Testing Equality of Multiple Power Spectral Density Matrices

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dc.contributor.author Ramírez García, David
dc.contributor.author Romero, Daniel
dc.contributor.author Vía, Javier
dc.contributor.author López Valcare, Roberto
dc.contributor.author Santamaría, Ignacio
dc.date.accessioned 2020-11-23T14:31:09Z
dc.date.available 2020-11-23T14:31:09Z
dc.date.issued 2018-12-01
dc.identifier.bibliographicCitation D. Ramírez, D. Romero, J. Vía, R. López-Valcarce and I. Santamaría, "Testing Equality of Multiple Power Spectral Density Matrices," in IEEE Transactions on Signal Processing, vol. 66, no. 23, pp. 6268-6280, 1 Dec.1, 2018
dc.identifier.issn 1053-587X
dc.identifier.uri http://hdl.handle.net/10016/31462
dc.description.abstract This paper studies the existence of optimal invariant detectors for determining whether P multivariate processes have the same power spectral density. This problem finds application in multiple fields, including physical layer security and cognitive radio. For Gaussian observations, we prove that the optimal invariant detector, i. e., the uniformly most powerful invariant test, does not exist. Additionally, we consider the challenging case of close hypotheses, where we study the existence of the locally most powerful invariant test (LMPIT). The LMPIT is obtained in the closed form only for univariate signals. In the multivariate case, it is shown that the LMPIT does not exist. However, the corresponding proof naturally suggests an LMPIT-inspired detector that outperforms previously proposed detectors.
dc.description.sponsorship This workwas supported in part by the Spanish MINECO under Grants COMONSENSNetwork (TEC2015-69648-REDC) and KERMES Network (TEC2016-81900-REDT/AEI), in part by the Spanish MINECO and the European Commission(ERDF) under Grants ADVENTURE (TEC2015-69868-C2-1-R), WIN-TER (TEC2016-76409-C2-2-R), CARMEN (TEC2016-75067-C4-4-R), andCAIMAN (TEC2017-86921-C2-1-R) and (TEC2017-86921-C2-2-R), in part bythe Comunidad de Madrid under Grant CASI-CAM-CM (S2013/ICE-2845), inpart by the Xunta de Galicia and ERDF under Grants GRC2013/009, R2014/037,and ED431G/04 (Agrupacion Estratéxica Consolidada de Galicia accreditation2016–2019), in part by the SODERCAN and ERDF under Grant CAIMAN(12.JU01.64661), and in part by the Research Council of Norway under GrantFRIPRO TOPPFORSK (250910/F20).
dc.description.sponsorship Comunidad de Madrid
dc.language.iso eng
dc.rights © 2018 IEEE
dc.subject.other Generalized likelihood tatio test (GLRT)
dc.subject.other Locally most powerful invariant test (LMPIT)
dc.subject.other Power spectral density (PSD)
dc.subject.other Toeplitz matrix
dc.subject.other Uniformly most powerful invariant test (UMPIT)
dc.subject.other Time-Series
dc.title Testing Equality of Multiple Power Spectral Density Matrices
dc.type article
dc.subject.eciencia Telecomunicaciones
dc.identifier.doi 10.1109/TSP.2018.2875884
dc.rights.accessRights openAccess
dc.relation.projectID Comunidad de Madrid. S2013/ICE-2845
dc.relation.projectID Gobierno de España. TEC2015-69868-C2-1-R
dc.relation.projectID Gobierno de España. TEC2017-86921-C2-2-R
dc.relation.projectID Gobierno de España. TEC2016-81900-REDT/AEI
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 6268
dc.identifier.publicationissue 23
dc.identifier.publicationlastpage 6280
dc.identifier.publicationtitle IEEE Transactions on Signal Processing
dc.identifier.publicationvolume 66
dc.identifier.uxxi AR/0000022718
dc.contributor.funder Ministerio de Economía y Competitividad (España)
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