Szegö's theorem states that the asymptotic behavior of the eigenvalues of a Hermitian Toeplitz matrix is linked to the Fourier transform of its entries. This result was later extended to block Toeplitz matrices, i.e., covariance matrices of multi-variate stationary processes. The present work gives a new proof of Szegö's theorem applied to block Toeplitz matrices. We focus on a particular class of Toeplitz matrices, those corresponding to covariance matrices of Single Input Multiple Output channels. They satisfy some factorization properties that lead to a simpler form of Szegö's theorem and allow one to deduce results on the asymptotic behavior of the lowest nonzero eigenvalue for which an upper bound is developed and expressed in terms of the subchannels frequency responces. This bound is interpreted in the context of blind channel identification using second order algorithms, and more particularly the case of bandlimited channels.