On the fluctuations of the mutual information for non centered MIMO channels: The non Gaussian case

The use of Multiple Input Multiple Output (MIMO) systems has been widely recognized as an efficient solution to increase the data rate of wireless communications. In this regard, several contributions investigate the performance improvement of MIMO systems in terms of Shannon's mutual information. In most of these contributions, elements of the MIMO channel matrix are assumed to belong to a multivariate Gaussian distribution. The non Gaussian case, which is realistic in many practical environments, has been much less studied. This contribution is devoted to the study of the mutual information of MIMO channels when the channel matrix elements are Ricean with the non-Ricean component being iid but non-Gaussian. In this context, the mutual information behavior is studied in the large dimensional regime where both channel matrix dimensions converge to infinity at the same pace. In this regime, a Central Limit Theorem on the mutual information is provided. In particular, the mutual information variance is determined in terms of the parameters of the channel statistical model. Since non Gaussian entries are allowed, a new term proportional to the fourth cumulant of their distribution arises in the expression of the asymptotic variance. In addition, a bias term proportional to this fourth order cumulant appears.