Asymptotic Mutual Information Analysis for Double-Scattering MIMO Channels: A New Approach by Gaussian Tools
Xin Zhang, Shenghui Song
Abstract
The asymptotic mutual information (MI) analysis for multiple-input multiple-output (MIMO) systems over double-scattering channels has achieved engaging results, but the convergence rates of the mean, variance, and the distribution of the MI are not yet available in the literature. In this paper, by utilizing the large random matrix theory (RMT), we give a central limit theory (CLT) for the MI and derive the closed-form approximation for the mean and the variance by a new approach—Gaussian tools. The convergence rates of the mean, variance, and the characteristic function are proved to be <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {O}}\left({\frac {1}{N}}\right)$ </tex-math></inline-formula> for the first time, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> is the number of receive antennas. Furthermore, the impact of the number of effective scatterers on the mean and variance was investigated in the moderate-to-high SNR regime with some interesting physical insights. The proposed evaluation framework can be utilized for the asymptotic performance analysis of other systems over double-scattering channels.