On the Detection of Low-Rank Signal in the Presence of Spatially Uncorrelated Noise: A Frequency Domain Approach

This paper analyzes the detection of a M-dimensional useful signal modeled as the output of a M × K MIMO filter driven by a K-dimensional white Gaussian noise, and corrupted by a M-dimensional Gaussian noise with mutually uncorrelated components. The study is focused on frequency domain test statist...

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Detalles Bibliográficos
Autores: Rosuel, A, Vallet, P, Loubaton, P, Mestre, X
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)
Repositorio:r-CTTC. Repositorio Institucional Producción Científica del Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)
OAI Identifier:oai:cttc.fundanetsuite.com:p3037
Acceso en línea:https://cttc.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=3037
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85112621311&doi=10.1109%2fTSP.2021.3099644&partnerID=40&md5=46f948f9add85705a7e9abe467e15178
Access Level:acceso abierto
Palabra clave:Eigenvalues and eigenfunctions
Frequency domain analysis
Matrix algebra
Statistical tests
Frequency domain approaches
Frequency domains
High-dimensional
Spectral coherence
Statistical performance
Uncorrelated noise
White Gaussian Noise
Wishart matrices
Gaussian noise (electronic)
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spelling On the Detection of Low-Rank Signal in the Presence of Spatially Uncorrelated Noise: A Frequency Domain ApproachRosuel, AVallet, PLoubaton, PMestre, XEigenvalues and eigenfunctionsFrequency domain analysisMatrix algebraStatistical testsFrequency domain approachesFrequency domainsHigh-dimensionalSpectral coherenceStatistical performanceUncorrelated noiseWhite Gaussian NoiseWishart matricesGaussian noise (electronic)This paper analyzes the detection of a M-dimensional useful signal modeled as the output of a M × K MIMO filter driven by a K-dimensional white Gaussian noise, and corrupted by a M-dimensional Gaussian noise with mutually uncorrelated components. The study is focused on frequency domain test statistics based on the eigenvalues of an estimate of the spectral coherence matrix (SCM), obtained as a renormalization of the frequency-smoothed periodogram of the observed signal. If N denotes the sample size and B the smoothing span, it is proved that in the high-dimensional regime where M,B,N converge to infinity while K remains fixed, the SCM behaves as a certain correlated Wishart matrix. Exploiting well-known results on the behaviour of the eigenvalues of such matrices, it is deduced that the standard tests based on linear spectral statistics of the SCM fail to detect the presence of the useful signal in the high-dimensional regime. A new test based on the SCM, which is proved to be consistent, is also proposed, and its statistical performance is evaluated through numerical simulations. © 1991-2012 IEEE.Institute of Electrical and Electronics Engineers Inc.2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://cttc.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=3037https://www.scopus.com/inward/record.uri?eid=2-s2.0-85112621311&doi=10.1109%2fTSP.2021.3099644&partnerID=40&md5=46f948f9add85705a7e9abe467e15178IEEE TRANSACTIONS ON SIGNAL PROCESSINGISSN: 19410476ISSNe: 1053587Xreponame:r-CTTC. Repositorio Institucional Producción Científica del Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)instname:Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)Inglésinfo:eu-repo/semantics/openAccessoai:cttc.fundanetsuite.com:p30372026-06-17T11:44:47Z
dc.title.none.fl_str_mv On the Detection of Low-Rank Signal in the Presence of Spatially Uncorrelated Noise: A Frequency Domain Approach
title On the Detection of Low-Rank Signal in the Presence of Spatially Uncorrelated Noise: A Frequency Domain Approach
spellingShingle On the Detection of Low-Rank Signal in the Presence of Spatially Uncorrelated Noise: A Frequency Domain Approach
Rosuel, A
Eigenvalues and eigenfunctions
Frequency domain analysis
Matrix algebra
Statistical tests
Frequency domain approaches
Frequency domains
High-dimensional
Spectral coherence
Statistical performance
Uncorrelated noise
White Gaussian Noise
Wishart matrices
Gaussian noise (electronic)
title_short On the Detection of Low-Rank Signal in the Presence of Spatially Uncorrelated Noise: A Frequency Domain Approach
title_full On the Detection of Low-Rank Signal in the Presence of Spatially Uncorrelated Noise: A Frequency Domain Approach
title_fullStr On the Detection of Low-Rank Signal in the Presence of Spatially Uncorrelated Noise: A Frequency Domain Approach
title_full_unstemmed On the Detection of Low-Rank Signal in the Presence of Spatially Uncorrelated Noise: A Frequency Domain Approach
title_sort On the Detection of Low-Rank Signal in the Presence of Spatially Uncorrelated Noise: A Frequency Domain Approach
dc.creator.none.fl_str_mv Rosuel, A
Vallet, P
Loubaton, P
Mestre, X
author Rosuel, A
author_facet Rosuel, A
Vallet, P
Loubaton, P
Mestre, X
author_role author
author2 Vallet, P
Loubaton, P
Mestre, X
author2_role author
author
author
dc.subject.none.fl_str_mv Eigenvalues and eigenfunctions
Frequency domain analysis
Matrix algebra
Statistical tests
Frequency domain approaches
Frequency domains
High-dimensional
Spectral coherence
Statistical performance
Uncorrelated noise
White Gaussian Noise
Wishart matrices
Gaussian noise (electronic)
topic Eigenvalues and eigenfunctions
Frequency domain analysis
Matrix algebra
Statistical tests
Frequency domain approaches
Frequency domains
High-dimensional
Spectral coherence
Statistical performance
Uncorrelated noise
White Gaussian Noise
Wishart matrices
Gaussian noise (electronic)
description This paper analyzes the detection of a M-dimensional useful signal modeled as the output of a M × K MIMO filter driven by a K-dimensional white Gaussian noise, and corrupted by a M-dimensional Gaussian noise with mutually uncorrelated components. The study is focused on frequency domain test statistics based on the eigenvalues of an estimate of the spectral coherence matrix (SCM), obtained as a renormalization of the frequency-smoothed periodogram of the observed signal. If N denotes the sample size and B the smoothing span, it is proved that in the high-dimensional regime where M,B,N converge to infinity while K remains fixed, the SCM behaves as a certain correlated Wishart matrix. Exploiting well-known results on the behaviour of the eigenvalues of such matrices, it is deduced that the standard tests based on linear spectral statistics of the SCM fail to detect the presence of the useful signal in the high-dimensional regime. A new test based on the SCM, which is proved to be consistent, is also proposed, and its statistical performance is evaluated through numerical simulations. © 1991-2012 IEEE.
publishDate 2021
dc.date.none.fl_str_mv 2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://cttc.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=3037
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85112621311&doi=10.1109%2fTSP.2021.3099644&partnerID=40&md5=46f948f9add85705a7e9abe467e15178
url https://cttc.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=3037
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85112621311&doi=10.1109%2fTSP.2021.3099644&partnerID=40&md5=46f948f9add85705a7e9abe467e15178
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers Inc.
publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers Inc.
dc.source.none.fl_str_mv IEEE TRANSACTIONS ON SIGNAL PROCESSING
ISSN: 19410476
ISSNe: 1053587X
reponame:r-CTTC. Repositorio Institucional Producción Científica del Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)
instname:Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)
instname_str Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)
reponame_str r-CTTC. Repositorio Institucional Producción Científica del Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)
collection r-CTTC. Repositorio Institucional Producción Científica del Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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