Functions of banded Hermitian block Toeplitz matrices in signal processing

The paper deals with the entries of functions of large banded Hermitian block Toeplitz matrices and their perturbations. For general continuous functions, convergence results are established, and for analytic functions, these results are accompanied by estimates of the convergence speed. The applications to signal processing include, among others, the direct derivation of a closed form solution of the minimum mean square error (MMSE) for a double-sided infinite-length linear equalizer for MIMO channels from the finite-length MMSE expression and the derivation of a formula for the contribution of each channel input to the overall MMSE.