Central Limit Theorem for Mutual Information of Large MIMO Systems With Elliptically Correlated Channels

This is the authors' abstract. We don't add key points for this paper.

By considering elliptical correlations in the channel matrix of a large MIMO system, this paper investigates how the non-linear dependency affects the asymptotic behaviors of Shannon's mutual information, as the numbers of antennas at transmitter and receiver both tend to infinity at the same rate. Beyond the almost sure convergence of the information per transmit antenna, we also propose several central limit theorems for the information statistics under various scenarios. The results show that the non-linear correlation has a little impact on the almost sure convergence but has a tremendous effect on the fluctuation of the information statistics. In particular, the centralized information statistics could experience a phase transition in convergence rate when the strength of the non-linear correlation increases. As extensions, several central limit theorems are established as well for general linear spectral statistics of large sample covariance matrices in elliptical distributions.