Space-Time Adaptive Processing (STAP) Some Performance Limiting Factors

Space-Time Aaptive Processing (STAP) Some Performance Limiting Factors Presente to IEEE AESS 26 October 2004 Dr. Siney W. Theis (sitheis@caesoft.biz) Robert J. Hancock (bob@caesoft.biz) 21 Oct 2004 Page 1 Copyright 2004, CAE Soft Corp.

Agena The Airborne Clutter Environment Space-Time Aaptive Processing What is it? Natural Evolution of Raar Signal Process Why Put the Aaptive in Space-Time Processing? Short Answer - Realities, Imperfect Knowlege, Uncertainties an Imperfections Simple case in point is open loop DPCA How is it Implemente? Limiting Factors List & Examples Current Investigations to Mitigate Limiting Factors 21 Oct 2004 Page 2 Copyright 2004, CAE Soft Corp.

Simple Example of target an interference environment as observe by a Pulse-Doppler Airborne Intercept Raar Receiver Receiver Blanking Blanking Main Main Beam Beam Clutter Clutter Range Range Bin Bin Containing Containing Target Target Peak Peak Target Target PRF Ieal clutter rejection filter Noise Noise PRI Slow Moving Targets require Fast Transition from Stopban to Passban Slow Moving Targets require Fast Transition from Stopban to Passban 21 Oct 2004 Page 3 Copyright 2004, CAE Soft Corp.

Space-Time Aaptive Processing is a Natural Evolution of Raar Signal Process Time Only Processing - Single Channel MTI Processing Pulse Doppler Processing Space Only Processing - Multiple Channel Jammer Cancellation Space-Time Processing (Non-Aaptive) Displace Phase Center Array (DPCA) Processing Simultaneous DPCA Space-Time Aaptive Processing Segmente Antenna Co-Aligne with Velocity Vector Arbitrary Antenna Manifoling an Alignment 21 Oct 2004 Page 4 Copyright 2004, CAE Soft Corp.

e in Simple MTI Raar (Time) Processing e out e in + Σ + Delay Line K - + Σ 1 2 e out -2 0 B R Target -2 Clutter 1 1-2*PRF -1*PRF 0 1*PRF 2*PRF Target Raar 21 Oct 2004 Page 5 Copyright 2004, CAE Soft Corp.

Pulse Doppler Processing Of Moving Targets (Time) T/R Pulse Matche Filter Sampler FFT xt () A cos( ω 0 t) Coherent Oscillator ( φ ) x () t A cos () t Pulse Moulator Stationary Clutter φ(t) Moving Target φ(t) Complex Signal x(t) 1 A 2 Ae j 2π f PRI 3 Ae j2 π f 2PRI 4 Ae j2 π f 3PRI 5 6 7 8 Ae j2 π f 7PRI PRI 21 Oct 2004 Page 6 Copyright 2004, CAE Soft Corp.

Jammer Nulling (Space) + Σ + A e j( π φ )/ 2 Sensor Array A θ Jammer Direction of Wave Propagation λ A B B A B e j( π φ )/ 2 The Path Difference Between Elements Is 21 Oct 2004 Page 7 Copyright 2004, CAE Soft Corp. B l sin( θ) Electrical Phase Difference Between of Jammer s Channels Signal in Channels A & B As a Result of The Angle of Arrival φ 2 π θ λ sin( )

Range, Doppler & Angle of Groun Clutter f clutter 2 λ 2 ( V U ) ( V sin( θ )) p p _ to _ clutter λ p clutter 0.70 V p 0.55 V p V p 0.40V p 0.25 V p 0.10V p θ -0.10V p Doppler Contour Range Contour -0.70V p Clutter Clutter Doppler Doppler Is Is Determine Determine By By The The Look Look Angle Angle From From The The Raar Raar Platform Platform Velocity Velocity 21 Oct 2004 Page 8 Copyright 2004, CAE Soft Corp.

