Living at the edge: a large deviations approach to the outage MIMO capacity

Pavlos Kazakopoulos Panayotis Mertikopoulos 1 Aris L. Moustakas Giuseppe Caire 2
1 MESCAL - Middleware efficiently scalable
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
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 $\\rho$.
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Pavlos Kazakopoulos, Panayotis Mertikopoulos, Aris L. Moustakas, Giuseppe Caire. Living at the edge: a large deviations approach to the outage MIMO capacity. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2011, 57 (4), pp.1984-2007. 〈10.1109/TIT.2011.2112050〉. 〈hal-00788778〉



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