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