This thesis considers the mutual information distribution of MIMO systems. This quantity provides valuable performance analysis to many applications in MIMO technologies, for example, the outage probability for block-fading channels, multiplexing-diversity-tradeoff optimal limit and base station scheduling strategy. The goal of this work is to establish a comprehensive characterization of the mutual information distribution and to provide useful insights. The fundamental single-user noise-limited system and multi-user interference-limited system are investigated....[ Read more ]

This thesis considers the mutual information distribution of MIMO systems. This quantity provides valuable performance analysis to many applications in MIMO technologies, for example, the outage probability for block-fading channels, multiplexing-diversity-tradeoff optimal limit and base station scheduling strategy. The goal of this work is to establish a comprehensive characterization of the mutual information distribution and to provide useful insights. The fundamental single-user noise-limited system and multi-user interference-limited system are investigated.

Building on the recent work [1], where the moment generating function (MGF) of mutual information was exactly characterized in terms of Painlevé equations, we develop a framework towards a unified understanding and effective calculation of its distribution. First, focusing on the single-user and multi-user scenarios respectively, we demonstrate systematical procedures to derive closed-form expressions for the cumulants of mutual information. Distinguished from the existing rich body of n-asymptotic analyses, our method is able to give the higher-order (in n) correction terms which provide improved accuracy for finite-length antenna arrays. These results yield considerable new insights, for example, examining the “Gaussianity” of the mutual information when system parameters (e.g., signal to noise ratio) change drastically.

In addition, by focusing on the single-user scenario and making use of our new expressions for the higher-order cumulants (i.e., beyond the mean and variance), we draw upon the Edgeworth expansion technique to propose a refined approximation in closed-form. This approximation is shown to give a very accurate characterization of the mutual information distribution, both around the mean (i.e., in the bulk) and also in the tail region of interest for the outage probability.

Finally, still focusing on the single-user scenario, we employ the saddle point method to represent the mutual information distribution in terms of the rate function, which depends on the MGF. This method investigates the distribution of the non-Gaussian tails with O(n) number of standard deviations away from the mean, which essentially take every cumulant into account, and thus Edgeworth expansion becomes impractical. Our results give accurate approximation to the O(n) tails and are able to recover some previous work, e.g, the diversity-multiplexing-tradeoff formula in [3].