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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
STAP Tutorial-2 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
STAP Tutorial-3 JW 1/12/2012
MIT Lincoln Laboratory
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
STAP Tutorial-5 JW 1/12/2012
MIT Lincoln Laboratory
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
STAP Tutorial-6 JW 1/12/2012
MIT Lincoln Laboratory
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
STAP Tutorial-7 JW 1/12/2012
Outline
IntroductionSTAP basics
Partially adaptive STAP architectures STAP CFAR detection STAP parameter estimation Multidisciplinary STAP perspective Summary
STAP Tutorial-8 JW 1/12/2012
MIT Lincoln Laboratory
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
STAP Tutorial-9 JW 1/12/2012
MIT Lincoln Laboratory
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)
STAP Tutorial-10 JW 1/12/2012
MIT Lincoln Laboratory
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
STAP Tutorial-11 JW 1/12/2012
MIT Lincoln Laboratory
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
MIT Lincoln Laboratory
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
MIT Lincoln Laboratory
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
STAP Tutorial-14 JW 1/12/2012
MIT Lincoln Laboratory
More Clutter IsoContoursIso (Velocity) Iso (Range) Iso (Angle)
Scan angle = 90 deg(Velocity vector and array axis pointing in different directions)
v
STAP Tutorial-15 JW 1/12/2012
MIT Lincoln Laboratory
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
STAP Tutorial-16 JW 1/12/2012
MIT Lincoln Laboratory
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
STAP Tutorial-17 JW 1/12/2012
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
STAP Tutorial-18 JW 1/12/2012
MIT Lincoln Laboratory
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
MIT Lincoln Laboratory
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
STAP Tutorial-20 JW 1/12/2012
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
STAP Tutorial-21 JW 1/12/2012
MIT Lincoln Laboratory
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
STAP Tutorial-22 JW 1/12/2012
MIT Lincoln Laboratory
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
STAP Tutorial-23 JW 1/12/2012
MIT Lincoln Laboratory
More STAP EigenbeamsUnweighted Eigenvalue Weighted
N ( M 1) F k !1
P (] , [ )k
N ( M 1) F
Pk !1
k
Pk (] , [ )
STAP Tutorial-24 JW 1/12/2012
MIT Lincoln Laboratory
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
STAP Tutorial-25 JW 1/12/2012
MIT Lincoln Laboratory
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
MIT Lincoln Laboratory
Outline
Introduction STAP basics Partially adaptive STAP architectures STAP CFAR detection STAP parameter estimation Multidisciplinary STAP perspective Summary
STAP Tutorial-27 JW 1/12/2012
MIT Lincoln Laboratory
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
MIT Lincoln Laboratory
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
STAP Tutorial-30 JW 1/12/2012
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
STAP Tutorial-31 JW 1/12/2012
MIT Lincoln Laboratory
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)
STAP Tutorial-32 JW 1/12/2012
MIT Lincoln Laboratory
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
STAP Tutorial-33 JW 1/12/2012
MIT Lincoln Laboratory
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
MIT Lincoln Laboratory
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
MIT Lincoln Laboratory
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
STAP Tutorial-36 JW 1/12/2012
MIT Lincoln Laboratory
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
STAP Tutorial-37 JW 1/12/2012
MIT Lincoln Laboratory
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
STAP Tutorial-38 JW 1/12/2012
MIT Lincoln Laboratory
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
STAP Tutorial-39 JW 1/12/2012
MIT Lincoln Laboratory
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
MIT Lincoln Laboratory
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
STAP Tutorial-41 JW 1/12/2012
MIT Lincoln Laboratory
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
STAP Tutorial-42 JW 1/12/2012
MIT Lincoln Laboratory
Outline
Introduction STAP basicsPartially adaptive STAP architectures
STAP CFAR detection STAP parameter estimation Multidisciplinary STAP perspective Summary
STAP Tutorial-43 JW 1/12/2012
MIT Lincoln Laboratory
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
MIT Lincoln Laboratory
Outline
Introduction STAP basics Partially adaptive STAP architecturesSTAP CFAR detection
STAP parameter estimation Multidisciplinary STAP perspective Summary
STAP Tutorial-45 JW 1/12/2012
MIT Lincoln Laboratory
Adaptive Detection Problem
)Bd( REWOP TUPTUO
STAP Tutorial-46 JW 1/12/2012
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)
MIT Lincoln Laboratory
Outline
Introduction STAP basics Partially adaptive STAP architectures STAP CFAR detection STAP parameter estimation
Multidisciplinary STAP perspective Summary
STAP Tutorial-47 JW 1/12/2012
MIT Lincoln Laboratory
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
MIT Lincoln Laboratory
Outline
Introduction STAP basics Partially adaptive STAP architectures STAP CFAR detection STAP parameter estimation Multidisciplinary STAP perspective
Summary
STAP Tutorial-49 JW 1/12/2012
MIT Lincoln Laboratory