High SNR approximations of the capacity of MIMO correlated Rician channels: a large system approach

This paper studies high SNR approximations of the ergodic mutual information of block fading MIMO correlated Rician channels. The exact expression of the mutual information of such channels is quite complicated, and difficult to use to obtain convenient high SNR approximations. In this paper, it is replaced by an accurate large system approximant obtained in the case where the number of transmit and receive antennas t and r converge to +infin at the same rate. The large system approximant is studied at high SNR, and it is shown that 3 different behaviours are possible depending on r/t, the rank of the line of sight component and the Rician factor. The accuracy of the high SNR approximant is shown to be connected to the support of the deterministic large system approximant of the eigenvalue distribution of the Gram matrix of the channel. This allows to infer that the approximant is accurate for realistic values of r and t if r and t or if r npar t, the line of sight component is invertible and the Rician factor is greater than a certain threshold.