Living at the Edge: A Large Deviations Approach to the Outage MIMO Capacity

TL;DR

This paper employs a large deviations approach to derive the full probability distribution of MIMO channel mutual information for large antenna systems, capturing tail behaviors and enabling analytical outage probability calculations.

Contribution

It introduces a method to compute the entire distribution, including tails, for MIMO mutual information, bridging Gaussian approximations and large SNR asymptotics.

Findings

Derived the full distribution of mutual information including tails.

Provided analytical outage probability calculations across parameters.

Discovered eigenvalue distributions follow Marcenko-Pastur form.

Abstract

Using a large deviations approach we calculate the probability distribution of the mutual information of MIMO channels in the limit of large antenna numbers. In contrast to previous methods that only focused at the distribution close to its mean (thus obtaining an asymptotically Gaussian distribution), we calculate the full distribution, including its tails which strongly deviate from the Gaussian behavior near the mean. The resulting distribution interpolates seamlessly between the Gaussian approximation for rates $R$ close to the ergodic value of the mutual information and the approach of Zheng and Tse for large signal to noise ratios $\rho$. This calculation provides us with a tool to obtain outage probabilities analytically at any point in the $(R, \rho, N)$ parameter space, as long as the number of antennas $N$ is not too small. In addition, this method also yields the probability distribution of eigenvalues constrained in the subspace where the mutual information per antenna is fixed to $R$ for a given $\rho$. Quite remarkably, this eigenvalue density is of the form of the Marcenko-Pastur distribution with square-root singularities, and it depends on the values of $R$ and $\rho$.