STAP Tutorial

Space-Time Adaptive Processing (STAP) for Airborne RadarJames Ward

Opinions, interpretations, conclusions, and recommendations are those of the authors and are not necessarily endorsed by the United States Air Force. This work was sponsored by DARPA under Air Force Contract F19628-95-C-0002

STAP Tutorial-1 JW 1/12/2012

MIT Lincoln Laboratory

Outline

Introduction STAP basics Partially adaptive STAP architectures STAP CFAR detection STAP parameter estimation Multidisciplinary STAP perspective Summary



Outline

Introduction

STAP basics Partially adaptive STAP architectures STAP CFAR detection STAP parameter estimation Multidisciplinary STAP perspective Summary



Space-Time Adaptive Processing (STAP)Target Jamming

Ground Clutter

40 30 20 10 0 1 0 0 1 PRF/2

SNR (dB)

PRF/2

vSurveillance RadarSTAP Tutorial-4 JW 1/12/2012

Two-dimensional filtering required to cancel interference Space-Time Adaptive Processing

(STAP)MIT Lincoln Laboratory

Radar Signal Processing Chain

Conventional (nonadaptive) radarBeamforming Pulse Compression RCVR A/DsFront-End filtering

Doppler Filtering

CFAR Detection & Metrics

Tracking & Display

Adaptive radar (example architecture)Pulse Compression Beamforming Doppler Filtering Adaptive Nulling

STAPCFAR Detection & Metrics Tracking & Display

RCVR A/DsFront-End filtering



Topics To Be Covered

Airborne radar clutter

properties Space-time covariance matrices Degrees of freedom Sample support / training data Pre-Doppler, post-Doppler algorithms SINR Loss MDV DPCA processing vs. STAP Principal components Cross spectral metric

Jamming issues Generalized sidelobe

canceller architecture Adaptive CFAR detection Maximum likelihood STAP Cramer-Rao bound on angle and Doppler accuracy Other application areas



Why Adaptive?

Interfering (clutter, jamming) signal locations not precisely known a priori Required rejection (sidelobe level) not achievable with conventional filtering in presence of system errors Beam broadening that results from uniformly lowering sidelobes is undesirable To gain target visibility as close as possible to interfering sources To react to the natural nonstationarity of typical dynamic radar operating environments

Let the signal processing adapt to the observed data!MIT Lincoln Laboratory


Outline

IntroductionSTAP basics

Partially adaptive STAP architectures STAP CFAR detection STAP parameter estimation Multidisciplinary STAP perspective Summary



Pulse Doppler Data CollectionRX TX

1

2

3

M Time Range Samples at same range gate

M Pulse Number (Slow time)

A/D

Baseband Quadrature Sampling

Pulse Compression

N 1 1 Range Gate (Fast time) L 1



Pulse Doppler Radar Datacube

Antenna Element (receiverchannel)

L

N(Angle)

The snapshot for space-time processing (single range gate)

1 1 M 1

Pulse Number (slow time)

(Doppler Frequency)



Ground Clutter Characteristics

Platform-induced coupling between clutter angle andDoppler frequency Radar platform velocity Radar PRF Antenna and velocity vector orientation Range dependenceShape of clutter locus

Strength of clutter signal: CNR Radar power and aperture Clutter reflectivity Range dependence

Power distribution along clutter locus

Intrinsic clutter motion Wind, waves, system instability Bandwidth dispersion

Width of clutter locus



A Hypothetical Radar Problem100 Target Clutter Jamming

80 70 Required SINR Improvement (dB) 60 50 40 30 20 10 0 50 100 150 Range (nmi) 200 250 Coherent SNR gain Additional rejection required from STAP

Input SNR (dB)

50

0

-50 20 0 Required for detection

SINR (dB)

-20 -40 -60 -80 Input

Heavy land clutter Strong sidelobe jamming100 150 200 250

50

Range (nmi)STAP Tutorial-12 JW 1/12/2012


Airborne Radar GeometryzVelocity vector:

v U R JClutter patch

v x v ! v y ! v uv v z yArray orientation (Linear array assumed):

x Clutter Doppler frequency

d x d ! d y ! d ud d z

fc (J ,U ) !

2v T uv u (J ,U ) P d T ud u (J ,U ) P

[c (J ,U ) ! fcTr !

