A New Approach for Capacity Analysis of Large Dimensional Multi-Antenna Channels

TL;DR

This paper introduces a rigorous, simple approach to analyze the mutual information of large correlated MIMO channels, confirming previous non-rigorous results and providing explicit mean and variance calculations.

Contribution

It presents a new method based on Poincaré-Nash inequality and integration by parts for capacity analysis of large MIMO channels, offering rigorous results.

Findings

Mutual information converges to a Gaussian distribution as antennas grow large.

Explicit formulas for the mean and variance of the mutual information are derived.

Results validate previous non-rigorous replica method evaluations.

Abstract

This paper adresses the behaviour of the mutual information of correlated MIMO Rayleigh channels when the numbers of transmit and receive antennas converge to infinity at the same rate. Using a new and simple approach based on Poincar\'{e}-Nash inequality and on an integration by parts formula, it is rigorously established that the mutual information converges to a Gaussian random variable whose mean and variance are evaluated. These results confirm previous evaluations based on the powerful but non rigorous replica method. It is believed that the tools that are used in this paper are simple, robust, and of interest for the communications engineering community.