Robust ABF for Large, Passive Broadband Sonar Arrays

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1 Robust ABF for Large, Passive Broadband Sonar Arrays Presented at: ASAP Workshop March 23 Presented by: Norman L. Owsley John A. Tague Undersea Signal Processing Team 1US 1

2 Introduction: Themes ABF for large arrays (1 < N < 1 elements) require particular attention to computing efficiency Element space DMR > O(ND 2 ) Ideal reduced complexity adaptive beamformer: Adaptation space dimension, N a, close to required adaptive degrees of freedom D Consistent with spatial sampling theory Steering direction invariant Robust robustness Broadband beamforming: computing efficiency inherent at low frequency can trade high SNR signal suppression for spatial resolution 2

3 LOPS AO Array Wet Subsystem(AWS) Trunk Terminus Segment (TTS) NSWC PEV Observatory Trunk Segment (OTS) Horizontal Array Segment (HAS) 1664 sensors Off-board Array Element Location Segment (OAELS) Non-Development Item (NDI) Legacy Sensor 3

4 Complexity (C) in Dominant Mode Rejection (DMR) Adaptive Beamforming (ABF) N = number of sensors S = number of steering directions N a = number of adaptively filtered channels D = number of adaptive degrees of freedom CBF update SVs update filters C = NS + O(N a D 2 ) + O(2N a DS) S invariant 4

5 Candidate ASAP Methods for Large BB Arrays Method Adaptation Description Space Minimum Variance Element Baseline for Comparison Dominant Mode Rejection (MV DMR) Adaptively Combined Beam Widely used for reduced Fixed Beams (ACFB) dimension adaptation space Subarray (SA) DMR Subarray Beam Subarray element grouping summed unsteered before EMVDR with WNGC. Steering Invariant Auxiliary Array Sparse subarray element summed (Generalized) Sidelobe group outputs cross-correlated with Cancellation (SI(G)SC ) CBF output to derive MV filters 5

6 Adaptive Degrees of Freedom: Frequency Dependence N = number of sensors? /2 spaced sensors in linear array N a = number of adaptive channels f = frequency normalized by the?/2 spacing design frequency f=1 is array design frequency Element Space Subarray Space N a N a N a N N/2 N/4 N/8 Auxiliary Space????????? f f f Area = N Area = 2N/3 Area = (? +1)N/3 N a = N a (Number of Sources, Number of??2-s in Aperture) (???) 6

7 Measures of Performance Qualitative: Bearing-Time-Recording (BTR) side-by-side beauty contest Quantitative: Array Gain (AG) AG(? targ )? ArraySignal Gain Array Noise Gain? w(? w(? targ ) targ H ) Q H true P true (? (all? targ? ) w(?? targ targ ) ) w(? targ ) w(? targ ) = beamforming filter vector for beam steered at? targ P true (? targ ) = Cross-Channel Spectral Density Matrix (CSDM) = d(? targ )d(? targ ) H, Trace(P true (? targ ) ) = N H Q true (all?? targ )? a md(? m) d(? m)? m?? a I N, Trace(Q true (? targ ) ) = N 7

8 AG MOP Usage AG is given as a function of? targ for static source examples AG is given along the bearing track of a clairvoyant designated target tracker for dynamic source examples 8

9 ABF with Subarray Preprocessing x(? ) A (? ) a(? ) w a (?, b) x y a (?,b) = w a H A(? ) H x(? ) Steering invariant subarray grouping: v a????b? = A??? H v(?, b) Suppress? and b notation: w a? v H a 1 R? 1 aa v a R? 1 aa v a Subarray phase centers consistent with spatial aliasing control. 9

