MIMO Radar -- Diversity Means Superiority - MIT Lincoln · PDF file ·...

SAL, Dept. of ECE 1

MIMO Radar-- Diversity Means Superiority

Jian Li

Department of Electrical and Computer Engineering University of Florida

Gainesville, Florida, USA

Petre Stoica

Department of Information Technology,

Uppsala University,Uppsala, Sweden

Collaborators: William Roberts, Yao Xie, Luzhou Xu

SAL, Dept. of ECE 2

Outline

IntroductionParameter Identifiability

Generic sufficient conditionsCramer-Rao boundsLeast-squares estimator

Adaptive MIMO TechniquesCaponGeneralized Likelihood Ratio Test

Flexible Transmit Beampattern DesignsBeampattern matching DesignMinimum Sidelobe Beampattern DesignComparison with Phased-Array CounterpartApplications

Summary

SAL, Dept. of ECE 3

Introduction

MIMO RadarMultiple DifferentTransmitted Waveforms

Either correlated or uncorrelated

Phased-Array RadarSingle Waveform Scaled and

TransmittedCan be MIMOSpecial Case:

SIMO: Single-Input Multiple-Output

SAL, Dept. of ECE 4

Outline





Summary

SAL, Dept. of ECE 5

Generic Sufficient Conditions

Parameter Identifiability: Maximum number of targets that can be uniquely identified

High SNRLarge Snapshot Number

Phased-Array:

MIMO Radar:

Depending on array geometry and the number of shared antennas between transmit and receive arrays.

SAL, Dept. of ECE 6

Superior Parameter Identifiability

The maximum number of targets that can be uniquely identified by a MIMO radar is up to times of its phased-array counterpart.

= Transmit Antenna Number

SAL, Dept. of ECE 7

Example 1

: Receiving antenna.

: Transmitting antenna,

1 2 3 4 5 6 7 8 9 10

ULAHalf-wavelength spacingOmnidirectional probing (orthogonal waveforms)

SAL, Dept. of ECE 8

Example 1: Cramer Rao Bound

Consistent with theoretical analysis:

- Phased-array:

- MIMO radar:

CRB of first target location vs. target number.

SAL, Dept. of ECE 9

Example 1: LS Estimator

All 12 target locations can be approximately determined from peak locations.

SAL, Dept. of ECE 10

Example 2

Receiving ULA: 0.5-wavelength spacing

Transmitting ULA: 2.5-wavelenth spacing

Orthogonal waveforms

: Receiving antenna.: Transmitting antenna,

1 2 3 8 94 5 6 7


Example 2: Cramer-Rao Bound

CRB of first target location vs. target number.

Consistent with theoretical analysis:

- Phased-array:

- MIMO radar:


Example 2: Least Squares Estimator

All 16 target locations can be approximately determined from peak locations.


Outline





Summary


Adaptive MIMO Radar MIMO Radar

Different Targets Reflect Different WaveformsAdaptive techniques directly applicable

Phased-ArrayDifferent Targets Reflect Identical WaveformAdaptive Techniques Not Directly Applicable

= covariance matrix of reflected waveforms


Example 3

: Receiving antenna.

: Transmitting antenna,

1 2 3 4 5 6 7 8 9 10

Three Targets at -40, 0, 40 degreesOne Strong Jammer at 25 degreesJammer Waveform Uncorrelated with Radar Transmitted WaveformsUncorrelated Radar Transmitted Waveforms

Omnidirectional ProbingULA

Half-wavelength spacing


Example 3: Capon and GLRT

−50 0 500

0.5

1

1.5

2

Cap

on

Sp

ectr

um

Angle (degree)−50 0 50

0

0.5

1

1.5

2

GL

RT

Angle (degree)

Capon Spatial Spectrum GLRT Pseudo-Spectrum

No false peak


Outline





Summary


Transmit Beampattern

Covariance Matrix of Transmitted Waveforms

Transmit Beampattern

Uniform Elemental Power Constraint


Beampattern Matching Design

Design GoalsMinimize difference between

synthesized and desired beampatternsMinimize cross-correlations

among target reflected waveformsConstraint

Total power or(Equal) elemental power

Can be formulated as Semi-definite Quadratic Program (SQP)

−50 0 500

0.5

1

1.5

Angle (degree)

Bea

mp

atte

rn

−50 0 500

0.5

1

1.5

2

2.5

3

Angle (degree)

Bea

mp

atte

rn


Several Examples

•M=10•Equal Elemental Power•Total Power = 1•ULA•Half-wavelength spacing -80 -60 -40 -20 0 20 40 60 800

0.5

1

1.5

2

2.5

3

Angle (degree)

Bea

mpa

ttern

-80 -60 -40 -20 0 20 40 60 800

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Angle (degree)

Bea

mpa

ttern

-80 -60 -40 -20 0 20 40 60 800

0.5

1

1.5

2

2.5

3

3.5

4

4.5

DOA (Degree)

