Random Matrix Approach for the Capacity of Large-Scale MIMO Systems using the Harish-Chandra Formula

The future communication networks tend to be denser and the use of large number of antennas becomes an attractive feature in 5G systems. However, the analysis and design of such networks become more challenging as engineers find a difficulty to deal with the scalability problem. That is it is not trivial to define the precise achievable rate region as the number of network terminals and bandwidth size increase (i.e., mmWave communications). However, it has been noticed that the macroscopic view of the network can provide a useful abstraction. As the system gets larger, the macroscopic view can ease the network optimization solution and provide attractive engineering insights. To this end, random matrix theory (RMT) has been used to model the interaction complexity between multiple terminals in multi-antenna systems, where it can provide the asymptotic behaviour of the eigenvalue distributions of the products and sums of matrices. In this paper, we present a random matrix approach to derive the capacity of multi-antenna systems over Rayleigh fading channels. We also study the impact of channel correlation on the capacity of multiple-input multiple-output (MIMO) systems.