10 GSC with Presteering and Signal Blocking Distortionless Response (DR) 1 N = [ 1 1 1] T (N-by-1) x(? ) S (??b) N-by-1 M-by-1 x y c (?,b) = v(?, b) H x(? ) w a (b,? ) y(? ) v(?, b) = S (?,b)1 N B??? Suppress? and b notation: x y a (?,b) = w ah B H S H x(? ) B H 1 N = M = [ ] T (M-by-1) w a = [B H S H R xx SB] -1 B H S H R xx v Unconstrained Weiner Filter The matrix inverted depends on steering direction. 1

11 x(? ) v (???b) x A(? ) Suppress? and b: Steering Invariant DR Sidelobe Cancellation (SISC) Process y c (?,b) = v(?, b) H x(? ) a(? ) x w a (b,? ) v a (??b) = A(? )v(?, b) y a (?,b) = w ah A H x(? ) H? 1?? racraav?? a wa? Raa? rac? H -1 va??? va Raava?? y(? ) Constrained Weiner Filter R aa not steering direction dependent Spatial aliasing avoided with auxiliary subarray (sparse) 11

12 Steering Invariant DR Sidelobe Cancellation (SISC) Process x(? ) v (???b) x A(? ) Suppress? and b: v - Awa w = 1- H H w A v a y c (?,b) = v(?, b) H x(? ) a(? ) x v a (??b) = A(? )v(?, b) with w a (b,? ) y a (?,b) = w ah A H x(? ) Constrained Weiner Filter??? w? R r? v? 1 a aa ac a y(? ) R aa not steering direction dependent Spatial aliasing avoided with auxiliary subarray (sparse) 12

13 Robust Robustness (RR): Robustness Management CBF (v) and unconstrained ABF (w ) linear blend w = (1?) v +? w, where on a beam-by-beam as-needed basis (RR), 2? 1,for w -v? G??? ß= G 1/2? 2??,for w - v >G? w - v?? G = WNGC 1. For a Sidelobe Cancellation ABF w = v - Aw a and the w = v?aw a ( really simple!). 13

14 ESMVDR (l) and SI(G)SC w/o RR (r): NumHydPerGroup = 6 (M = 8, N = 48, pert=.) Response (db) C/MVDR: f =.2 p = Response (db) C/GSC: shade = Angle(deg) Angle(deg) 14 Figure 3.

15 ESMVDR (l) and SI(G)SC w/o RR (r): NumHydPerGroup = 6 (M = 8, N = 48, pert=.7) Response (db) C/MVDR: f =.2 p = Response (db) C/GSC: shade = Angle(deg) Angle(deg) 15 Figure 3.1

16 ESMVDR (l) and SI(G)SC with RR (r): NumHydPerGroup = 6 (M = 8, N = 48, pert=.7) Response (db) C/RMV: f =.2 p = Response (db) C/RGSC: WNGC(db) = Angle(deg) Angle(deg) 16 Figure 3.2

17 Subarray Preprocessing w/o (l) and with (r) RR: NumHydPerSA = 6 (M = 8, N = 48, pert=.7) Response (db) C/SAMV: f =.2 p = Response (db) C/RSAMV: WNGC(db) = Angle(deg) Angle(deg) 17

18 Blended CBF-DMR Point Design (Owsley, SAM 2) db sp: frq =.4, g =.25, s = db - 3 db Response (db) ABF Resp: frq =.4, g = 25, s = Design Procedure: One step pre-solution for G in terms of specified allowable signal suppression v. SNR Angle(deg) \^2: isl = 5, e = 1 cbf dmr u dmr c magsq(db) Angle(deg) \w\^2: isl = 5, e = 1 cbf dmr u dmr c Angle(deg) Angle(deg) 18

19 Six Stationary Sources: ES (pert =., N = 48, D = 7, f =.2, sa group size = 4) Power (db) Source Levels (db): CBF w/25 db SLL (...) MVDR (---) Loaded DMR (-.-.) Excision DMR (ooo) 11 WNGC = 12 db Cosine 1 19 Figure 4.1