Mag

nitu

de o

f Bea

mpa

ttern


Example 3: Further Probing

Blockdiagram

Optimal Probing

Initial probing

Initial Omnidirectional

Probing

GLRT

Angle/Amplitude Estimation

Capon

BeampatternMatching

AML CaponEnhanced Angle/Amplitude Estimation


Example 3: MSE Improvement

Angle MSE vs. Reciprocal of Noise Power

10+ dB 10+ dB

Amplitude MSE vs. Reciprocal of Noise Power

•M=10, ULA, Half-wavelength spacing•Equal Elemental Power, Total Power = 1•Targets at -40, 0, 40 degrees; Jammer at 25 degrees


Example 3: Resolution

Targets now at -40, 0, 3 degrees Omnidirectional Beampattern Matching

Capon

GLRT

-80 -60 -40 -20 0 20 40 60 800

0.5

1

1.5

Cap

on S

pect

rum

Angle (degree) -80 -60 -40 -20 0 20 40 60 800

0.5

1

1.5

Cap

on S

pect

rum

Angle (degree)

-80 -60 -40 -20 0 20 40 60 800

0.5

1

1.5

GLR

T

Angle (degree)-80 -60 -40 -20 0 20 40 60 80

0

0.5

1

1.5

GLR

TAngle (degree)


Beampattern MatchingMIMO vs. Phased-Array

Phased-Array counterpart no longer convex optimization problemMIMO design is Semi-Definite Relaxation (SDR) of Phased-Array design

Can be used as initial condition of Newton-type search).

Phased-arrayDOF = 9

MIMO DOF = 90

−50 0 500

0.5

1

1.5

2

2.5

3

Angle (degree)

Bea

mp

atte

rn

−50 0 500

0.5

1

1.5

2

2.5

3

Angle (degree)B

eam

pat

tern

•M=10•Equal Elemental Power•Total Power = 1•ULA•Half-wavelength spacing


Minimum Sidelobe BeampatternDesign

Design GoalMinimize peak sidelobe levelAchieve prescribed 3 dB main-

beam widthSubject to either total power or (equal) elemental power constraint

Can be formulated as Semi-Definite Program (SDP)

MIMO Design is SDR of Phased-Array Design

MIMO design is used as initial condition for Newton-type search to obtain phased-array design


Minimum Sidelobe Design Example

M=10 (uniform elemental power constraint, 0.1 per element)Mainbeam pointing at3 dB Mainbeam width = 20 degreesSidelobe regionULA, Half-wavelength spacing

0 0θ =

MIMO Phased-array

−50 0 50−30

−20

−10

0

10

20

Angle (degree)

Bea

mp

atte

rn (

dB

)

−50 0 50−30

−20

−10

0

10

20

Angle (degree)

Bea

mp

atte

rn (

dB

)

90 , 20 20 ,90⎡ ⎤ ⎡ ⎤− − ∪⎣ ⎦ ⎣ ⎦


Minimum Sidelobe Design Example

Relaxed Elemental Power ConstraintWithin 20% of 0.1 for each elemental powerTotal transmitted power = 1

−50 0 50−30

−20

−10

0

10

20

Angle (degree)

Bea

mp

atte

rn (

dB

)

−50 0 50−30

−20

−10

0

10

20

Angle (degree)B

eam

pat

tern

(d

B)

MIMO Phased-array


Applications

Directed Energy System for Homeland Defense

All antennas transmit at their maximum powerLarge apertureSufficient mainbeamwidth since target is movingNo impact on friendly targets


Thermal Therapy

Thermal Therapy System in Medicine

Ultrasound has good penetrationAll transducers transmit at a low power to avoid harming healthy tissueLarge aperture needed to deliver sufficient energySufficient mainbeam width needed


Drowning in Sound

“It’s clear that the ocean is under siege from a lot of different sources.”

[1] Jean Kumagai, “Drowning in Sound,” IEEE Spectrum, April 2006.

Whale stranded during a military sonar exercise near Canary Islands in July 2004 [1]


Reduce Ocean Noise

Distributed Sensor Network?Large Aperture to Deliver Sufficient Energy At Focal PointLow Power Transmitted by Each SensorWaveform Diversity to Achieve Desired Mainbeam Width

Currently, 220 dB pulses generated by active sonar and air-gun arrays [1]


Outline





Summary


Summary

Waveform Diversity Offered by MIMO Radar Enables Significant Superiority Over Its Phased-Array Counterpart

Parameter IdentifiabilityDirect Applicability of Adaptive TechniquesFlexible Transmit Beampattern Designs

MIMO Applications are DiverseDefenseMedicine

Probing FurtherMany fundamental issues need to be addressed on MIMO Your thoughts?

MIMO Radar -- Diversity Means Superiority - MIT Lincoln · PDF file ·...

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