Structure of Optimal Input Covariance Matrices for MIMO Systems with Covariance Feedback under General Correlated Fading

TL;DR

This paper characterizes the optimal input covariance matrices for MIMO systems with covariance feedback under general correlated fading, introducing the concept of right commutant to simplify the optimization.

Contribution

It introduces the novel concept of right commutant to analyze and simplify the optimization of input covariance matrices in correlated MIMO channels.

Findings

Derived conditions for simplifying the optimization problem.

Reproduced known results for Kronecker product models.

Provided a unified framework for general correlated fading.

Abstract

We describe the structure of optimal Input covariance matrices for single user multiple-input/multiple-output (MIMO) communication system with covariance feedback and for general correlated fading. Our approach is based on the novel concept of right commutant and recovers previously derived results for the Kronecker product models. Conditions are derived which allow a significant simplification of the optimization problem.