Range, Doppler & Angle of Moving Targets 2 fclutter p λ 2 ftar p λ 2 fclutter ftar λ sin( θ ) sin( θ clutter 2 ( V U ) ( V sin( θ )) 0.70 Vλ p 2 ( V U + V U ) ( V sin( θ ) + V ) p _ to _ tar 0.55 V sin( θ p ) 2 ( V ) ( V sin( θ ) + V ) tar p _ to _ clutter p ) V tar clutter 0.40V tar _ closin g p 0.25 V p 0.10V p tar _ to _ p / V p p λ p λ clutter p tar tar tar _ closin g tar _ closin g V p Clutter Angle x θ Target Angle Exo-Clutter x x x Doppler Contour Range Contour -0.70V p Clutter Clutter Doppler Doppler Is Is Determine Determine By By The The Look Look Angle Angle From From The The Raar Raar Platform Platform Velocity Velocity Target Target Returns Returns Do Do Not Not Originate Originate From From The The Same Same Angle Angle of of Arrival Arrival As As Directly Directly Competing Competing Clutter Clutter at at same same Doppler Doppler as as Target Target (Exo-Clutter) (Exo-Clutter) Returns Returns From From Slow Slow Moving Moving Or Or Turning Turning Targets Targets Must Must Compete Compete With WithMainlobe MainlobeClutter (Eno-Clutter) (Eno-Clutter) 21 Oct 2004 Page 9 Copyright 2004, CAE Soft Corp.

Simple Example of target an interference environment as observe by a Pulse-Doppler Airborne Intercept Raar Receiver Receiver Blanking Blanking Main Main Beam Beam Clutter Clutter Range Range Bin Bin Containing Containing Target Target Peak Peak Target Target PRF Ieal clutter rejection filter Noise Noise PRI More Clutter Rejection Require With Slower Target More Clutter Rejection Require With Slower Target 21 Oct 2004 Page 10 Copyright 2004, CAE Soft Corp.

Ae j 2π f PRI Ae j2 π f 2PRI Ae j2 π f 3PRI A e A j 2π f ( m 1) PRI Complex Pulse Signal x(t) How Space relates to Time (Doppler) in Space-Time Processing (Co-Aligne Array) Target Signal Vector T Target Signal Vector s x A 1 V t Competing Clutter θ V p e j 2 π sin( θ ) λ f β θ 21 Oct 2004 Page 11 Copyright 2004, CAE Soft Corp. 1 e j 2π 2 sin( θ ) λ e j 2 π n sin( θ ) λ W 1 W 2 W 3 W 4 W N Σ v A( θ) e e 2 e 2π j sin( θ) λ 2π j 2sin( θ) λ M π j ( N 1) sin( θ) λ Spatial Steering Vector 2V p PRI NormalizeDoppler f f / PRF fpri sinθ clutter λ 2V p PRI λ 2V p PRI f sinθ clutter sinθ clutter λ λ λ θ sin( θclutter) ( SpatialFrequency/ NormalizeAngle) λ 2V PRI β (Slopeof theclutter Rige Spatial/Do ppler Frequency t

Pulse N Pulse N+1 Full Aperture TX & Segmente RX Aperture DPCA 1. Delay Line Cancellation Processing 2. Cancels clutter from all angles an Dopplers 3. PRF tie to Aircraft Velocity 4. Matche Sub-Arrays & Channels 5. Constraints on Antenna mounting & Aircraft Motion 6. Not satisfying 3 & 4 Degraes Performance Pulse 21 Oct 2004 Page 13 Copyright 2004, CAE Soft Corp. Phase Center Displacement TX RX Total N 0 V*Tr+/2 V*Tr+/2 N+1 /2 V*Tr V*Tr+/2 2V p PRI Normalize Doppler f f / PRF f PRI sinθclutter λ 2V p PRI λ 2V p PRI f sinθclutter sinθclutter λ λ λ θ sin( θclutter ) ( Spatial Frequency/Normalize Angle) λ 2V PRI β (Slope of the Clutter Rige Spatial/Doppler Frequency) f β θ 2V PRI 2V ( β 1 for DPCA); 1; PRF Phase Center Displacement uring PRI : Displacement V * Time V *1/ PRF V * 2V 2

Why Aaptive Processing DPCA & Non-Aaptive Space-Time Processing Implementations are limite by: Channel Matching (both spatial an temporal) Errors in the knowlege of Harware Characteristics Trajectories/Antenna Mounting Limitations Nose Mounte CRAB Angles Aaptive Processing Dynamic Compensation Technique Flexible in that it automatically ajusts to the interference environment 21 Oct 2004 Page 14 Copyright 2004, CAE Soft Corp.

