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

Robust Adaptive Nullingin Matched Field Processing

• 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

Outline

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

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]

• Augmentation of convariance matrix : Mailloux

• Frequency synthesis : Zatman

• Weight vector

I am theinterferer.

I am theinterferer.

N

q

ksin

NsinkK

)(

)(

mnmnw

mnwb

bw

kb

w

w

b

bsinkdfK

f

f

)(1 2/

2/

dKd

dKw

1H

1

How Does It Work ?

Normalized Wave Number

dB

Normalized Wave Number

dB

Null-broadening in Plane Wave Beamforming

• 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

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

where a Pekeris waveguide has a

r'

'r

1

1

Theory on Waveguide Invariants

z=213m

z = 0 m

C=1500 m/sec

C=1600 m/sec

3cm/g

35 cm/g.

Pekeris Waveguide

Broken Line: BartlettSolid Line: W/out Null-BroadeningThick Solid Line: W/ Null-Broadening

Null-Broadening in Pekeris Waveguide

• Ideal CSDM, target at r = 5000 m, interferer at r = 3300 m.

Sound Speed Profile for Simulation and SWellEX96

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

From the figure,

Theory on Waveguide Invariants : SWellEx-96

r'

'r

1

1

Null-Broadening Simulationin SWellEx-96 Environment

Broken Line: BartlettSolid Line: W/out Null-BroadeningThick Solid Line: W/ Null-Broadening

• Ideal CSDM, target at r = 5040 m, interferer at r = 3300 m.

Plan View of Event S59 in SWellEx-96

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

2f

1f

3t

2t

1t

f Focused at

target depth

Range

Time

Range

Dep

th

Range

Dep

th

Constructing Display ofAmbiguity Surface and Beam Pattern

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

Solid Line: W/out Null-BroadeningThick Solid Line: W/ Null-Broadening

TargetInterferer

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

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

Beam Patterns at 62Hz : WNC

Slice of Beam Pattern

Solid Line: W/out Null-BroadeningThick Solid Line: W/ Null-Broadening

Target

Interferer

Conventional TRMfocused at (6000m,60m)

Application toAdaptively Weighted Time Reversal Mirror

Adaptively weighted TRM with a nullsteered at (6300 m, 80 m)

Application toAdaptively Weighted Time Reversal Mirror

Adaptively weighted TRM with a nullsteered at (6300 m, 80 m)with null-broadening

Application toAdaptively Weighted Time Reversal Mirror

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