Asymptotic eigenvalue distribution of block toeplitz matrices and application to blind SIMO channel identification

Szego's theorem states that the asymptotic behavior of the eigenvalues of a Hermitian Toeplitz matrix is linked to the Fourier transform of its entrie s. This result was later extended to block Toeplitz matrices, i.e., covaria nce matrices of multivariate stationary professes. The present work gives a new proof of Szego's theorem applied to block Toeplitz matrices. We focus on a particular class of Toeplitz matrices, those corresponding to covarian ce matrices of single-input multiple-output (SIMO) channels. They satisfy s ome Factorization properties that lead to a simpler form of Szego's theorem and allow one to deduce results on the asymptotic behavior of the lowest n onzero eigenvalue for which an upper bound is developed and expressed in te rms of the subchannels frequency responses, This bound is interpreted in th e context of blind channel identification using second-order algorithms, an d more particularly in the case of band-limited channels.