Distribution of MIMO mutual information: A large deviations approach

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 to the distribution close to its most probable value, thus obtaining an asymptotically Gaussian distribution, we calculate the full distribution including its tails, which behave quite differently from the bulk of the distribution. Our resulting probability distribution seamlessly interpolates between the Gaussian approximation for rates R close to the ergodic value of the mutual information and the approach of Zheng and Tse [1], valid for large signal to noise ratios rho. This provides us with a tool to analytically calculate outage probabilities 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.