Maximizing mutual information in general MIMO fading AWGN channels under a rank constraint

The maximization of mutual information in a general point-to-point MIMO fading channel with additive white Gaussian noise (AWGN) is considered under a rank constraint on the covariance of the vector Gaussian input. The channel is assumed to have an arbitrarily distribution with the channel state information (CSI) available at the receiver and the channel distribution information known at the transmitter. Solutions to such a problem, for instance, would enable us to investigate the tradeoff between complexity and performance while using low rank signalling as a communication strategy. A numerical algorithm is developed to compute the optimal input covariance that maximizes mutual information, which is a non-convex optimization problem, over the space of rank-constrained positive semi-definite matrices. The necessary Karush-Kuhn Tucker (KKT) conditions are solved to obtain the iterative algorithm.