Applications of large empirical spatio-temporal covariance matrix in multipath channels detection

This paper addresses the detection of a single signal in a multipath propagation channel using a sensors array in the case where the number of sensors M and the number of observations N are large and of the same order of magnitude and where the number of paths P is much smaller than M and N. In contrast with the single path context, the GLRT test cannot be implemented, and we evaluate the behaviour of tests based on the largest eigenvalues of the empirical spatio-temporal covariance matrix. Using a technical result showing that the largest singular values of low rank deterministic pertubation of certain Gaussian block-Hankel large random matrices behave as if the entries of the latter random matrices were independent identically distributed, we obtain a clear understanding of the advantages of the use of the spatial-temporal covariance matrix.