Effect of Medium Attenuation on the Asymptotic Eigenvalues of Noise Covariance Matrices

TitleEffect of Medium Attenuation on the Asymptotic Eigenvalues of Noise Covariance Matrices
Publication TypeJournal Article
Year of Publication2013
AuthorsMenon R, Gerstoft P, Hodgkiss WS
JournalIeee Signal Processing Letters
Volume20
Pagination435-438
Date Published2013/05
Type of ArticleArticle
ISBN Number1070-9908
Accession NumberWOS:000316408700001
Keywordsarray; Attenuating media; covariance matrix; eigenvalues; function; model; samples; signals; spatial coherence; toeplitz matrices
Abstract

Covariance matrices of noise models are used in signal and array processing to study the effect of various noise fields and array configurations on signals and their detectability. Here, the asymptotic eigenvalues of noise covariance matrices in 2-D and 3-D attenuating media are derived. The asymptotic eigenvalues are given by a continuous function, which is the Fourier transform of the infinite sequence formed by sampling the spatial coherence function. The presence of attenuation decreases the value of the large eigenvalues and raises the value of the smaller eigenvalues (compared to the attenuation free case). The eigenvalue density of the sample covariance matrix also shows variation in shape depending on the attenuation, which potentially could be used to retrieve medium attenuation properties from observations of noise.

DOI10.1109/lsp.2013.2250500
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