## 2015 |

Ramírez, David; Schreier, Peter J; Via, Javier; Santamaria, Ignacio; Scharf, Louis L Detection of Multivariate Cyclostationarity Journal Article IEEE Transactions on Signal Processing, 63 (20), pp. 5395–5408, 2015, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: ad hoc function, asymptotic GLRT, asymptotic LMPIT, block circulant, block-Toeplitz structure, Correlation, covariance matrices, Covariance matrix, covariance structure, cycle period, cyclic spectrum, Cyclostationarity, Detectors, Frequency-domain analysis, generalized likelihood ratio test, generalized likelihood ratio test (GLRT), hypothesis testing problem, locally most powerful invariant test, locally most powerful invariant test (LMPIT), Loe{&amp;amp;}{#}x0300, maximum likelihood estimation, multivariate cyclostationarity detection, power spectral density, random processes, s theorem, scalar valued CS time series, signal detection, spectral analysis, statistical testing, Testing, Time series, Time series analysis, Toeplitz matrices, Toeplitz matrix, ve spectrum, vector valued random process cyclostationary, vector valued WSS time series, wide sense stationary, Wijsman theorem, Wijsman{&amp;amp;}{#}x2019 @article{Ramirez2015, title = {Detection of Multivariate Cyclostationarity}, author = {David Ramírez and Peter J Schreier and Javier Via and Ignacio Santamaria and Louis L Scharf}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7134806}, doi = {10.1109/TSP.2015.2450201}, issn = {1053-587X}, year = {2015}, date = {2015-10-01}, journal = {IEEE Transactions on Signal Processing}, volume = {63}, number = {20}, pages = {5395--5408}, publisher = {IEEE}, 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'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.}, keywords = {ad hoc function, asymptotic GLRT, asymptotic LMPIT, block circulant, block-Toeplitz structure, Correlation, covariance matrices, Covariance matrix, covariance structure, cycle period, cyclic spectrum, Cyclostationarity, Detectors, Frequency-domain analysis, generalized likelihood ratio test, generalized likelihood ratio test (GLRT), hypothesis testing problem, locally most powerful invariant test, locally most powerful invariant test (LMPIT), Loe{&amp;amp;}{#}x0300, maximum likelihood estimation, multivariate cyclostationarity detection, power spectral density, random processes, s theorem, scalar valued CS time series, signal detection, spectral analysis, statistical testing, Testing, Time series, Time series analysis, Toeplitz matrices, Toeplitz matrix, ve spectrum, vector valued random process cyclostationary, vector valued WSS time series, wide sense stationary, Wijsman theorem, Wijsman{&amp;amp;}{#}x2019}, pubstate = {published}, tppubtype = {article} } 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. |