On slow-fading non-separable correlation MIMO systems

TL;DR

This paper develops a method using operator-valued free probability to compute the asymptotic eigenvalue distribution of large block matrices in slow-fading MIMO channels with correlated Gaussian entries, aiding performance analysis.

Contribution

It introduces a novel approach to determine the eigenvalue distribution of block matrices in slow-fading MIMO systems with non-separable correlation, extending free probability techniques.

Findings

Derived a system of equations for eigenvalue distribution

Provided a numerical method for computation

Applied to correlated Gaussian MIMO channels

Abstract

In a frequency selective slow-fading channel in a MIMO system, the channel matrix is of the form of a block matrix. We propose a method to calculate the limit of the eigenvalue distribution of block matrices if the size of the blocks tends to infinity. We will also calculate the asymptotic eigenvalue distribution of $HH^*$, where the entries of $H$ are jointly Gaussian, with a correlation of the form $E[h_{pj}\bar h_{qk}]= \sum_{s=1}^t \Psi^{(s)}_{jk}\hat\Psi^{(s)}_{pq}$ (where $t$ is fixed and does not increase with the size of the matrix). We will use an operator-valued free probability approach to achieve this goal. Using this method, we derive a system of equations, which can be solved numerically to compute the desired eigenvalue distribution.