  In this contribution, an algorithm for evaluating the capacity-achieving
input covariance matrices for frequency selective Rayleigh MIMO channels is
proposed. In contrast with the flat fading Rayleigh cases, no closed-form
expressions for the eigenvectors of the optimum input covariance matrix are
available. Classically, both the eigenvectors and eigenvalues are computed
numerically and the corresponding optimization algorithms remain
computationally very demanding. In this paper, it is proposed to optimize
(w.r.t. the input covariance matrix) a large system approximation of the
average mutual information derived by Moustakas and Simon. An algorithm based
on an iterative water filling scheme is proposed, and its convergence is
studied. Numerical simulation results show that, even for a moderate number of
transmit and receive antennas, the new approach provides the same results as
direct maximization approaches of the average mutual information.
