Robust Adaptive Nulling in Matched Field Processing

1. Robust Adaptive Nullingin Matched Field Processing J.S. Kim, W.A. Kuperman, H.C. Song, and W.S. Hodgkiss Marine Physical Lab Scripps Institution of Oceanography University of California, San Diego

2. Outline • Motivation • Null-broadening in plane wave beamforming • Null-broadening in matched field processing • Demonstration of null-broadening in ocean data • Application to null-broadening in adaptively weighted time-reversal mirror • Summary

3. Array signal processing in passive array: null-broadening might provide robust nulling of fast moving interferers in matched field processing with mismatch in array element location and environment Transmission: null-broadening technique provides the control of transmitting beam pattern Motivation

4. Null-broadening in Plane Wave Beamforming • Null-broadening in plane wave beamforming by Augmentation of Covariance Matrix : Mailloux [Electron. Lett., vol. 31, no. 10, pp.771-772, 1995] • Null-broadening in plane wave beamforming by integration of covariance matrix over finite frequency band : Zatman [Electron. Lett., vol. 31, no. 25, pp.2141-2142, 1995]

5. How Does It Work ? I am the interferer. • Augmentation of convariance matrix : Mailloux • Frequency synthesis : Zatman • Weight vector I am the interferer.

6. Null-broadening in Plane Wave Beamforming dB dB Normalized Wave Number Normalized Wave Number • Simulation with ideal cross-spectral density matrix (CSDM) • Target at u=-0.2, and two interferers at u=0.2 and u=0.4 • Broken line : Bartlett, thick solid line : MV-based WNC • Left panel : without null-broadening, right panel : with null-broadening with integrated CSDM over frequency

7. Null-broadening in Plane Wave Beamforming • Simulation with white noise and isotropic noise • 256 Monte-Carlo simulation • Interferer’s level is 30dB higher than target

8. Null-broadening in Matched Field Processing • In plane wave beamforming, the tapering function is explicitly derived as a multiplier to CSDM • No explicit null-broadening formulation has been found in matched field processing to date • Fortunately the invariant property of the waveguide can apply the method of augmentation to the CSDM in the vicinity of the true interferer • This is seemingly similar to the method of Zatman that is based on integrating the CSDM over frequency

9. Theory on Waveguide Invariants • The theory of waveguide invariance shows that a shift in range can be defined as: • where a Pekeris waveguide has a

10. Pekeris Waveguide z = 0 m C=1500 m/sec z=213m C=1600 m/sec

11. Null-Broadening in Pekeris Waveguide Broken Line: Bartlett Solid Line: W/out Null-Broadening Thick Solid Line: W/ Null-Broadening • Ideal CSDM, target at r = 5000 m, interferer at r = 3300 m.

12. Sound Speed Profile for Simulation and SWellEX96

13. Theory on Waveguide Invariants : SWellEx-96 • The theory of waveguide invariance shows that a shift in range can be defined as: • From the figure,

14. Null-Broadening Simulation in SWellEx-96 Environment Broken Line: Bartlett Solid Line: W/out Null-Broadening Thick Solid Line: W/ Null-Broadening • Ideal CSDM, target at r = 5040 m, interferer at r = 3300 m.

15. Plan View of Event S59 in SWellEx-96

16. Requirements on the Data • In order to apply the technique of null-broadening the signal must be broadband • Event S59 recorded a random radiator passing near the FLIP with closest point of 3 Km • The random radiator has a detectable acoustic radiation between 50-75 Hz

17. Constructing Display of Ambiguity Surface and Beam Pattern Depth Range Focused at target depth Time Depth Range Range

18. Ambiguity Surface : Bartlett and WNC • Broadband simulation of second interferer using real data • Ten frequency components between 53 Hz - 74 Hz are incoherently averaraged

19. Beam Patterns : WNC • For null-broadening, 15 frequency bins are used. • Ten frequency components between 53Hz - 74Hz are incoherently averaged.

20. Slice of Beam Pattern Target Interferer Solid Line: W/out Null-Broadening Thick Solid Line: W/ Null-Broadening

21. Ambiguity Surface at 62Hz : Bartlett and WNC • Broadband simulation of second interferer using real data • Ten frequency components between 53 Hz - 74 Hz are incoherently averaraged

22. Beam Patterns at 62Hz : WNC • For null-broadening, 15 frequency bins are used.

23. Slice of Beam Pattern Target Interferer Solid Line: W/out Null-Broadening Thick Solid Line: W/ Null-Broadening

24. Application to Adaptively Weighted Time Reversal Mirror Conventional TRM focused at (6000m,60m)

25. Application to Adaptively Weighted Time Reversal Mirror Adaptively weighted TRM with a null steered at (6300 m, 80 m)

26. Application to Adaptively Weighted Time Reversal Mirror Adaptively weighted TRM with a null steered at (6300 m, 80 m) with null-broadening

27. Null-broadening technique in plane wave beamforming: theory and simulation Null-broadening technique in matched field processing: theory and simulation Null-broadening in sea-going data of SWellEX-96 Application to null-broadening in adaptively weighted time-reversal mirror Summary