A Deterministic Equivalent for the Analysis of Correlated MIMO Multiple Access Channels

TL;DR

This paper introduces deterministic equivalents for analyzing correlated MIMO multiple access channels, enabling accurate approximation of ergodic rates and optimal precoders even under strong correlation, validated through simulations.

Contribution

It provides novel deterministic equivalents for large random matrices, facilitating analysis of correlated MIMO channels and deriving practical precoding strategies.

Findings

Deterministic equivalents accurately approximate ergodic rates.

Precoders designed using these equivalents achieve boundary rates.

Results are validated with Monte Carlo simulations.

Abstract

In this article, novel deterministic equivalents for the Stieltjes transform and the Shannon transform of a class of large dimensional random matrices are provided. These results are used to characterise the ergodic rate region of multiple antenna multiple access channels, when each point-to-point propagation channel is modelled according to the Kronecker model. Specifically, an approximation of all rates achieved within the ergodic rate region is derived and an approximation of the linear precoders that achieve the boundary of the rate region as well as an iterative water-filling algorithm to obtain these precoders are provided. An original feature of this work is that the proposed deterministic equivalents are proved valid even for strong correlation patterns at both communication sides. The above results are validated by Monte Carlo simulations.