20 Six Stationary Sources (pert =., N = 48, D = 7, f =.2, sa group size = 4) Power (db) phase interval = ; Sources at: CBF w/25 db SLL (...) MVDR (---) CBF-EDMR Blend (-) DMR GSC (-) GSCmlm = db Hyd. Group Size = 4 WNGC = 12 db Cosine 2 Figure 4.2

21 Six Stationary Sources (pert =., N = 48, D = 7, f =.2, sa group size = 4) 5 45 phase interval = ; Sources at: CBF w/25 db SLL (...) CBF-EDMR Blend (-) CBF-GSC Blend (-) Excision DMR blend (ooo) Subarray ABF blend (-) 35 Power (db) Cosine 21 Figure 4.3

22 Six Stationary Sources (pert =., N = 48, D = 7, f =.2, sa group size = 4) Array Gain (db) phase interval = ; Sources at: Max Load Its = CBF w/25 db SLL (..) MVDR (-) CBF-GSC Blend (x) DMR Excision (+) DMR Diag. Load (-.) CBF-EDMR Blend (-) Subarray DMR Blend (-) Cosine 1 22 Figure 4.4

23 Six Stationary Sources (pert=.7, D = 7, N=48, M=12, f =.2, sa group size = 4) Power (db) Source Levels (db): CBF w/25 db SLL (...) MVDR (---) Loaded DMR (-.-.) Excision DMR (ooo) WNGC = 12 db Cosine 23 Figure 5.1

24 Six Stationary Sources (pert=.7, D = 7, N=48, M=12, f =.2, sa group size = 4) phase interval =.7; Sources at: CBF w/25 db SLL (...) CBF-EDMR Blend (-) CBF-GSC Blend (-) Excision DMR blend (ooo) Subarray ABF blend (-) Figure 5.3

25 Six Stationary Sources (pert=.7, D = 7, N=48, M=12, f =.2, sa group size = 4) Array Gain (db) phase interval =.7; Sources at: Max Load Its = CBF w/25 db SLL (..) MVDR (-) CBF-GSC Blend (x) DMR Excision (+) DMR Diag. Load (-.) CBF-EDMR Blend (-) Subarray DMR Blend (-) Cosine 1 25 Figure 5.4

26 Six Stationary Sources (pert =.7, N =48, M = 8, D = 7, f =.2, number of sensors per sa = 6) Power (db) phase interval =.7; Sources at: CBF w/25 db SLL (...) MVDR (---) CBF-EDMR Blend (-) DMR GSC (-) 11 GSCmlm = db Hyd. Group Size = 6 WNGC = 12 db Cosine 26 Figure 6.2

27 Six Stationary Sources (pert =.7, N =48, M = 8, D = 7, f =.2, number of sensors per sa = 6) phase interval =.7; Sources at: CBF w/25 db SLL (...) CBF-EDMR Blend (-) CBF-GSC Blend (-) Excision DMR blend (ooo) Subarray ABF blend (-) Figure 6.3

28 Six Stationary Sources (pert =.7, N =48, M = 8, D = 7, f =.2, number of sensors per sa = 6) Array Gain (db) phase interval =.7; Sources at: Max Load Its = CBF w/25 db SLL (..) MVDR (-) CBF-GSC Blend (x) DMR Excision (+) DMR Diag. Load (-.) CBF-EDMR Blend (-) Subarray DMR Blend (-) Cosine 1 28 Figure 6.4

29 Ship Tracks: 3 Minute Event Multiple Source Tracks Re: Own Ship at Origin 2 1 wavelengths wavelengths 29

30 ONR Acoustic Observatory Segment (L = 1, N = 48) or (L = 4, N = 192)???? at f Horizontal Beam Pattern: f =.2, s = f = 1. at f Horizontal Beam Pattern: f = ????? at f V B P: f =.2, shading = V B P: f = ? at f =.4 (auxiliary array 2 hyd. groups).25? at f =.2 (auxiliary array 4 hyd. groups) 3

BTR Comparison: f =.2, D = 1 (PKE = Phase Known Exactly) (L = 1, N =48) CBF ES (Na = 48) SISC(Na = 12) SAPP (Na = 12) CBF: f =.

