On the Ergodic Capacity of Frequency Selective MIMO Systems Equipped with MMSE Receivers: An Asymptotic Approach

This paper is devoted to the study of the ergodic capacity of frequency selective MIMO systems equipped with a MMSE receiver when the channel state information is available at the receiver side and when the second order statistics of the channel taps are known at the transmitter side. As the expression of this capacity is rather complicated and difficult to analyse, it is studied in the case where the number of transmit and receive antennas converge to +oo at the same rate. In this asymptotic regime, the main results of the paper are related to the design of an optimal precoder in the case where the transmit antennas are correlated. It is shown that the left singular eigenvectors of the optimum precoder coincide with the eigenvectors of the mean of the channel taps transmit covariance matrices, and its singular values are solution of a certain maximization problem.