2vTr T uv u (J ,U ) P

Clutter spatial frequency

] c (J ,U ) !STAP Tutorial-13 JW 1/12/2012


Clutter Iso-ContoursIso (Velocity) Iso (Range) Iso (Angle)

Scan angle = 0 deg(Velocity vector and array axis pointing in same direction)

v

IsoDoppler and IsoAngle contours are identical



More Clutter IsoContoursIso (Velocity) Iso (Range) Iso (Angle)

Scan angle = 90 deg(Velocity vector and array axis pointing in different directions)

v



Ground Clutter Doppler vs. Range CharacteristicsScan angle = 0 deg v Scan angle = 20 deg v

Clutter angle Doppler locus is range independent

Clutter azimuth-60 deg -30 deg 0 deg 30 deg 60 deg

Clutter angle Doppler locus depends on range



Clutter Ridges: Angle and DopplerScan angle = 0 deg Scan angle = 30 deg

F=1 9 km altitude

500 km 200 km 100 km 20 km 10 km MIT Lincoln Laboratory


Clutter RidgesDoppler unambiguous F=1 Doppler ambiguous F = 2.5

Doppler ambiguous clutter:

F!

2v df r

4v p P fr

! 2F

d P " 1 F " 1 for d ! P 2



Optimum Space-Time Processing... wN1N antennasT T T

T

T

T

T

T

T

} M pulses } NM weights (degrees of freedom)STAP weight vector Element / Pulse measurements

w11

w1M

wNM

7Optimum weights

STAP output = wHxR = covariance matrix v = steering vector

w=

R1v

Dimensionality can be very large: NM can be 102 to >104 Covariance matrix unknown a priori and must beestimated from the radar dataSTAP Tutorial-19 JW 1/12/2012


STAP Optimality Criteria

w ! QR v1Criterion Formulation Weight Normalization

Maximum SINR

maxw

w v

H

2

Q {0

w H Rw 1 Q ! H 1 1 / 2 (v R v ) 1 Q ! H 1 v R vMIT Lincoln Laboratory

Maximum PD while maintaining CFAR PF Minimum output power subject to unit gain constraint in look direction

max PD (w ) PF ! Lw

min w H Rww

w Hv ! 1


Clutter Covariance Matrix Rank

Mainlobe clutter

N = 16 Elements M = 16 Pulses Sidelobe clutter Uniformly weighted transmit pattern CNR = 50 dB per element per pulse

F !0

F !1

F !2

F !3

2v F! df r(F=1 is the DPCA condition)

rank ( Rc ) ! N ( M 1) F

Number of DOF occupied by the full (mainlobe plus sidelobe) clutter ridge



Brennans Rule for Clutter RankExample: N=4 elements, M=3 pulses, F=1Element #1 Pulse #1 Element #4 d Space Pulse #2 T Clutter signal on nth element, mth pulse

xnm ! e j ( n] m[ ) ! ej 2T ( n mF ) dP1 sin J

Effective position for nth element, mth pulse

Pulse #3 Time

~ d nm ! ( n mF )dRank(Rc) = N + (M-1)F = 4 + (3-1)1 = 6

Clutter rank is the number of distinct effective element positions, or the length of effective synthetic array aperture



Space-Time Clutter EigenbeamsEigenbeam #1 Eigenbeam #2

kth Eigenbeam:

Pk (] , [ ) ! e v(] , [ )H k

2

Eigenbeam #10

Eigenbeam #20

8 Pulses 8 Elements F=1 Uniform transmit taper



More STAP EigenbeamsUnweighted Eigenvalue Weighted

N ( M 1) F k !1

P (] , [ )k

N ( M 1) F

Pk !1

k

Pk (] , [ )



STAP Radar Data ModelPrimary snapshot (target range gate)

x0 E_ 0 a! E v (] , [ ) x Cov_ 0 a! R xSNR (dB)Secondary snapshots (target-free range gates for covariance estimation) Noise Jamming Clutter

x1 , x 2 , - , x K E_ k a! 0 x Cov_ k a! R xAssumptions

Target

Multivariate Gaussian Target only in primary snapshot Common interference covariance matrix



Radar Data and Interference EstimationRadar data cubeT T T

Pulses

Estimate interference using this data (training region)

ElementsT = pulse repetition interval z = A/D sampling period

Rangegatesz z z z

The degrees of freedom (DOF) problem: More DOF requires more computation O(DOF3) More DOF requires more training data In data limited environment, increasing DOF can degrade performance

Reduced DOF STAP approaches are requiredSTAP Tutorial-26 JW 1/12/2012


Outline

Introduction STAP basics Partially adaptive STAP architectures STAP CFAR detection STAP parameter estimation Multidisciplinary STAP perspective Summary



Reduced-Dimension STAP ArchitectureData cubeFront-End Filtering Apply STAP Weights DetectionsReduced dimension space