2 R1LS48-1SAS D=1 T=31 12 snapshot number 2 6 8 1 12 1 16 18 1 2 3 cosine of bearing index CBF: f =.

31 BTR Comparison: f =.2, D = 1 (PKE = Phase Known Exactly) (L = 1, N =48) CBF ES (Na = 48) SISC(Na = 12) SAPP (Na = 12) CBF: f =.2, R1LS48-1ELE ES s DMR: = 1 f=.2 R1LS48-1ELE SISC: D=1 T=31 f=.2 R1LS48-1SAS D=1 SAPP: T=31 f=.2 R1LS48-1SAS D=1 T=31 12 snapshot number cosine of bearing index CBF: f =.2, R4LS192-ESD s = cosine of bearing index ES DMR: f=.2 R4LS192-ESD D=1 T= cosine of bearing index SISC: f=.2 R4LS192-SAS D=1 SAPP: T=31 f=.2 R4LS192-.ma D=1 T=31 (L = 4, N =192) CBF ES (Na = 192) SISC(Na = 24) SAPP (Na = 48) snapshot number snapshot number cosine of bearing index cosine of bearing index cosine of bearing index cosine of bearing index 5

CBF: f =.4, R1LS48-1ELE ES s DMR: = 1 f=.4 R1LS48-1ELE D=12 SISC: T=31 f=.

4 R1LS48-1SAS D=12 T=31 12 snapshot number 2 6 8 1 12 1 16 11 1 9 8 7 6 18 1 2 3 cosine of bearing

4 R4LS192-ESD D=12 T=31 1 2 cosine of bearing index SISC: f=.

32 BTR Comparison: f =.4, D = 12 (PKE = Phase Known Exactly) (L = 1, N =48) CBF ES (Na = 48) SISC(Na = 24) SAPP (Na = 24) CBF: f =.4, R1LS48-1ELE ES s DMR: = 1 f=.4 R1LS48-1ELE D=12 SISC: T=31 f=.4 R1LS48-1SAS D=12 SAPP: T=31 f=.4 R1LS48-1SAS D=12 T=31 12 snapshot number cosine of bearing index CBF: f =.4, R4LS192-ESD s = cosine of bearing index ES DMR: f=.4 R4LS192-ESD D=12 T= cosine of bearing index SISC: f=.4 R4LS192-SAS D=12 T= cosine of bearing index SAPP: f=.4 R4LS192-.ma D=12 T=31 (L = 4, N =192) CBF ES (Na = 192) SISC(Na = 48) SAPP (Na = 96) 5 12 snapshot number cosine of bearing index cosine of bearing index cosine of bearing index cosine of bearing index

33 AG ES DMR: N = 48, D = 1/12 (PKE WNGC = 12 db) CBF f1 CBF f2 MVDR f1 MVDR f2 ABFCl f1 ABFCl f2 ABFBlnd f1 ABFBlnd f2 Array Gain (db) Comparison AG Snapshot Number 33

34 AG ES DMR: N = 192, D = 1/12 (PKE WNGC = 12 db) CBF f1 CBF f2 MVDR f1 MVDR f2 ABFCl f1 ABFCl f2 ABFBlnd f1 ABFBlnd f2 Array Gain (db) Comparison AG Snapshot Number 34

35 AG DMR: f =.2, N_a = 12, D = 1 (PKE) 12 1 CBF SISC SISCb SAPP Clairv Array Gain at Frequency.2, N = 48, RunWL-1 8 AG (db) Snapshot Number 35

36 AG SA/SC DMR: f =.2, N = 192, D = 1/12 (PKE) Array Gain at Frequency.2, N = 192, RunWL-4 CBF SISC SISCb SAPP Clairv AG (db) Snapshot Number 36