Aaptive Processing Math Target Signal Vector Target Signal Vector Receive Signal Vector Receive Signal Vector STAP Filter Output STAP Filter Output Constraine STAP Weight Vector* Constraine STAP Weight Vector* s xt () A( n) t x αst + n H H y w x αw st + w ~ T Target Signal Vector ~ R H n 1 1 w κr s H ~ 1 s R s Thermal Noise + Interference s Desire Signal Vector Taper SINR SINRout Ps Pn 2 α w w H H s t Rw 2 Interference Covaraince Matrix Desire Signal Vector * Brennan & Ree (1973) 21 Oct 2004 Page 15 Copyright 2004, CAE Soft Corp.

STAP Integration Into Raar Signal Processing Element-Space Pre-Doppler Temporal Filter (DFT) Element-Space Post-Doppler (Factore) Spatial Filter (DFT) Space-Time Filtering (2D-DFT) Spatial Filter (DFT) Beam-Space Pre-Doppler Temporal Filter (DFT) Beam-Space Post-Doppler (Factore) 21 Oct 2004 Page 19 Copyright 2004, CAE Soft Corp.

Limiting Factors we will emonstrate Spatial Mismatch between antenna phase centers Non-Homogeneity Terrain Shaowing Discretes Backscatter Variations Estimation Moving Winow vs Global Movers in training set Uner Nulling / Over Nulling Internal clutter motion Mis-alignment between Antenna Center Line an Velocity Vector, i.e. Crabbing Range Ambiguities Non Planar Antenna Arrays Conformal Deformation 21 Oct 2004 Page 21 Copyright 2004, CAE Soft Corp.

DPCA + Doppler Processing VEL 241.912 meters/secon ANTENNA SA1 0.6096 m 0.6096 m 0.6096 m 0.6096 m SA2 SA3 SA4... DELAY PRI PRI PRI PRI SUBTRACTION + - + - + -... DOPPLER PROCESSOR DP DP DP Outputs shown Here... DIGITAL BEAMFORMER Output shown Here DBF PRI 1260 Microsecons Satifies DPCA Conition: PRI * VEL SubarraySpacing / 2 21 Oct 2004 Page 23 Copyright 2004, CAE Soft Corp.

Diagram illustrating the relationship between the current J-Stars Array an the 16 Subaperture Array use in the Example J-STARS Antenna Envelope 16 Sub-Aperture Antenna Array SA # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16-102.6 in. -13.2 in. 137.4 in. 21 Oct 2004 Page 24 Copyright 2004, CAE Soft Corp. FRONT EDGE OF ENGINE NACELLE @ 218 IN.

Far-Fiel from Column Subarrays (Slats) at Front an Rear of Array Vertical Vertical Cut Cut Scattering Scattering from from engine engine nacelle nacelle Slat Slat # 1 Horizontal Horizontal Cut Cut Co-Pol Co-Pol X-Pol X-Pol Slat Slat # 256 256 21 Oct 2004 Page 25 Copyright 2004, CAE Soft Corp.

Conventional Doppler Processor Output, Azimuth 15 Deg. Main Main Beam Beam Clutter Clutter Channel Channel 1 Main Main Beam Beam Clutter Clutter Channel Channel 8 Main Main Beam Beam Clutter Clutter Channel Channel 16 16 Altitue Altitue Line Line 21 Oct 2004 Page 29 Copyright 2004, CAE Soft Corp.

DPCA + Doppler Processing, Azimuth 15 Deg. Channels Channels 1 1 & 3 3 Target Target Channels Channels 8 8 & 9 9 Target Target Main Main Beam Beam Clutter Clutter Channels Channels 15 15 & & 16 16 Altitue Altitue Line Line 21 Oct 2004 Page 31 Copyright 2004, CAE Soft Corp.

