6533b86efe1ef96bd12cc7f9

RESEARCH PRODUCT

Testing Equality of Multiple Power Spectral Density Matrices

Daniel RomeroJavier ViaRoberto Lopez-valcarceIgnacio SantamariaDavid Ramirez

subject

Multivariate statisticsGaussian02 engineering and technologyGeneralized likelihood tatio test (GLRT)Toeplitz matrixUniformly most powerful invariant test (UMPIT)01 natural sciencesElectronic mail010104 statistics & probabilitysymbols.namesakePower spectral density (PSD)0202 electrical engineering electronic engineering information engineeringApplied mathematics0101 mathematicsElectrical and Electronic EngineeringGeneralized likelihood ratio test (GLRT)MathematicsTelecomunicaciones1299 Otras Especialidades MatemáticasDetectorUnivariateSpectral density020206 networking & telecommunicationsInvariant (physics)Toeplitz matrixSignal ProcessingsymbolsTime-SeriesLocally most powerful invariant test (LMPIT)

description

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. This work was partly supported by the Spanish MINECO grants COMONSENS Network (TEC2015-69648-REDC) and KERMES Network (TEC2016-81900-REDT/AEI); by the Spanish MINECO and the European Commission (ERDF) grants ADVENTURE (TEC2015-69868-C2-1- R), WINTER (TEC2016-76409-C2-2-R), CARMEN (TEC2016-75067-C4-4- R) and CAIMAN (TEC2017-86921-C2-1-R and TEC2017-86921-C2-2-R); by the Comunidad de Madrid grant CASI-CAM-CM (S2013/ICE-2845); by the Xunta de Galicia and ERDF grants GRC2013/009, R2014/037 and ED431G/04 (Agrupacion Estratexica Consolidada de Galicia accred- ´ itation 2016-2019); by the SODERCAN and ERDF grant CAIMAN (12.JU01.64661); and by the Research Council of Norway grant FRIPRO TOPPFORSK (250910/F20). This paper was presented in part at the 2018 IEEE International Conference on Acoustics, Speech and Signal Processing.

yearjournalcountryeditionlanguage
2018-12-01
http://hdl.handle.net/10016/31462