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ABF-SCJM

JDG 12/19/2005

MIT Lincoln Laboratory

Adaptive Beamforming Techniques for

Sidelobe Control and Mitigation ofNonstationary Interference

JAM

JAM

Jacob D. GriesbachGerald Benitz

MIT Lincoln Laboratory

June 7th, 2005This work is sponsored by the 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.


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MIT Lincoln LaboratoryABF-SCJM 2 of 25

JDG 12/19/2005

Adaptive Beamforming Motivation

Adaptive Beamforming (ABF) suppresses interference to improve SINR

Low sidelobe beams benefit clutter suppression techniques and requirefewer ABF DOFs to mitigate sidelobe jamming

Allow nulling to track inter-CPI interference motion


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Lincoln Multi-Mission ISR Testbed(LiMIT)

System Parametersfor GMTI Mode

System Parametersfor GMTI Mode

9.72 GHz

180 MHz

2,000 Hz

56 ms

8

48 cm

18 cm

Center Freq.

Bandwidth

PRF

CPI

Rx Subarrays

Horiz. Aperture

Vert. Aperture

Boeing 707

Ft. Huachuca, AZ

N

8 km

25 km

NAimpoint

Aircraft

Noise Jammer20-30 dB JNR


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LiMIT GMTI Processing

Receiver /Front-End

8 Receive-Only PRIs provide ABF training data before and after CPI

LiMIT-tuned 2-Parameter Power-Variable-Training STAP algorithm1

LiMIT aperture transmits with a uniform taper that results in multiple Doppler-wrapped clutter ridges

STAP algorithm uses phase to select training samples from modeled clutter ridge

Will not cancel residual interference left over from ABF

Adaptive beamforming goals

Mustsuppress unwanted interference

Low sidelobe beams from ABF help STAP suppress secondary clutter ridges

Must also form a beamset that covers clutter to be mitigated by STAP

CFARDetect

DopplerProcessing

STAP(Adaptive)

BeamformingParam.

EstimateCluster Track

RO ROTransmit / Receive Data (96 PRIs)

8 Receive-Only PRIs 8 Receive-Only PRIs

1G. Benitz, J.D. Griesbach, C. Rader, Two-Parameter Power-Variable Training STAP, Proceedings of the 38th

Asilomar conference on signals, systems, and computers, Pacific Grove, CA, Nov. 7-10, 2004, pp. 2359-2363


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Outline

Colored Noise Loading for Low Sidelobes

Constrained DBU for stable tracking of jammer motion

Data Results

Conclusion


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Low Sidelobe Beamforming

Conventional

B

eamforming

(CBF)

Hv x

Channel

Data (x)

Steering

Vector (v)

Output

Beam Data

CBF

withSVtap

er

Hv Dx

Channel

Data (x)

Steering

Vector (v)

Output

Beam Data

Dv

Taper

( )H

=D D

CBF optimally maximizes SNR to a given v

Sidelobes are controlled (not data adaptive)

Does not necessarily suppress strong or mainbeam interference sources


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Low Sidelobe Adaptive Beamforming

Adaptive

Be

amforming

(ABF)

1H v R x

Channel

Data (x)

Steering

Vector (v)

Output

Beam Data

ABF

withSVtap

er

1H v D R x

Channel

Data (x)

Steering

Vector (v)

Output

Beam Data

Dv

Taper

ABF optimally maximizes SINR to a given v

Sidelobes are not necessarily controlled (data adaptive)

Can suppress strong or mainbeam interference sources


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Colored Noise Loading

Idea: Optimally suppress sidelobes+interference, by modelingexternal sidelobe interference in data covariance

L

clf

clf

Parameters:

= Loading Level

= Loading Frequencyclf

L

( )1 2

( ) ( ) ( ) ( )

cl

H H H

cl

f

L d = + v vR D v v v v D

( )diag=vD v

1( )cl

= +w R R v

Steering

Vector (v)

1( )Hcl

+v R R xChannel

Data (x)

Output

Beam Data


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Sidelobe Jamming Comparison

ABF Tapered SV

Using a tapered steering

vector works with

sidelobe jamming:

Colored noise loading

also works well withsidelobe jamming:

ABF + CNL


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JDG 12/19/2005

Mainbeam Jamming Comparison

ABF Tapered SV

TSV ABF does not

appropriately model

steering vector:

Mainbeam jamming

causes CNL ABF totrade-off jammer &

sidelobe suppression:

ABF + CNL


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ABF Colored Noise Loading

1. Let u1- u

kdenote eigenvectors ofR that have eigenvalues, 2 > T

ev2. Let C denote linear constraints such that CHw = c

=C v 1=c (MVDR constraint)3. Solve

( ) ( )( )

