RT Journal Article
T1 Detection of multivariate cyclostationarity
A1 Ramírez García, David
A1 Schreier, Peter J.
A1 Vía, Javier
A1 Santamaría, Ignacio
A1 Scharf, Louis L.
AB This paper derives an asymptotic generalized likelihood ratio test (GLRT) and an asymptotic locally most powerful invariant test (LMPIT) for two hypothesis testing problems: 1) Is a vector-valued random process cyclostationary (CS) or is it wide-sense stationary (WSS)? 2) Is a vector-valued random process CS or is it nonstationary? Our approach uses the relationship between a scalar-valued CS time series and a vector-valued WSS time series for which the knowledge of the cycle period is required. This relationship allows us to formulate the problem as a test for the covariance structure of the observations. The covariance matrix of the observations has a block-Toeplitz structure for CS and WSS processes. By considering the asymptotic case where the covariance matrix becomes block-circulant we are able to derive its maximum likelihood (ML) estimate and thus an asymptotic GLRT. Moreover, using Wijsman's theorem, we also obtain an asymptotic LMPIT. These detectors may be expressed in terms of the Loève spectrum, the cyclic spectrum, and the power spectral density, establishing how to fuse the information in these spectra for an asymptotic GLRT and LMPIT. This goes beyond the state-of-the-art, where it is common practice to build detectors of cyclostationarity from ad-hoc functions of these spectra.
SN 1053-587X
YR 2015
FD 2015-10-15
LK https://hdl.handle.net/10016/31470
UL https://hdl.handle.net/10016/31470
LA eng
DS e-Archivo
RD 1 may. 2024