Some results on MIMO mutual information: the high SNR case

We consider multiple-input multiple-output (MIMO) communication systems where the transmitted vector has a zero-mean complex Gaussian distribution, independently and identically distributed across the transmit antennas. For arbitrary fading statistics, we decompose a high-SNR approximation of the mutual information as a sum of three terms involving: (1) average SNR; (ii) SNR fading; and (iii) a term characterizing the "effective rank", or eigenvalue dispersion, of the channel matrix. For further insight, we derive the probability densities of the latter two terms under frequency-flat Rayleigh iid fading, and show that the component of mutual information due to SNR fading is asymptotically Gaussian (in the number of antennas) with variance depending only on the ratio of the number of transmit and receive antenna elements.