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