Preprocessor

Estimate Interference

Compute STAP Weights

Beam Angle & Target Doppler Selection

Compute Steering Vectors

Preprocessing may involve beamforming and/or Dopplerfiltering Reject some interference nonadaptively Adapt on small number of preprocessor outputsSTAP Tutorial-28 JW 1/12/2012


Taxonomy of STAP ArchitecturesPulse Element Doppler bin ElementSpatial filtering Doppler filtering

Element-Space Pre-Doppler

Element-Space Post-Doppler

Spatial filtering

Beam

Beam-Space Pre-Doppler

Beam Doppler bin

Doppler filtering

Beam-Space Post-Doppler

Pulse

STAP algorithms classified by domain in which STAP Tutorial-29 JW 1/12/2012

adaptivity occurs There are performance differences between algorithmsMIT Lincoln Laboratory

Partially Adaptive STAP Clutter RankWhat is clutter DOF here? PreprocessorN Elements M Pulses

T=FG

Reduced DimensionDs Spatial DOF Dt Temporal DOF

Output

STAP


Separable processors easily implemented with cascade of beamformer and Doppler filter Toeplitz structures represent equivalent subaperture filtering in space and/or time Judicious preprocessor design can lessen required DOF after preprocessor MIT Lincoln Laboratory

DualityBeamspace Pre-Doppler Element-space Post-DopplerElement #1 Pulse #1 Space Pulse #2 Pulse #2 Element #4

Element #1 Pulse #1

Element #4

d

dSpace

T

T

Pulse #3 Time

Pulse #3 Time

Effectively combine displaced spatial subapertures from different pulses

Effectively combine displaced temporal subapertures from different elements



Beamspace Post-Doppler Clutter RankExample: N=4 elements, M=3 pulses, F=1 Ds=3, Dt=2 subaperture beamsElement #1 Pulse #1 Element #4 d Space Pulse #2 T Each subaperture processed with 2 element, 2 pulse subaperture filter

Pulse #3 Time

Rank(Rc) = Ds + (Dt-1)F = 4

Implicit subaperture filters can be formed with Uniform weighted filters spaced at nominal resolution Ideal sum and difference filters (space and/or time)



Example: Post-Doppler Sum-Delta STAP Useful for backfitting existingSum / Difference Beamforming

(

7

Pulse Data

monopulse radars Need more than two spatial DOF (beams/subapertures) for Jammer nulling Simultaneous clutter cancelling and angle estimation

Doppler FFT(s)

Doppler FFT(s)

Doppler filter bank design isSTAP weight calculation and filtering (4 DOF)Output Doppler Bins

important

Adjacent bin (uniform) PRI-staggered Sum-Delta tapers



Two Step NullingSequential Rejection of Jamming then ClutterStep 1N Elements M Pulses

Step 2B Beams M Pulses

Adaptive Beamforming Jammer Nulling

Beamspace

STAPClutter Nulling

CFAR Detection and Metrics

Jammer Training

Clutter Training

Lessens total DOF required for STAP Requires training data free of mainlobe clutter for Step 1 Beyond the horizon range gates in low PRF Doppler filter away from mainlobe clutter

Beamspace pre- or post-Doppler STAP clutter nullingSTAP Tutorial-34 JW 1/12/2012


A Hypothetical Airborne Radar Problem100 Target Clutter Jamming

80 70 Required SINR Improvement (dB) 60 50 40 30 20 10 0 50 100 150 Range (nmi) 200 250 Coherent SNR gain Additional rejection required from STAP

Input SNR (dB)

50

0

-50 20 0 Required for detection

SINR (dB)

-20 -40 -60 -80 Input

Radar altitude = 25 kft Heavy land clutter Strong sidelobe jamming100 150 200 250

50

Range (nmi)STAP Tutorial-35 JW 1/12/2012


Displaced Phase Center Antenna (DPCA) Processing -- Predecessor to STAPdTransmit Pulse #1 Receive Pulse #1

v

Distance

Element / subaperture phase center Transmit phase center Receive phase center Equivalent monostatic phase center

Transmit Pulse #2 Receive Pulse #2

T

DPCA Condition 2vT / d = 1Slope = velocity Time

DPCA: Subtract clutter signals from same equivalent monostatic phase center for perfect clutter cancellation



Another DPCA ViewpointdPulse #1

v

Distance

Clutter signal on nth element, mth pulse has phases commensurate with effective position dnm = (n+mF)d = (n+m)d

Pulse #2

Pulse #3

Identical clutter signals for elements, pulses where (n+m) = constant

Time

DPCA Condition F = 2vT / d = 1DPCA subtracts signals with same effective position for perfect (ideally) clutter cancellation



Displaced Phase Center Antenna Processing (DPCA)Principle Block DiagramSpace A two element, two pulse space-time filter

d

-

Tr+ -

Tr

+2TrTime

7+Doppler FFT

0 1 w! 1 0

Choose PRF to satisfy the DPCA Condition (F!)

