Publication:
Testing Equality of Multiple Power Spectral Density Matrices

Thumbnail Image
Identifiers
URI: https://hdl.handle.net/10016/31462
ISSN: 1053-587X
DOI: 10.1109/TSP.2018.2875884
UXXI: AR/0000022718
Files
testing_ITSP_2018_ps.pdf (3.18 MB)
Publication date
2018-12-01
Defense date
Authors
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Impact
Google Scholar
Export
Research Projects
Organizational Units
Journal Issue
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.
Description
Keywords
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
Bibliographic citation
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
Collections
DTSC - GTSA - Artículos de Revistas