Bias for the Trace of the Resolvent and Its Application on Non-Gaussian and Non-centered MIMO Channels

TL;DR

This paper derives the bias for the trace of the resolvent in large random matrix theory and applies it to improve the accuracy of mutual information distribution estimates in non-Gaussian MIMO channels.

Contribution

It introduces a novel bias calculation for the trace of the resolvent and extends it to non-Gaussian MIMO channels, enhancing mutual information analysis.

Findings

Derived the bias for the trace of the resolvent.

Extended bias computation to linear spectral statistics.

Modified CLT improves outage probability estimation.

Abstract

The mutual information (MI) of Gaussian multi-input multi-output (MIMO) channels has been evaluated by utilizing random matrix theory (RMT) and shown to asymptotically follow Gaussian distribution, where the ergodic mutual information (EMI) converges to a deterministic quantity. However, with non-Gaussian channels, there is a bias between the EMI and its deterministic equivalent (DE), whose evaluation is not available in the literature. This bias of the EMI is related to the bias for the trace of the resolvent in large RMT. In this paper, we first derive the bias for the trace of the resolvent, which is further extended to compute the bias for the linear spectral statistics (LSS). Then, we apply the above results on non-Gaussian MIMO channels to determine the bias for the EMI. It is also proved that the bias for the EMI is $-0.5$ times of that for the variance of the MI. Finally, the derived bias is utilized to modify the central limit theory (CLT) and calculate the outage probability. Numerical results show that the modified CLT significantly outperforms previous methods in approximating the distribution of the MI and improves the accuracy for the outage probability evaluation.