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In this contribution, the capacity-achieving input covariance matrices for coherent block-fading correlated MIMO Rician channels are determined. In contrast with the Rayleigh and uncorrelated Rician cases, no closed-form expressions for the eigenvectors of the optimum input covariance matrix are available. Classically, both the eigenvectors and eigen-values are computed by numerical techniques. New results related to the accuracy of the corresponding large system approximation are provided. An attractive optimization algorithm of this approximation is proposed and the authors establish that it yields an effective way to compute the capacity achieving covariance matrix for the average mutual information.
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