Joseph Tabrikian Signal Processing Laboratory

Department of Electrical and Computer Engineering

Ben-Gurion University of the Negev

Involved collaborators and Research Assistants: Prof. R. Shavit, Prof. H. Messer, Dr. I. Bilik, I. Bekkerman, W. Huleihel, M. Teitel, N. Sharaga, O. Isaacs

BGU Radar Symposium 2016

Cognitive MIMO Radar

Outline

MIMO radar at a glance

Cognitive radar - introduction

Cognitive MIMO radar for beamforming and detection

Conclusion

MIMO Radar at a Glance

Data model: ( ) X H Θ S W

,

,

- Rx signal at sensor and time index

- Tx signal by element and time index

( ) - Tx-Rx channel matrix

- Unknown targets' parameters

1

MIMO -

Phased array - rank( )=1

m n

i n

H

m n

i n

N

c

S

s

s

X

S

H Θ

Θ

R SS

R I

R

Tx elements

Rx elements

MIMO Radar at a Glance

Orthogonal Tx signals can be decomposed at the receiver, allowing adaptive beamforming of the Tx signals → Virtual receiving elements:

Tx elements

Rx element

Single

Tx element

Rx element

Virtual

Rx elements

MIMO Radar at a Glance

Virtual receiving elements: Orthogonal Tx signals can be decomposed at the receiver, allowing adaptive beamforming of the Tx signals.

Tx elements

Rx elements

Colocated (mono-static) MIMO radar: Bekkerman-Tabrikian 2004

Distributed (multi-static) MIMO radar: Fishler et al. 2004

Single

Tx element

Rx elements

Virtual

Rx elements

MIMO Radar Properties

Array aperture extension:

Virtual elements

Transmit elements

Receive elements

Receive elements

Transmit elements

Virtual elements

MIMO Radar Properties

Array aperture extension:

Virtual elements

Transmit/Receive elements

MIMO Radar Advantages

More degrees of freedom due to the virtual sensors:

Higher angular resolution.

Higher number of targets/clutter in a given range-Doppler cell, which can be detected and localized.

Lower sidelobes by virtual spatial windowing.

Digital beamforming of the Tx beams in addition to the Rx beams, and therefore avoid beam shape loss in cases that the target is not in the center of the beam.

Decrease the spatial power density of the Tx signal – spatial spread spectrum (SSS) which is critical for low probability of intercept radars (LPIR).

MIMO Radar Disadvantage

Implementation

Gain loss (omni-directional transmission)

Not a real problem in search mode: omni-directional coverage allows large time-on-target (requires quasi-stationarity or track-before-detect).

A real problem in track/acquisition modes:

If the target direction is known with a given degree of accuracy, then MIMO radar “wastes” its energy towards undesired directions.

Solution: Cognitive MIMO Radar

Cognitive Radar

Proposed by Simon Haykin 2006.

A cognitive radar employs adaptive Tx-Rx based on

history observation and environmental information.

Cognitive Radar

Why the term cognitive is used?

Biological Cognitive Properties versus Cognitive Radars

Cognitive Property Cognitive Radar Equivalent

Perceiving Sensing

Thinking, Reasoning, Judging,

Problem Solving

Expert Systems, Adaptive

Algorithms, and Computation

Remembering Memory, Environmental Database

[Guerci 2011]

NIH definition: “Cognition: conscious mental activity that informs a person about his or her environment. Cognitive actions include perceiving, thinking, reasoning, judging, problem solving and remembering.”

Cognitive MIMO Radar

Optimal Adaptive

Waveform Design Optimal

Receiver/Processor

Detection/

Estimation/

Tracking/

Classification

noise

( )kH Θ

Side Information

kS kX

Data model at the kth step: ( )k k k k X H Θ S W

( ) - MIMO channel matrix, - Target parameterskH Θ Θ

Optimal processor: Detect/localize/track/classify the target(s) based on available measurements, .

Optimal adaptive waveform design: Design the transmit signal at the kth pulse, , based on the measurements during the previous pulses, to optimize a given criterion.

( )

1[ , , ]k

kX X X

kS( 1)

1 1[ , , ]k

k

X X X

Cognitive MIMO Radar

Optimal Adaptive

Waveform Design Optimal

Receiver/Processor

Detection/

Estimation/

Tracking/

Classification

noise

( )kH Θ

Side Information

kSkX

Data model at the kth step: ( )k k k k X H Θ S W

( ) - MIMO channel matrix, - Target parameterskH Θ Θ

( ) ( 1)arg max ( , )

s.t. Tx power constraint

k

opt k

k kC S

S S X

( 1)( , ) - Criterion for perofrmance optimizationk

kC S X

Cognitive Beamforming

Criterion for estimation accuracy: performance bound on the mean-squared-error (MSE):

Bayesian Cramér-Rao bound (BCRB): Simple, but not tight.

