Statistical Properties of Eigen-Modes and Instantaneous Mutual Information in MIMO Time-Varying Rayleigh Channels

TL;DR

This paper analyzes the statistical behavior of eigen-modes and instantaneous mutual information in MIMO Rayleigh channels, providing exact formulas and insights into their correlation, fade durations, and environmental sensitivity.

Contribution

It offers new closed-form expressions for second-order statistics of eigen-modes and IMI, revealing their correlation properties and environmental sensitivities in MIMO channels.

Findings

Eigen-modes tend to be uncorrelated in large MIMO systems.

IMI correlation can be approximated by the squared channel correlation.

LCR of IMI is highly sensitive to scattering environment.

Abstract

In this paper, we study two important metrics in multiple-input multiple-output (MIMO) time-varying Rayleigh flat fading channels. One is the eigen-mode, and the other is the instantaneous mutual information (IMI). Their second-order statistics, such as the correlation coefficient, level crossing rate (LCR), and average fade/outage duration, are investigated, assuming a general nonisotropic scattering environment. Exact closed-form expressions are derived and Monte Carlo simulations are provided to verify the accuracy of the analytical results. For the eigen-modes, we found they tend to be spatio-temporally uncorrelated in large MIMO systems. For the IMI, the results show that its correlation coefficient can be well approximated by the squared amplitude of the correlation coefficient of the channel, under certain conditions. Moreover, we also found the LCR of IMI is much more sensitive to the scattering environment than that of each eigen-mode.