mimo radar: resolution, performance, and waveforms · mimo radar: resolution, performance, and...

MIT Lincoln Laboratoryasap06Radar-1

Bliss/Forsythe/Fawcett

MIMO Radar:Resolution, Performance, and Waveforms

Dan BlissKeith ForsytheGlenn Fawcett

MIT Lincoln Laboratory

This work was sponsored by the United States Air Force under Air Force Contract FA8721-05-C-0002. Opinions, interpretations, conclusions, and

recommendations are those of the authors and are not necessarily endorsed by the United States Government.



Topics

• MIMO radar introduction

• MIMO resolution improvement

• Waveform optimization for improved SINR

• Waveform optimization for angle estimation



Static MIMO Radar

• Simultaneously transmit different (but possibly correlated) signals from each antenna

• Use transmitted and received signals to produce virtual MIMO response

• Translate MIMO response to bearing-range image

TransmitAntenna

Array

ReceiveAntenna

Array

Scatterers

Range

Bea

ring



MIMO versus Traditional Radar

TransmitArray

ReceiveArray

TraditionalRadar

Illuminated Area

TransmitArray

Illuminated AreaReceiveArray

MIMORadar

IndependentSignals

Range

Bea

ring

Range

Bea

ring

Multi-BeamMIMORadar

TransmitArray

ReceiveArray

Illuminated Area

IndependentSignals

ASNRAng

le E

rror



-d

0

d

MIMO Radar Channel

TransmitArray

ReceiveArray

ReceivedSignals

ChannelMatrices

TransmittedSignals

Notional Model

-d

0

d

Array Responses

MIMOVirtualArray

-d

0

d

2d

-2d

x 2

x 3

x 2

• Channel estimate provides estimate of MIMO virtual array

• Virtual array may over-represented elements

– Convolution of real arrays produces produces virtual array

– Suggesting sparse arraysx 1

x 1



MIMO Virtual Array Geometry

• MIMO virtual array positions are convolution of traditional transmit and receive array element positions

Real ReceiveArray

Element Weighting On Regular Array

MIMO Virtual ArrayReal TransmitArray

∗

MIMO Virtual Array

• Sparse real arrays can produce filled virtual arrayReal Transmit Array Real Receive Array

∗



Topics





APERTURE



MIMO Sidelobe Bounds

• MIMO enables use of sparse arrays while maintaining sidelobe levels

• Difficult to compare arrays– Resolution vs. sidelobe tradeoff– Optimization problem dependent

• Use regular filled array for comparison

• Indirect bound

• Maximum virtual contiguous region

MIMO Virtual Array

Consider Only Contiguous Region Real Sparse Array

Real Filled Array

Beam Pattern

Bearing (filled beamwidths)

Rel

ativ

e Po

wer

(dB

) SIMO

MIMO

SparseFilled

*



“Monostatic” MIMO Filled-Aperture

MIMO Aperture Bounds

Con

tiguo

us V

irtua

lM

IMO

Ape

rtur

e (λ

/2)

Number of Real Antennas

LowerBound

UpperBound

• Upper contiguous MIMO aperture bound

“Mono-Static” MIMO

Transmit &Receive

Array

Real Array

MIMO ApertureMaximize

• Lower contiguous MIMO aperture bound

– Specific construction

Contiguous Length:

# Real Antennas:



Distributed MIMO Virtual Filled Aperture

• Virtual aperture limited by• Achievable if transmit and receive

locations are independent

Distributed MIMO

TransmitArray

ReceiveArray

∗Real Transmit Array Real Receive

Array

MIMO Virtual Array

Beam Pattern

Bearing (Filled Beamwidths)

Rel

ativ

e Po

wer

(dB

)

Rece

ive

Tran

smit

MIMO



Topics







ConvolveWith

Channel

ReceiveSignal

Space-Time

Channel

RemapTo Virtual

Array

MatchedFilter

Basic MIMO Radar Processing

ReceiveAntenna

Array

TransmitAntenna

Array

ReceivedSignals

ChannelMatrices

TransmittedSignals

Notional Model

Independent TXWaveforms

TX #1

TX #2

TX #N

…

Scattering Field

Range

Bea

ring

Least Squared Estimator

Space-Time Channel Est.

