Testing Equality of Multiple Power Spectral Density Matrices
Fecha de edición:
2018-12-01
Cita:
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
ISSN:
1053-587X
DOI:
10.1109/TSP.2018.2875884
Patrocinador:
Ministerio de Economía y Competitividad (España)
Agradecimientos:
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).
Comunidad de Madrid
Proyecto:
Comunidad de Madrid. S2013/ICE-2845
Gobierno de España. TEC2015-69868-C2-1-R
Gobierno de España. TEC2017-86921-C2-2-R
Gobierno de España. TEC2016-81900-REDT/AEI
Palabras clave:
Generalized likelihood tatio test (GLRT)
,
Locally most powerful invariant test (LMPIT)
,
Power spectral density (PSD)
,
Toeplitz matrix
,
Uniformly most powerful invariant test (UMPIT)
,
Time-Series
Derechos:
© 2018 IEEE
Resumen:
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
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.
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