37 AG DMR: f =.4, N a = 24, D = 12 (PKE) Array Gain at Frequency.4, N = 48, RunWL-1 CBF SISC SISCb SAPP Clairv AG (db) Snapshot Number 37

38 AG SA/SC DMR: f =.4, N = 192, D = 1/12 (PKE) Array Gain at Frequency.4, N = 192, RunWL-4 CBF SISC SISCb SAPP Clairv AG (db) Snapshot Number 38

39 Clue to SISC AG Degradation: Stochastic v. Clairvoyant Weight Vector MS Weight Magnitude Squared, db Weight Magnitudes at Frequency.4, N = 192, RunWL-4 dtargu SISCU SISC SISCblend Subarray SISCUClair SISCClair dtarg Snapshot Number 39

40 Final Comments Candidate ABF spaces for efficient DMR ABF: Beam, subarray, auxiliary (sparseness is key) Adaptation space sample vector should/can be independent of beam steering direction and have N a order O(D + safety factor). The Steering Invariant Sidelobe Canceller (SISC) is an auxiliary space method that can hedge on the spatial sampling theorem and increase efficiency. AG is an open issue. Measure the need for ABF at higher frequencies. Signal Suppression v. Spatial Resolution: Clairvoyant ABF without an infinite number of beams suppresses loud sources but, by definition, produces the best spatial resolution.

41 BACKUP 41

42 AG ES DMR: N = 48, D = 1/12 (2 degree phase pert) Array Gain (db) Comparison CBF f1 CBF f2 MVDR f1 MVDR f2 ABFCl f1 ABFCl f2 ABFBlnd f1 ABFBlnd f2 AG Snapshot Number 42

43 Session V: Sonar I (Classified) Adaptive Beamforming with the T-16 Array for Broadband Detection H. Cox/ Orincon Corporation S. Kogon/ MIT Lincoln Laboratory H. Lai/ Orincon Corporation T. Phipps/ UT ARL Adaptive Array Processing for the MK-48 Torpedo in a Shallow Water Countermeasure Scenario A. Mirkin/ NUWC N. Pulsone/ MIT Lincoln Laboratory An Adaptive Beamformer for Spectrum Analysis in Passive Sonar Systems S. Kogon/ MIT Lincoln Laboratory K. Arsenault/ MIT Lincoln Laboratory Sub-Aperture Beamspace Adaptive Array Processing H. Freese/ SAIC B. Sperry / SAIC K. Votaw/ / SAIC 43

44 Session V: Sonar I - Themes Detection v. Classification in Clutter ABF for Detection in Clutter Spatial resolution is key Aggressive/minimally constrained BB ABF High SNR signal suppression is acceptable ABF for Classification in Clutter Minimum spectral distortion is key Highly constrained mainlobe ABF Must balance rejection of undesired interference in the beam with suppression of desired signal in the same beam Rapid Adaptivity Reverberation, shipping dynamics, array motion and high data dimensionality 44

45 Shipping Parameters Number of sources = 8 Source SoA = 1.5 knts. Source SoA = 4.1 knts. Source SoA = 8.2 knts. Source SoA = 6.8 knts. Source SoA = 7.5 knts. Source SoA = 6.8 knts. Source SoA =.5 knts. Source SoA =.3 knts. Source Level Range(wl) Prop Loss Amb Level SNR SoA(wl/s) Heading (SourceInfo = 1.e+3 *)

46 Figure 3.4 Response (db) C/SAMV: f =.2 p = Response (db) C/RSAMV: WNGC(db) = Angle(deg) Angle(deg) 46

47 Six Stationary Sources (pert=.7, D = 7, N=48, M=12, f =.2, sa group size = 4) Power (db) phase interval =.7; Sources at: CBF w/25 db SLL (...) MVDR (---) CBF-EDMR Blend (-) DMR GSC (-) GSCmlm = db Hyd. Group Size = 4 WNGC = 12 db Cosine 47 Figure 5.2

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