Rec

eive

Ant

.

Range x Transmit Ant.

MIMO Response

Range

MIM

O V

irtua

l Arr

ay

RemapRemap

Image

Range

Bea

ring

MatchedFilter

MatchedFilter



Adaptive Waveform MIMO Radar

• Iterative approach• Second pass use

knowledge from first• Modify transmitted

waveforms

QuickTime™ and a decompressor

are needed to see this picture.



FFT



Remap

MIMO Processing

SelectPixels of Interest

SelectPixels of Interest

WaveformOptimizationWaveform

Optimization

Optimized TXWaveforms

TX #1

TX #2

TX #N

…



Waveform Optimization

Options• Maximize estimated channel power• Maximize estimated target response

Received Signal

Transmitted Signal

Not Necessarily AchievableDue to Block Toeplitz Structure

of

User-Defined Importance Weighted

Space-TimeChannel Estimate

Constrained Optimization

Solution (sort of)



Random WaveformScattering Field

Bea

ring

Rel

ativ

e En

ergy

(dB

)

Range Range

Performance Enhancementbearing/Range Images

8x8 MIMO Radar

8 Tr

ansm

itAn

tenn

as

8 Re

ceiv

eAn

tenn

as

Target Optimized Waveform

Range

Optimized Waveform

Range

Bea

ring



Performance EnhancementStatistics

Target-to-Clutter RatioImprovement

CD

FTarget

Optimized

ChannelOptimized

Spat

ial-o

nly

• Effects of waveform optimization

• Target-to-clutter ratio improvement significant

• Subtle benefit of space-time optimization is disappointing

Spac

e-tim

e

Better



Topics







Clutter-Free Single TargetWaveform Optimization

target

8 x 8 MIMO RadarTransmit & Receive Patterns

Transmit Aperture = 6 x Receive Aperture

• Cramér-Rao-based optimization• “Optimal” waveform uses

difference beam only– Minimizes power on target

• Employ difference and other beams

– Transmit independent sequences on each beam

Transmit

DifferenceB

eam

Receive SumPattern

Transmit

SumB

eam

ReceiveAntenna

Array

TransmitAntenna

Array

Single Target



Accuracy of Angle EstimatesComparison of Simulation and Bounds

Sum-Beam BoundMixture BoundDifference-BeamBound

75% Sum Beam25% Difference Beam

ASNR (dB)

ML estimator agrees at higher SNR

ML

Sum-Beam BoundMixture BoundDifference-BeamBound

ASNR (dB)

10% Sum Beam90% Difference Beam

MLEstimateML estimator agrees at even higher SNR

Sum-Beam BoundMixture BoundDifference-BeamBound7% Each Ortho Beam50% Difference Beam

ASNR (dB)

ML

• Vary mixture of transmit power

• Transmit difference beam improves asymptotic performance

• Transmitting in all modes (full MIMO) improves finite performance



Summary

• Introduced new MIMO radar concepts

• Demonstrated up to order N improvement in MIMO virtual array aperture

• Improved MIMO radar target SINR using waveform optimization techniques

• Reduced angle-estimation error using MIMO waveform optimization technique



MIMO Radar Degrees of Freedom

• Dimension of space:• Dimension of subspace depends upon

transmit and receive array geometry

Assuming

Tradition Array Processingn Degrees Of Freedom

AdaptiveReceiver

Adaptive TransmitAnd Receive

2 n Degrees Of FreedomAdaptiveReceiver

& Transmitter

Distributed MIMOn2 Degrees Of Freedom

TransmitIndependentWaveforms

ReceiveWaveforms

“Mono-Static” MIMOn(n+1)/2 Degrees Of Freedom

Transmit &Receive

IndependentWaveforms



Performance EnhancementStatistics

Target-to-Clutter RatioImprovement

CD

F

TargetOptimized

ChannelOptimized

CD

F TargetOptimized

ChannelOptimized

Target PowerImprovement

spat

ial

spat

ial

mimo radar: resolution, performance, and waveforms · mimo radar: resolution, performance, and...

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