Random Matrix Systems with Block-Based Behavior and Operator-Valued Models

TL;DR

This paper introduces a flexible operator-valued model for multiantenna channels that accounts for arbitrary correlations and antenna pattern effects, providing a method to compute asymptotic mutual information using free probability.

Contribution

It develops an operator-valued Kronecker correlation model for multiantenna channels and offers a practical computational approach for asymptotic mutual information.

Findings

The model captures both channel and antenna pattern correlations.

Explicit calculations are simplified using diagonal matrices.

The approach enhances the accuracy of mutual information estimation.

Abstract

A model to estimate the asymptotic isotropic mutual information of a multiantenna channel is considered. Using a block-based dynamics and the angle diversity of the system, we derived what may be thought of as the operator-valued version of the Kronecker correlation model. This model turns out to be more flexible than the classical version, as it incorporates both an arbitrary channel correlation and the correlation produced by the asymptotic antenna patterns. A method to calculate the asymptotic isotropic mutual information of the system is established using operator-valued free probability tools. A particular case is considered in which we start with explicit Cauchy transforms and all the computations are done with diagonal matrices, which make the implementation simpler and more efficient.