@article {453, title = {Detection of Multivariate Cyclostationarity}, journal = {IEEE Transactions on Signal Processing}, volume = {63}, year = {2015}, month = {October}, pages = {5395-5408}, abstract = {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{\textquoteright}s theorem, we also obtain an asymptotic LMPIT. These detectors may be expressed in terms of the Lo{\`e}ve 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.}, author = {Ram{\'\i}rez, David and Schreier, Peter J. and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Louis L. Scharf} }