The ocean noise coherence matrix and its rank

Area of Science:

• Ocean acoustics
• Signal processing
• Array processing

Background:

• Ocean noise cross-spectral density matrix analysis.
• Separation into Toeplitz and Hankel components.
• Rank deficiency implications in acoustic scenarios.

Purpose of the Study:

• Investigate the influence of the Hankel part on passive fathometry.
• Analyze the effect of the Hankel part on adaptive beamforming.
• Demonstrate findings using numerical simulations and experimental data.

Main Methods:

• Decomposition of the cross-spectral density matrix into Toeplitz and Hankel parts.
• Analysis of rank deficiency for the Toeplitz component.
• Numerical simulations using a half-space model with Rayleigh reflection coefficient.
• Processing of experimental data using conventional and adaptive methods.

Main Results:

• The Toeplitz part of the ocean noise cross-spectral density matrix is substantially rank-deficient.
• The Hankel part has a weak or negligible effect on adaptive beamforming.
• Eigenvalue spectra and beam patterns were derived using circulant matrices.
• Analysis of experimental data confirmed simulation findings.

Conclusions:

• The rank deficiency of the Toeplitz component has significant implications for adaptive beamforming.
• The Hankel component's limited influence simplifies the understanding of passive fathometry.
• A potential solution to long-standing processing inconsistency puzzles is suggested.