Characterizing the mutual information distribution of MIMO systems: Beyond the Gaussian approximation

This paper investigates the mutual information distribution of MIMO channels. We further develop our recent work, where an exact expression was derived for the moment generating function in terms of a Painleve V differential equation, along with a Gaussian approximation. Based on the exact representation, we systematically compute closed-form expressions for the high-order cumulants of the mutual information distribution to leading order in the number of antennas, as well as first-order correction terms which provide improved accuracy for finite-length arrays. These results yield considerable new insight, for example, providing a technical explanation as to why the Gaussian approximation is quite robust to the system parameters for the case of unequal transmit and receive antenna arrays, whilst for equal antenna arrays it deviates strongly as the SNR increases. In addition, by employing our new expressions for the higher order cumulants, we draw upon the Edgeworth expansion technique to propose a refined Gaussian approximation. This approximation is shown to give a very accurate closed-form characterization of the mutual information distribution, both around the mean and also in the tail region of interest for the outage probability.