Effects of correlated noise on the cross‐spectral matrix in modal composition space

Abstract

Computer simulations of hydrophone cross‐spectral matrices in a shallow‐water waveguide were generated for signals with different mixtures of, correlated and white noise. These matrices were then mapped to modal composition space, a space populated by vectors whose elements are the amplitudes for the trapped modes. It was found that, in modal composition space, the cross‐spectral matrix is not sensitive to the difference between correlated and white noise, but is sensitive to the difference between noise and signal. While the distribution of signal and white noise among the elements of the cross‐spectral matrix is similar before and after the mapping to modal composition space, the distribution of correlated and white noise is not. Temporally discrete noise sources, which are correlated at the hydrophones, but not from sample to sample, make little or no contribution to the off‐diagonal elements of the cross‐spectral matrix in modal composition space. This fact has significant implications for matched field processing in low signal‐to‐noise situations.