Mutual information distribution of interference-limited MIMO: A joint Coulomb fluid and Painlevé based approach

This paper investigates the mutual information distribution of interference-limited multiple-input multiple-output channels. We further develop our recent work, where an exact expression was derived for the moment generating function in terms of a Painlevé VI differential equation, along with a Gaussian approximation based on the Coulomb fluid method. In this paper, we adopt a framework based on appropriately combining these results to obtain insight into the distributional behavior. First, we demonstrate that the Coulomb fluid approximation is in fact exact to leading order in the number of antennas, thereby yielding the correct asymptotic mean and variance. We then compute closed-form expressions for the first-order correction terms to the mean and variance, as well as expressions for the third cumulant. These results provide valuable insight into the “Gaussianity” of the mutual information distribution, indicating how the deviations from Gaussian are affected by parameters such as the signal-to-interference-ratio and the number of interferers.