Bobrovski-Zakai, Reuven-Messer, or Weiss-Weinstein bounds: High computational complexity, but tighter.

2

,

Power constraint: tr

or / , 1, ,

k

k

k F

T Tn n

P

P N n N

S

S

S R

R

It can be shown that with Gaussian noise, the bounds depend on

1the Tx auto-correlation matrix:

k

H

k kN

SR S S

Cognitive Beamforming

For single unknown parameter, θ, with total Tx power constraint, and zero-mean Gaussian noise with cov. :

( )

( 1) 1 ( 1)

- eigenvector corresponding to the maximum eigenvalue of

( ) E ( ) ( )

k

opt H

k k

k

k H k

k k k

P

S

v

R u u

u

Γ X H R H X

vR

Vector parameter case, - weighted BCRB:

Convex optimization problems, and thus can be solved efficiently (Boyd and Vandenberghe (2004)).

QΘ

Example – Cognitive Beamforming

2

2 2

:

Uniform linear array of transceivers 7 elements

with /2 inter-element spacing.

AWGN with covariance .

ASNR / 6dB.

R

R T

N

R

N N

NPN

Scenario

R I

Posterior pdf’s versus transmit beampatterns .

Auto-focusing effect: Automatic beamforming before detection/estimation.

Example – Cognitive Beamforming *( ) ( ) ( )

k

T

k T TP Sa R a

Single target – direction estimation accuracy, 7 transceivers

Example – Cognitive Beamforming

Probability of resolution compared to space-reversal method.

Two targets – SNR=-2 dB, k=10, 7 transceivers.

Example – Cognitive Beamforming

Cognitive Detection

Sequential Hypothesis Testing (SHT):

Goal: Minimize Average

Sample Number (ASN) to

achieve given error

probabilities: .

, , ,

, ,

1 ,

0

: ( ), 1, ,

: 1,2

,

,

,

k l k l k l

k l

k l

k l

Hl L

Hk

x H Θ w

x w

s

1 , D FAP P

( )

( )

( )

( )

( )

1

( )

0

( )

1

(

1

0 )

0

Decide if:

De

( | )log

(

cide

| ) 1

(

| ) 1log

( | )if:

k

k

k

k

k

D

k

D

k

FA

k

FA

f H PH

H

f H P

f H P

f H P

X

X

X

X

X

X

X

X

Cognitive Detection

Two hypotheses:

Optimal signal design:

( 1),

1 0 0 1

log(1 ) logmax , .

( || ) ( || )

kk

D FA

k k

C

P P

KLD H H KLASN

D H H

S X

1 0

,

0 1

log(1 ) logarg min max , .

( || ) ( || )k

D FAk opt

k k

P P

KLD H H KLD H H

S

S

( 1)( || ) - conditional Kullback-Leibler Divergence given .k

k m nKLD H H X

Cognitive Detection

( 1)

, ,

1

,

1

,

2

1

, ,arg min E

s.t

( )

(

.

)

k

H H

k l k l k l

Lk

k opt k l

l

L

k l

l

P

vS

H Rs Θ Θ

s

sHS X

2

, ) ) 1,2, , ,( ) ( ( , 1,Dj l

Tk Tk l

j T

R T e k l Le

H aΘ a

, max maxk

H

opt Ps

R u u

max

* ( 1)

Eigenvector corresponding to the maximal eigenvalue of the matrix

( (

-

E ) ) .T k

T T

u

a a X

Example - Cognitive Detection

2

4Tx, 16 Rx

/2 inter-element spacing

NF 7dB

RCS 1m

Range=50m

Azimuth=30

Example - Cognitive Detection

24Tx, 16 Rx, NF 7dB, RCS 1m , range=50m, azimuth=30

Conclusions and Future Research

MIMO radar offers great advantages but needs to be used with care.

In cognitive MIMO radar, Tx signal auto-correlation matrix is adaptively optimized. The optimized signal is not necessarily orthogonal (MIMO) or fully correlated (phased array).

Two new cognitive Tx beamforming approaches were presented to optimize: localization accuracy and detection performance

This approach provides an automatic focusing array: beamforming before detectionqestimation.

Future research:

Considering other criteria, such as probability of resolution, or target classification performance.

Thank you!