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In this contribution, an algorithm for evaluating the capacity-achievinginput covariance matrices for frequency selective Rayleigh MIMO channels isproposed. In contrast with the flat fading Rayleigh case, no closed-formexpressions for the eigenvectors of the optimum input covariance matrix areavailable. Classically, both the eigenvectors and eigenvalues are computednumerically and the corresponding optimization algorithms remaincomputationally very demanding. In this paper, it is proposed to optimize(w.r.t. the input covariance matrix) a large system approximation of theaverage mutual information derived by Moustakas and Simon. The validity of thisasymptotic approximation is clarified thanks to Gaussian large random matricesmethods. It is shown that the approximation is a strictly concave function ofthe input covariance matrix and that the average mutual information evaluatedat the argmax of the approximation is equal to the capacity of the channel upto a O(1/t) term, where t is the number of transmit antennas. An algorithmbased on an iterative waterfilling scheme is proposed to maximize the averagemutual information approximation, and its convergence studied. Numericalsimulation results show that, even for a moderate number of transmit andreceive antennas, the new approach provides the same results as directmaximization approaches of the average mutual information.

On the Capacity Achieving Covariance Matrix for Frequency Selective MIMO Channels Using the Asymptotic Approach