2v fr ! d

d vTr ! 2

Subtract signals from same effective phase center for perfect clutter cancellation

F (] , [ ) ! w H v ! e j 2T] e j 2T[DPCA filter produces a null along the F! clutter ridge ]![

Array effectively moves one element spacing with each PRI



Example DPCA Canceller Response

0 0.4 -5 -10 Relative Power (dB) -15 -20 -25 -30 -35 -40 -0.4 -0.2 0 0.2 Spatial Frequency 0.4

Temporal Frequency

0.2

Deep null along F! clutter ridge Doppler cuts are two-pulse canceller responses Performance depends only on true target velocity

0

-0.2

-0.4



DPCA IssuesAdvantages Simple, straightforward processing chain Can be implemented with subaperture beams, sum and difference beams Disadvantages Requires PRF matched to platform velocity Requires precise element pattern matching to get cancellation over whole ridge Velocity and array axis misalignment degrades performance No inherent provision to suppress clutter and jamming simultaneously No inherent provision to adapt to intrinsic clutter motion

Solution: STAPSTAP Tutorial-40 JW 1/12/2012


Sum/Delta DPCA Implementation1 Amplitude Sum / Difference Beamforming 0.5 0 -0.5 -1 1 DPCA Canceller Amplitude 0.8 0.6 0.4 0.2 0 2 4 6 8 10 12 Element Number 14 16 18 Left Right

7

7

(

DPCA Beamforming Left Right

O

(

T+ -

7

Doppler FFT



Equivalence Between 7( Beams and Shifted Subaperture BeamsExample 1 Amplitude 0.5 0 -0.5 Matrix Beamformer -1 1 0.8 Amplitude 0.6 0.4 0.2 0 2 4 6 8 10 12 Element Number 14 16 18 Left Right

7

Sum / Difference Beamforming

7

(

(

7j(

7j(

Left subaperture

Right subaperture



Outline

Introduction STAP basicsPartially adaptive STAP architectures

STAP CFAR detection STAP parameter estimation Multidisciplinary STAP perspective Summary



Multibin Post-Doppler Performance5 0 5 10OPTIMUM

SINR LOSS (dB)

151Bin

16 elements 16 pulses Heavy clutter(CNR = 40 dB)

20 25 30 35 40 45 50 0 RELATIVE VELOCITY (m/s)

2Bin 3Bin 4Bin

50

Near optimum performance with only 48 = 3 16 DOF A fraction of optimum STAPs 256 DOFSTAP Tutorial-44 JW 1/12/2012


Outline

Introduction STAP basics Partially adaptive STAP architecturesSTAP CFAR detection

STAP parameter estimation Multidisciplinary STAP perspective Summary



Adaptive Detection Problem

)Bd( REWOP TUPTUO


081 571 071 ATAD POTNIATNUOM

DLOHSERHT NOITCETED

EVITPADANON

EVITPADA

)mk( EGNAR561 061 551 051 541 01 01 02 03 0

Signal/Noise Statistics Affected by AdaptivityH0 : H1 :z= n z = bv+nINPUT

ADAPTIVE DETECTOR

OUTPUT

H1

THRESHOLDH0

N DIMENSIONAL (Complex)

1 DIMENSIONAL (Real)


Outline

Introduction STAP basics Partially adaptive STAP architectures STAP CFAR detection STAP parameter estimation

Multidisciplinary STAP perspective Summary



STAP Estimation Problem0.5 0.4 0.3 TEMPORAL FREQUENCY 0.2 SINR (dB) 0.1 0 0.1 0.2 0.3 0.4 0.5 0.5 0 SPATIAL FREQUENCY 0.5 16 14 12 10 8 6 4 2 0 2

8 elements 8 pulses Heavy clutter(CNR = 50 dB)

Uncertainty indicated by error ellipses (95% confidence) Angle-Doppler estimation a joint problem with STAPSTAP Tutorial-48 JW 1/12/2012


Outline

Introduction STAP basics Partially adaptive STAP architectures STAP CFAR detection STAP parameter estimation Multidisciplinary STAP perspective

Summary



STAP Tutorial

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