Adaptive Beamforming Techniques for Sidelobe Control · PDF file ·...

ABF-SCJMJDG 12/19/2005

MIT Lincoln Laboratory

Adaptive Beamforming Techniques for Sidelobe Control and Mitigation of

Nonstationary Interference

JAMJAM

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.

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 require fewer 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 GHz180 MHz2,000 Hz56 ms848 cm18 cm

Center Freq.BandwidthPRFCPIRx SubarraysHoriz. ApertureVert. Aperture

Boeing 707

Ft. Huachuca, AZN

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– Must suppress 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.

Estimate Cluster 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 BeamformingC

onve

ntio

nal

Bea

mfo

rmin

g(C

BF)

Hv xChannelData (x)

SteeringVector (v)

OutputBeam Data

CB

Fw

ith S

V ta

per

Hv DxChannelData (x)

SteeringVector (v)

OutputBeam Data

DvTaper ( )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 BeamformingA

dapt

ive

Bea

mfo

rmin

g(A

BF)

1H −v R xChannelData (x)

SteeringVector (v)

OutputBeam Data

AB

Fw

ith S

V ta

per

1H −v DR xChannelData (x)

SteeringVector (v)

OutputBeam Data

DvTaper

• 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 modeling external sidelobe interference in data covariance

L

clfclf−

Parameters:= Loading Level= Loading Frequencyclf

L

( )1 2

( ) ( ) ( ) ( ) cl

H H Hcl

f

L dφ φ φ φ φ= + − −∫v vR D v v v v D

( )diag=vD v

1( )cl−= +w R R v

SteeringVector (v)

1( )Hcl

−+v R R xChannelData (x)

OutputBeam 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 with sidelobe jamming:

ABF + CNL


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Mainbeam Jamming Comparison

ABF Tapered SV

TSV ABF does not appropriately model

steering vector:

Mainbeam jamming causes CNL ABF to trade-off jammer &

sidelobe suppression:

ABF + CNL


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ABF Colored Noise Loading

1. Let u1- uk denote eigenvectors of R that have eigenvalues, σ2 > Tev2. Let C denote linear constraints such that CHw = c

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

( ) ( )( ) 11 1Hcl cl

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

ABF + CNL


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Inequality Constrained ABFColored Noise Loading

1. Let u1- uk denote eigenvectors of R that have eigenvalues, σ2 > Tev2. Let C denote linear constraints such that CHw = c

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

( ) ( )( ) 11 1Hcl cl

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

2 2

1 11T

i jσ σ⎡ ⎤

= ⎢ ⎥⎢ ⎥⎣ ⎦

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

Hk

kσ σ⎡ ⎤

< ⎢ ⎥⎣ ⎦

u u w

5a. If all constraints are satisfied → done5b. 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 k denotes the relative pulse index throughout the CPI and n 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 Hk n k n k n k n

H Hk 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

Hk k n

k n=∑

w vw xSolve such

that 0k k= +w w w

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


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DBU Effects(Example Simulation)

Conventional ABF

Spatially Moving Jammer

DBU

k = -1k = 0k = 1

Inter-CPI Gain Variation

Spatially Moving Jammer


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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

0 1H

⎡ ⎤ ⎡ ⎤=⎢ ⎥ ⎢ ⎥

⎣ ⎦ ⎣ ⎦

w vw 0

0 0H

⎡ ⎤ ⎡ ⎤=⎢ ⎥ ⎢ ⎥

⎣ ⎦ ⎣ ⎦

w 0w v

⎡ ⎤= ⎢ ⎥⎣ ⎦

v 0C

0 v [ ]1 0 T=c

( ) 10 1 1H −− −⎡ ⎤=⎢ ⎥

⎣ ⎦

wR C C R C c

w

0k k= +w w w

2

,1 ,

minHk

Hk k n

k n=∑

w vw x


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Constrained DBU Results

Conventional DBU Constrained DBU

k = -1k = 0k = 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


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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 over sidelobes

Constrained DBU

k = -1k = 0k = 1

Constrained DBU w/ CNL

2

11

1 1cl cl

kK

k kK K

⎡ ⎤⎢ ⎥

= ⊗⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

∑

∑ ∑R R

⎡ ⎤= ⎢ ⎥⎣ ⎦

v 0 uC

0 v 2

11 0T

σ⎡ ⎤= ⎢ ⎥⎣ ⎦

c


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Outline



• Data Results

• Conclusion


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Ft. Huachuca GMTI Displays

SAR Image (1m resolution)

Range/Doppler DetectionRange/Doppler ClusterRange/Angle LocalizationGPS Ground TruthJammer Angle

07/24/04 CPI# 98045687


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GMTI Movie

Range/Doppler DetectionRange/Doppler ClusterRange/Angle LocalizationGPS Ground TruthJammer Angle

Desired Beams Jamming Angles

07/24/04 CPI# 98045687 – 98047507


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Selected Frames

Doppler Aliased Clutter Filling in

Jammer Null

Close-In Detection

07/24/04 CPI# 98046337 & 98046437


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Tapered Steering Vector (TSV) Comparison30dB Taylor

TSV Undernulled Jammer false

alarms

New ABF


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Standard ABF Comparison

New ABFReg. ABFSidelobe

False Alarms


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Conclusions

• Propose two ABF modifications– Colored noise loading for low sidelobes with inequality

constraints to ensure mainbeam interference suppression– Constrained DBU for constant aimpoint gain with

nonstationary 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 SONAR data

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