Scale-invariant subspace detectors based on first- and second-order statistical models

The problem is to detect a multi-dimensional source transmitting an unknown sequence of complex-valued symbols to a multi-sensor array. In some cases the channel subspace is known, and in others only its dimension is known. Should the unknown transmissions be treated as unknowns in a first-order sta...

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Detalhes bibliográficos
Autores: Santamaría Caballero, Luis Ignacio|||0000-0003-0040-7436, Scharf, Louis L., Ramírez García, David
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/20606
Acesso em linha:http://hdl.handle.net/10902/20606
Access Level:acceso abierto
Palavra-chave:Detection
Generalized likelihood ratio (GLR)
Likelihood
Multi-sensor array
Multivariate normal model (MVN)
Scale-invariant detector
Subspace signals
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spelling Scale-invariant subspace detectors based on first- and second-order statistical modelsSantamaría Caballero, Luis Ignacio|||0000-0003-0040-7436Scharf, Louis L.Ramírez García, DavidDetectionGeneralized likelihood ratio (GLR)LikelihoodMulti-sensor arrayMultivariate normal model (MVN)Scale-invariant detectorSubspace signalsThe problem is to detect a multi-dimensional source transmitting an unknown sequence of complex-valued symbols to a multi-sensor array. In some cases the channel subspace is known, and in others only its dimension is known. Should the unknown transmissions be treated as unknowns in a first-order statistical model, or should they be assigned a prior distribution that is then used to marginalize a first-order model for a second-order statistical model? This question motivates the derivation of subspace detectors for cases where the subspace is known, and for cases where only the dimension of the subspace is known. For three of these four models the GLR detectors are known, and they have been reported in the literature. But the GLR detector for the case of a known subspace and a second-order model for the measurements is derived for the first time in this paper. When the subspace is known, second-order generalized likelihood ratio (GLR) tests outperform first-order GLR tests when the spread of subspace eigenvalues is large, while first-order GLR tests outperform second-order GLR tests when the spread is small. When only the dimension of the subspace is known, second-order GLR tests outperform first-order GLR tests, regardless of the spread of signal subspace eigenvalues. For a dimension-1 source, first-order and second-order statistical models lead to equivalent GLR tests. This is a new finding.The work by I. Santamaria was supported by the Ministerio de Ciencia e Innovación of Spain, and AEI/FEDER funds of the E.U., under Grants TEC2016-75067-C4-4-R (CARMEN) and PID2019-104958RB-C43 (ADELE). The work by Louis Scharf is supported by the Air Force Office of Scientific Research under contract FA9550-18-1-0087, and by the National Science Foundation (NSF) under contract CCF-1712788. The work of David Ramírez was supported by the Ministerio de Ciencia, Innovación y Universidades under grant TEC2017-92552-EXP (aMBITION), by the Ministerio de Ciencia, Innovación y Universidades, jointly with the European Commission (ERDF), under Grant TEC2017-86921-C2-2-R (CAIMAN), and by The Comunidad de Madrid under grant Y2018/TCS-4705 (PRACTICO-CM).Institute of Electrical and Electronics Engineers, Inc.Universidad de Cantabria20202020-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttp://hdl.handle.net/10902/20606IEEE Transactions on Signal Processing, 2020, 68, 6432-6443reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/206062026-06-02T12:39:31Z
dc.title.none.fl_str_mv Scale-invariant subspace detectors based on first- and second-order statistical models
title Scale-invariant subspace detectors based on first- and second-order statistical models
spellingShingle Scale-invariant subspace detectors based on first- and second-order statistical models
Santamaría Caballero, Luis Ignacio|||0000-0003-0040-7436
Detection
Generalized likelihood ratio (GLR)
Likelihood
Multi-sensor array
Multivariate normal model (MVN)
Scale-invariant detector
Subspace signals
title_short Scale-invariant subspace detectors based on first- and second-order statistical models
title_full Scale-invariant subspace detectors based on first- and second-order statistical models
title_fullStr Scale-invariant subspace detectors based on first- and second-order statistical models
title_full_unstemmed Scale-invariant subspace detectors based on first- and second-order statistical models
title_sort Scale-invariant subspace detectors based on first- and second-order statistical models
dc.creator.none.fl_str_mv Santamaría Caballero, Luis Ignacio|||0000-0003-0040-7436
Scharf, Louis L.
Ramírez García, David
author Santamaría Caballero, Luis Ignacio|||0000-0003-0040-7436
author_facet Santamaría Caballero, Luis Ignacio|||0000-0003-0040-7436
Scharf, Louis L.
Ramírez García, David
author_role author
author2 Scharf, Louis L.
Ramírez García, David
author2_role author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Detection
Generalized likelihood ratio (GLR)
Likelihood
Multi-sensor array
Multivariate normal model (MVN)
Scale-invariant detector
Subspace signals
topic Detection
Generalized likelihood ratio (GLR)
Likelihood
Multi-sensor array
Multivariate normal model (MVN)
Scale-invariant detector
Subspace signals
description The problem is to detect a multi-dimensional source transmitting an unknown sequence of complex-valued symbols to a multi-sensor array. In some cases the channel subspace is known, and in others only its dimension is known. Should the unknown transmissions be treated as unknowns in a first-order statistical model, or should they be assigned a prior distribution that is then used to marginalize a first-order model for a second-order statistical model? This question motivates the derivation of subspace detectors for cases where the subspace is known, and for cases where only the dimension of the subspace is known. For three of these four models the GLR detectors are known, and they have been reported in the literature. But the GLR detector for the case of a known subspace and a second-order model for the measurements is derived for the first time in this paper. When the subspace is known, second-order generalized likelihood ratio (GLR) tests outperform first-order GLR tests when the spread of subspace eigenvalues is large, while first-order GLR tests outperform second-order GLR tests when the spread is small. When only the dimension of the subspace is known, second-order GLR tests outperform first-order GLR tests, regardless of the spread of signal subspace eigenvalues. For a dimension-1 source, first-order and second-order statistical models lead to equivalent GLR tests. This is a new finding.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10902/20606
url http://hdl.handle.net/10902/20606
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
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, 2020, 68, 6432-6443
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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