This material is based upon work supported by the Air Force Research Laboratory.

A study of STAP in A study of STAP in Nonhomogeneous Nonhomogeneous EnvironmentsEnvironmentsR. S. BlumR. S. Blum EECS Dept. EECS Dept. Lehigh UniversityLehigh University

R. S. Blum’s Grad. R. S. Blum’s Grad. studentsstudentsF. Golbasi K. McDonaldY. Zhang Z. LinW. Xu Z. ZhangZ. Gu

TopicsTopics

• PASTAP performance with MCARM PASTAP performance with MCARM data.data.

• STAP using prior knowledge.STAP using prior knowledge.• Closed-form expressions for Closed-form expressions for

performance analysis in performance analysis in nonhomogeneous cases.nonhomogeneous cases.

Topic 1:Topic 1:PASTAP Performance PASTAP Performance with MCARM Data.with MCARM Data.Collaboration with Collaboration with M. C. Wicks and W. L. MelvinM. C. Wicks and W. L. MelvinAFRL and Georga Tech.AFRL and Georga Tech.

STAP Algorithms STAP Algorithms ConsideredConsidered

• ADPCAADPCA

• Factored Post Doppler (FTS)Factored Post Doppler (FTS)

• Extended Factored Approach (EFA)Extended Factored Approach (EFA)

• Joint-domain Localized Approach (JDL)Joint-domain Localized Approach (JDL)

• Subarraying ADPCA (BDPCA) Subarraying ADPCA (BDPCA)

• Subarraying EFA (BEFA)Subarraying EFA (BEFA)

• Subarraying FTS (BFTS)Subarraying FTS (BFTS)

• Beamspace ADPCA (BeamAD)Beamspace ADPCA (BeamAD)

Real data PerformanceReal data Performance

• MCARM flight 5 acq. 575MCARM flight 5 acq. 575• Insert target, Amp 0.05, given Ang & DopInsert target, Amp 0.05, given Ang & Dop• Use Normalized (CFAR) test stat.Use Normalized (CFAR) test stat.• compare Mag at target to neighborcompare Mag at target to neighbor• Use Q neighboring range cells to Use Q neighboring range cells to

estimate Covariance matrixestimate Covariance matrix

JDL BEFA BeamAD

Norm. Test Stat. - Range Norm. Test Stat. - Range 150150

Conclusions for Topic 1Conclusions for Topic 1

• JDL and EFA usually best or near best.JDL and EFA usually best or near best.• Subarraying EFA next best.Subarraying EFA next best.• Post Doppler processing important?Post Doppler processing important?• ADPCA best in a few cases ADPCA best in a few cases (just for (just for

nonhomogeneous cases).nonhomogeneous cases).

Topic 2:Topic 2:STAP using Prior STAP using Prior KnowledgeKnowledge

STAP using Prior STAP using Prior KnowledgeKnowledge

Numerical resultsNumerical results• Compare modified (using prior Compare modified (using prior

knowledge) to traditional schemeknowledge) to traditional scheme• Representative case: Representative case: SMISMI Range bin Range bin

415415 Target spatial Freq. 0.164Target spatial Freq. 0.164Norm Doppler 0.078, 0.156, 0.312Norm Doppler 0.078, 0.156, 0.312Amp 0.05Amp 0.05

Numerical results - Numerical results - NDF:0.078NDF:0.078

Traditional

Modified

Numerical results - Numerical results - NDF:0.156NDF:0.156

Traditional

Modified

Numerical results - Numerical results - NDF:0.312NDF:0.312

Traditional

Modified

Conclusions for Topic 2:Conclusions for Topic 2:• Modified scheme generally very good for Modified scheme generally very good for

nonhomogeneous cases nonhomogeneous cases • Especially when target near clutter ridgeEspecially when target near clutter ridge• Largest improvement for SMI, ADPCA. Significant Largest improvement for SMI, ADPCA. Significant

improvement for EFA and JDL, but not as large.improvement for EFA and JDL, but not as large.• Can apply to other Schemes Can apply to other Schemes • Can consider other knowledgeCan consider other knowledge

Topic 3: Topic 3:

Analysis of STAP Analysis of STAP Algorithms for Cases with Algorithms for Cases with MismatchMismatch

ObservationObservations:s:

Cell under test:

Secondary data:

),(~ tRsCNx

),0(~,...,1),( sdRCNLjjx 0 if signal

absent Independent

L

k

He kxkxR

1)()(

Covariance Est.

N dimensional vectors

Mismatch

Mismatch

Test StatisticTest Statistic

qRq

xRq

eH

eH

AMF 1

21

xRx eH 11 >

<

q: steering mismatch: sensitivity parameter

=0: MSMI or AMF=1: GLR

as const: ACE

Airborne Radar ExampleAirborne Radar Exampleextra hump

targetposition

normalized Doppler frequency (NDF)

normalizedspatial frequency (NSF)

d fctd, fcsd, ftd, fsd, cd,1 -0.35 -0.35 0.03 0.03 8.002 -0.20 -0.20 0.03 0.03 8.003 0.00 0.00 0.03 0.03 9.984 0.20 0.20 0.03 0.03 8.005 0.35 0.35 0.03 0.03 8.00

extra hump 0.38 0.18 0.03 0.03 7.00

Airborne Radar ExampleAirborne Radar Example

Target: NDF=0.40 NSF=0.20X-hump: NDF=0.38 NSF=0.18line: theoretical value : Monte Carlo test

X-hump inreference data

no mismatch

X-hump incell-under-test

Steering offset Covar Steering offset Covar mismatchmismatch

Both mismatchA=0.8000C=[1.4, 2, 3]Var[d]=0.6/k=[0.037, 0, 0]

Only covariance mismatchA=1C=[1, 2, 3]Var[d]=1/k=[0, 0, 0]

Line: theoretical value*: Monte Carlo TestB=0.0095N=4L=32

Conclusions for Topic 3:Conclusions for Topic 3:

• Have obtained closed form Have obtained closed form expressions for performance with expressions for performance with mismatchmismatch

• Tells which types of mismatch are Tells which types of mismatch are important and which are notimportant and which are not

• Steering vector mismatch can offset Steering vector mismatch can offset covariance matrix mismatchcovariance matrix mismatch