Clutter Analytic (Clairvoyant) Covariance Matrix Calculation Technique ( k ξ k, ak (φ,θ), b (φ,θ)) k th clutter patch a k Spatial Vector exp( j2π (0 : N 1) sin( φk )cos( θ k ) λ K 1 2 k Meta V4 Meta V4 b k Temporal Vector 2v exp( j 2π (0 : M 1) sin( φk + φ λ prf vma )cos( θ ) k i+1 k i ICM ICM Can Can Vary Vary From From Region Region to to Region Region Depening Depening On On Clutter Clutter Type Type k 4 k 3 H 2 O Homogeneous Clutter Clutter in in Low Low Fielity Fielity Meta-Moel Heterogeneous Clutter Clutter in in Higher Higher Fielity Fielity k 1 k 2 v Space Time Vector k ( b k a k ) C NM 1 Analytic Covariance Matrix Calculation K 2 H R ξ k vk vk k 1 21 Oct 2004 Page 33 Copyright 2004, CAE Soft Corp.

Aaptive Processing Metrics GMTI Requires Robust MDV Performance Moving Platform Clutter Couple in Angle an Doppler Use STAP Aaptive Matche Filter With Known Covariance Matrix R Metric Use: SINR Loss Receive Signal Vector Receive Signal Vector STAP Filter Output STAP Filter Output Constraine STAP Weight Vector Constraine STAP Weight Vector SNR SNR x αst + n H H y w x αw st + w The Known Interference Covariance Matrix, R, Was Use The Known Interference Covariance Matrix, R, Was Use w s, 2 α s SNR H s H s 2 2 NMα 2 2 ( σ I) s σ SINR SINR SINR Loss SINR Loss 21 Oct 2004 Page 34 Copyright 2004, CAE Soft Corp. ~ ~ R H n 1 1 w κr s H ~ 1 s R SINRout SINR Loss Ps Pn SINR SNR Target Signal Vector 2 α w w H H s s t Rw Thermal Noise + Interference s 2 Desire Signal Vector Estimate Interference Covariance Matrix SINR Loss Performance of STAP Filter Relative to Interference Free Case SINR Loss Performance of STAP Filter Relative to Interference Free Case

Example of Heterogeneous Clutter Backgroun Raar positione just on left borer of plot, ½ way own plot Looking out over Great Salt Lake towars SLC an Wasatch Mt. Range Clutter Power Range Range Rings Rings are are Approximately Approximately 10 10 KM KM apart apart Very Very Strong Strong Returns Returns ue ue to to Mountains Mountains 60 KM 60 KM Lan Cover 20 KM 20 KM Very Little Main Very Little Main Beam Clutter ue Beam Clutter ue to Shaowing to Shaowing 21 Oct 2004 Page 37 Copyright 2004, CAE Soft Corp.

Appearance of Heterogeneous Backgrouns in High an Meium Fielities High Fielity Waveform Gen. & Doppler Processing Range - Doppler K 1 2 k k i+1 k i k 2 k 1 Analytic Covariance Gen & Aaption k 4 k 3 ICM Can Vary From ICM Can Vary From Region to Region Region to Region Depening On Clutter Type Depening On Clutter Type 21 Oct 2004 Page 38 Copyright 2004, CAE Soft Corp. SINR Loss

Aitional SINR Loss ue to errors in estimation process Uner-Nulling Uner-Nulling Over-Nulling Over-Nulling Blue Blue curve curve is is the the optimal optimal solution solution Blue Blue curve curve is is the the optimal optimal solution solution Meium Meium CNR CNR 20 20 B B region region was was use use to to estimate estimate STAP STAP weights weights that that were were applie applie to to High High CNR CNR 40 40 B B region region High High CNR CNR 40 40 B B region region was was use use to to estimate estimate STAP STAP weights weights that that were were applie applie to to Low Low CNR CNR 10 10 B B region region 21 Oct 2004 Page 40 Copyright 2004, CAE Soft Corp.