11 1H

cl cl

= + +w R R C C R R C c (Constrained LS)

ABF + CNL

Inequality Constrained ABF


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Inequality Constrained ABFColored Noise Loading

1. Let u1- u

kdenote eigenvectors ofR that have eigenvalues, 2 > T

ev2. Let C denote linear constraints such that CHw = c

=C v 1=c (MVDR constraint)3. Solve

( ) ( )( )

11 1H

cl cl

= + +w R R C C R R C c (Constrained LS)

2 2

1 11

T

i j

=

c

?

i j = C v u u

The ABF now prioritizes the interference above sidelobes by

ensuring the interference is adequately suppressed

4. Check eigenvector inequality constraints

[ ]1 2 21

1 1T

H

k

k

<

u u w

5a. If all constraints are satisfied done

5b. If not add unmet constraints to constraint matrix

6. Go to step 3

Constrained ABF + CNL


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Outline



Data Results

Conclusion


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Derivative Based Updating (DBU)

DBU2 allows an ABF to track a spatially moving jammer Weight vector changes linearly in slow time

where kdenotes the relative pulse index throughout the CPI andn indexes fast-time (range)

An augmented covariance matrix is computed

An adaptive solution is formed for the center of the CPI

DBU may also be applied in frequency for wideband jamming

1 1k

, , , ,2

, , , , ,

1

H H

k n k n k n k nH H

k n k n k n k n k n

kk kKN

=

x x x x

Rx x x x

1

=

0w v

Rw 0

Augmented steering

vector with k= 0

CPI center weight vector

Weight vector derivative

0

2

,1

,

minH

H

k k n

k n=

w v

w xSolvesuch

that 0kk= +w w w

2S.D. Hayward, Adaptive beamforming for rapidly moving arrays, in CIE International Conference Proceedings,Oct. 1996, pp. 480--483

DBU Effects


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DBU Effects(Example Simulation)

Conventional ABF

Spatially

MovingJammer

DBU

k= -1

k= 0

k= 1

Inter-CPI Gain

Variation

Spatially

MovingJammer

C t i d DBU


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Constrained DBU

Constrain DBU result to have constant gain throughout CPI Ensure unit gain on target (MVDR constraint)

Ensure derivative is orthogonal to center weight vector(new constraint)

Optimal solution now given by

01

H

=

w v

w 0

00

H

=

w 0

w v

=

v 0C

0 v[ ]1 0

T=c

( )1

0 1 1H

=

wR C C R C c

w

0k k= +w w w

2

,1

,

minH

k

H

k k n

k n

=

w v

w x

C t i d DBU R lt


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Constrained DBU Results

Conventional DBU Constrained DBU

k= -1

k= 0

k= 1

Constraining the weight derivative to be orthogonal to the

steering vector provides a gain invariant solution Holds gain fixed for steering vector direction

May disrupt sidelobes

Constrained DBU with


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Constrained DBU withColored Noise Loading

Constrained DBU modifications for colored noise loading Add colored noise loading covariance to augmented covariance

Add eigenvector inequality constraints to prioritize jammers oversidelobes

Constrained DBU

k= -1

k= 0

k= 1

Constrained DBU w/ CNL

2

11

1 1cl cl

kK

k kK K

=

R R

=

v 0 u

C 0 v

2

11 0

T

=

c

O tli


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Outline



Data Results

Conclusion

Ft Huachuca GMTI Displays


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Ft. Huachuca GMTI Displays

SAR Image (1m resolution)

Range/Doppler Detection

Range/Doppler Cluster

Range/Angle Localization

GPS Ground Truth

Jammer Angle

07/24/04 CPI# 98045687

GMTI Movie


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GMTI Movie

Range/Doppler Detection

Range/Doppler Cluster

Range/Angle Localization

GPS Ground Truth

Jammer Angle

Desired Beams JammingAngles

07/24/04 CPI# 98045687 98047507

Selected Frames


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Selected Frames

Doppler Aliased

Clutter Filling in

Jammer Null

Close-In

Detection

07/24/04 CPI# 98046337 & 98046437

Tapered Steering Vector (TSV) Comparison


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p g ( ) p30dB Taylor

TSVUndernulled

Jammer false

alarms

New ABF

Standard ABF Comparison


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Standard ABF Comparison

New ABFReg. ABF

Sidelobe

False Alarms

Conclusions


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Conclusions

Propose two ABF modifications

Colored noise loading for low sidelobes with inequalityconstraints to ensure mainbeam interference suppression

Constrained DBU for constant aimpoint gain withnonstationary interference

Both techniques may be utilized together to form a robust

ABF algorithm Demonstrated performance enhancements on data relative to

standard adaptive beamforming techniques

May be applied to multi-channel SAR, GMTI, and SONARdata

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