Statistical MIMO Radar

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Statistical MIMO Radar

Abstract Inspired by recent advances in multiple-input multiple-output (MIMO)communications, we introduce the statistical MIMO radar concept. Unlikebeamforming, array radar, or STAP, which presuppose a high correlationbetween signals either transmitted or received by an array, the proposedMIMO radar exploits the independence between signals at the array elements.Whereas correlation-based array techniques are capable of providing degreesof freedom for spatial ltering, they have no bearing on the effects of targetscattering. Radar targets generally consist of many small elemental scatterersthat are fused by the radar waveform and the processing at the receiver toresult in echoes with uctuating amplitude and phase. In conventional radar,

Alex Haimovich and Eran Fishler New Jersey Institute of Technology

phone: 973-596-3534email: [email protected]: eran. [email protected]

Rick BlumLehigh University

email: [email protected]

Len Cimini University of Delaware

email: [email protected]

Dmitry Chizhik and Reinaldo ValenzuelaBell LabsLucent Technologies

email: [email protected]: [email protected]

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4. TITLE AND SUBTITLE Statistical MIMO Radar

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7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) New Jersey Institute of Technology; Lehigh University

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13. SUPPLEMENTARY NOTES See also, ADM001741 Proceedings of the Twelfth Annual Adaptive Sensor Array Processing Workshop,16-18 March 2004 (ASAP-12, Volume 1)., The original document contains color images.

14. ABSTRACT

15. SUBJECT TERMS


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Motivation

Radar targets provide a richscattering environment.

Conventional radars experiencetarget fluctuations of 5-25 dB.

Slow RCS fluctuations (SwerlingI model) cause long fades intarget RCS, degrading radarperformance.

In statistical MIMO the angularspread of the target backscatter

is exploited in a variety of waysto extend the radarsperformance envelope.

Backscatter as a function of azimuth angle,10-cm wavelength [Skolnik 2003].


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The S-MIMO Concept Statistical-MIMO radar offers the potential for significant

gains: Detection/estimation performance Resolution performance

Here, we focus only on detection performance

Our results question the common belief that one shouldmaximize the coherent processing gain.

With S-MIMO a very sparse array of sensors transmits a setof orthogonal waveforms.

By using this approach, we create many "independent"radars, that average out target scintillations.


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Signal Model Point source assumption dominates current models used in

radar theory. This model is not adequate for an array of sensors with large

spacing between the array elements. Distributed target model

Manyrandomscatterers


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Signal Model (Cont.)

1 2

1 2

Denote by the gain between the th transmitter and

th receiver. It can be shown that ~ 0,1 .

Take and . We can show that if either /

or ' ' / ' , then 0,

jk

jk

jk il c

H c jk il

k

j CN

d d d

d d d E

and otherwise

1H jk il E

r1r2

d

d1

d2

d1

t1 t2

d2

d

Target beamwidth


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Phased Array Radar

Phased array radars consist of closely spaced sensors.The gain between each transmitter receiver pair is the same.

Transmitted waveform is

This gives rise to the following received signal m

t s

0 0 0 0

2

0 0 0

odel

, ,

If beamformer is applied at both the transmitter and the receiver,then the received signal at the output of the beamformer equals

, ,

H E t x y x y t t M

E y t x y x

M

r a b s n

a b 2

0y s t n t


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S-MIMO Radar

In S-MIMO radar, the inter element spacing is large. The gain between everytransmitter receiver pair is different.

The received signal is given by

vec ~ CN ,

Each

E t t t

M r Hs n H 0 I

transmitting element transmits one of M orthogonal waveforms.

By matched filtering the received signal at each sensor with each of thetransmitted waveforms we can reconstract

ji r t

Therefore, instead of coherent gain of , we created independent radars.

ji i ji E s t n t M

MN MN


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The Radar Detection Problem

0

1

The radar detection problem:: Target does not exists at delay: Target exists at delay

Assume that all the parameters are known. The optimal detector is the LRTdetector, and it

H H

0

1

1

0

|lo

is given by,

g |

H

H

f t H T

f t H

r

r

S-MIMO Radar

1

22

0

22 1

Denote by the vector that contains the output of a bank of matched filterssampled at . The op

,

timal detector is

whe re 12 MN

H n

FAH

T F P

x

x


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2 22 2

21

2

It is possible to compute the probability of detection as afunction of the probability of false alarm, and i

t equa s

1 1

l

MN MN

n D FA

n

P F F P E M

0

22

1

2 22 2

22

0 0

1

21 1

2

Let , . The optimal detector:

| | 12

1 1

H n

FAH

n D FA

H

n

x t x y s t dt

N T x F P

P F F P EN

r aPhased Array Radar


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The Invariance Detector

2

Assume access to a vector that contains samples ofthe noise process.

Note that is the ML estimate of the noise level.

The optimal detector whose performance depends only onSNR

L

/

(not

Ly

y

1

0

2

2

on the noise level)

This test statistic is very intuitive. It normalizes the UMPtest by the best estimate of the noise level.

H

H

T x

y


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Example: Miss Probability Assume a system with four receiving and one or two transmitting

antennas, M=2, N=4, and the probability of false alarm is 1e-6

0 5 10 15 20 25 3010

-3

10-2

10-1

100

S NR

P M D

S -MIMOPhas ed ArrayI-S -MIMO L=64I-Phas ed Array L=64


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Example: ROC The following figure depicts the ROC. SNR=10dB.

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

P FA

P D

S -MIMOPhased ArrayI-S -MIMO L=64I-Phas ed Array L=64


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Concluding Remarks S-MIMO is a new concept for radar systems.

This concept utilizes spatial diversity in order to overcometarget scintillations.

At 90% probability of detection, the proposed systemoutperform phased array radars by 5 dB, which is equivalentto almost twice the range.

The S-MIMO radar can be shown to have superiorperformance in range estimation and resolution as well.


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Statistical MIMO Radar