Doppler Warping ue to earth s rotation H OB OB 500 500 KM KM V I I 7613 7613 m/s m/s R OB ω OB e e 458 458 m/s m/s R OB ω e θ LOS Doppler Shift Varies With Range Doppler Shift Varies With Range Vsat fop c ECEF ωe R OB 2R& 2 LOS Vsat ECEF - 2 R OB ωe Cos θ λ λ VI 0 R ; LOS OB e Cos ω for a raial along ECEF θ 0 Sin θ 5 7.2722 x10 ra / sec earth rotation angle rate istance from earth center to satellite equator Range Range Unambiguous Unambiguous With With Range Range Ambiguities Ambiguities 21 Oct 2004 Page 42 Copyright 2004, CAE Soft Corp.

Space Raar Systems Present a new set of problems ue to weight an packaging constraints: The array must be fole up to fit into the launch vehicle shrou On orbit the array is unfole an attache to a truss structure The resulting array will not be flat to within λ/20 because istortions will occur which cannot be controlle by mechanical means alone. These may be ue to: Static istortions ue to eployment errors Dynamic istortions ue to station keeping, heating, etc. The ynamic istortions must be sense at a temporal rate higher than the natural frequency of the structure an spatially at a rate greater than the highest orer moe of significance. A robust realtime metrology scheme couple with ynamic electronic compensation is require to live with expecte mechanical eformations. X Total Array Size: 50 x 2 Meters Center Freq: 1.25 GHZ 2 Meters Y 1.5 Meters 21 Oct 2004 Page 43 Copyright 2004, CAE Soft Corp.

Volumetric patterns with no errors, out of plane, an orientation errors Pk Directive Gain 41.7 BI Pk Directive Gain 41.7 BI RMS Sielobes - 55.7 BML RMS Sielobes - 55.7 BML No No Errors Errors Pk Directive Gain 41.7 BI Pk Directive Gain 41.7 BI RMS Sielobes - 55.5 BML RMS Sielobes - 55.5 BML L-Ban L-Ban 50m 50m x 2.5m 2.5m array array 32 32 panels panels Zerror Zerror 1 1 mm mm rms rms Pk Directive Gain 41.6 BI Pk Directive Gain 41.6 BI RMS Sielobes - 51.8 BML RMS Sielobes - 51.8 BML Zerror Zerror 5 5 mm mm rms rms Pk Directive Gain 41.6 BI Pk Directive Gain 41.6 BI RMS Sielobes - 54.8 BML RMS Sielobes - 54.8 BML Orient Orient Angle Angle Error Error 0.2 0.2 eg eg rms rms 21 Oct 2004 Page 44 Copyright 2004, CAE Soft Corp.

Azimuthal Cuts to show the Effect of some Errors No No Errors Errors Pk Pk Directive Directive Gain Gain 41.7 41.7 BI BI RMS RMS Sielobes Sielobes - - 55.7 55.7 BML BML σ σ Z Z 1 1 mm mm rms rms Pk Pk Directive Directive Gain Gain 41.7 41.7 BI BI RMS RMS Sielobes Sielobes - - 55.5 55.5 BML BML σ σ Z Z 5 5 mm mm rms rms Pk Pk Directive Directive Gain Gain 41.6 41.6 BI BI RMS RMS Sielobes Sielobes - - 51.8 51.8 BML BML σ σ P P 0.2 0.2 eg eg rms rms Pk Pk Directive Directive Gain Gain 41.6 41.6 BI BI RMS RMS Sielobes Sielobes - - 54.8 54.8 BML BML 21 Oct 2004 Page 45 Copyright 2004, CAE Soft Corp.

Antenna Performance & SINR Loss changes with parabolic bening of array truss (uncompensate) Azimuthal Azimuthal cut cut thru thru pattern pattern SINR SINR Loss Loss Zmax Zmax 00 00 mm mm Zmax Zmax 24 24 mm mm Zmax Zmax 60 60 mm mm 21 Oct 2004 Page 46 Copyright 2004, CAE Soft Corp.

Current Investigations to Mitigate Limiting Factors Knowlege-Base Approaches Select Training Set Mix Aaptive an Non-Aaptive Techniques Techniques that require less Sample Support in Training Set Orthogonal Waveforms Many Others 21 Oct 2004 Page 48 Copyright 2004, CAE Soft Corp.