

0 10 20 30 40 50 60

Receiver3 elements


Virtual array15 elements

0 10 20 30 40 50 600

5

10

Histogram ofSpacings

}{ ,, nRmT xx

}{ ,mTx

}{ ,nRx

}

{

',',

,,

nRmT

nRmT

xx

xx

0 20 40 60

0 20 40 60

0 20 40 60

0 20 40 60

0 20 40 60

0 20 40 60



Receiver

Transmitter

Virtual array

Histogram ofSpacings

Minimum Redundancy Uniform

0 10 20 30 40 50 600

5

10

0 10 20 30 40 50 600

5

10

15

Simulations: MVDR beamformer


-80 -60 -40 -20 0 20 40 60 80-60

-50

-40

-30

-20

-10

0

10

20

30

40

Angle (degree)

Beam

patt

ern

(d

B)

Target: 0°, 0dB

Interference: [2°, 15°, -60°]

[10, 10, 20] dB

Minimum

Redundancy

SINR=9.74 dB

Uniform

SINR=4.70 dB

Mainlobe interference

White noise: 0dB

The minimum redundancy MIMO structure improves the rejection of mainlobe interferences.

The minimum redundancy MIMO structure improves the rejection of mainlobe interferences.



-80 -60 -40 -20 0 20 40 60 80-60

-50

-40

-30

-20

-10

0

10

20

30

40

Angle (degree)

Beam

patt

ern

(d

B)

Target: 0°, 0dB

Interference: [2°, 15°, -60°]

[10, 10, 20] dB

-20°

White noise: 0dB

No Mainlobe interference



-80 -60 -40 -20 0 20 40 60 80-60

-50

-40

-30

-20

-10

0

10

20

30

40

Angle (degree)

Beam

patt

ern

(d

B)

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.

When there is no mainlobe interference, the minimum redundancy and uniform MIMO structure have about the same SINR.

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.


Q&AThank You!

Any questions?




)2( xkTftje

N-1

I/Q Down-Convert and ADC

w*N-1

1


w*1

0


w*0

+

…

Plane wave-front q

sindsin)1( dN

ywH

HH

H

E yyR

sw

Rwww

1 subject to

min



)2( xkTftje

N-1


w*N-1

1


w*1

0


w*0

+

…

Plane wave-front q

sindsin)1( dN

ywH

HH

H

E yyR

sw

Rwww

1 subject to

min

s1 Rw MVDR beamformer

(Minimum Variance Distortionless Response)

2

2

vw

swvsy

H

H

ESINR

Documents

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