Robust adaptive nulling in matched field processing
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Robust Adaptive Nulling in 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. Outline. • Motivation • Null-broadening in plane wave beamforming

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Robust adaptive nulling in matched field processing

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


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


Motivation

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


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]


How Does It Work ?

I am the

interferer.

  • Augmentation of convariance matrix : Mailloux

  • Frequency synthesis : Zatman

  • Weight vector

I am the

interferer.


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


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


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


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


Pekeris Waveguide

z = 0 m

C=1500 m/sec

z=213m

C=1600 m/sec


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.



Theory on Waveguide Invariants : SWellEx-96

  • The theory of waveguide invariance shows that a shift in range can be defined as:

  • From the figure,


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.



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


Constructing Display of

Ambiguity Surface and Beam Pattern

Depth

Range

Focused at

target depth

Time

Depth

Range

Range


Ambiguity Surface : Bartlett and WNC

  • Broadband simulation of second interferer using real data

  • Ten frequency components between 53 Hz - 74 Hz are incoherently averaraged


Beam Patterns : WNC

  • For null-broadening, 15 frequency bins are used.

  • Ten frequency components between 53Hz - 74Hz are incoherently averaged.


Slice of Beam Pattern

Target

Interferer

Solid Line: W/out Null-Broadening

Thick Solid Line: W/ Null-Broadening


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


Beam Patterns at 62Hz : WNC

  • For null-broadening, 15 frequency bins are used.


Slice of Beam Pattern

Target

Interferer

Solid Line: W/out Null-Broadening

Thick Solid Line: W/ Null-Broadening


Application to

Adaptively Weighted Time Reversal Mirror

Conventional TRM

focused at (6000m,60m)


Application to

Adaptively Weighted Time Reversal Mirror

Adaptively weighted TRM

with a null

steered at (6300 m, 80 m)


Application to

Adaptively Weighted Time Reversal Mirror

Adaptively weighted TRM

with a null

steered at (6300 m, 80 m)

with null-broadening


Summary

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


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