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

08/22/2021
by   Xin Zhang, et al.
0

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 approximate the outage probability. Numerical results show that the modified CLT significantly outperforms the previous results in approximating the distribution of the MI and can accurately determine the outage probability.

READ FULL TEXT
research
07/26/2022

Asymptotic Mutual Information Analysis for Double-scattering MIMO Channels: A New Approach by Gaussian Tools

The asymptotic mutual information (MI) analysis for multiple-input multi...
research
04/01/2023

Fundamental Limits of Holographic MIMO Channels: Tackling Non-Separable Transceiver Correlation

Holographic MIMO communication was proposed to sufficiently exploit the ...
research
11/24/2022

Optical MIMO communication with unequal power allocation to channels

Multiple input multiple output (MIMO) approach in fiber optical communic...
research
01/28/2023

On the Mutual Information of Multi-RIS Assisted MIMO: From Operator-Valued Free Probability Aspect

The reconfigurable intelligent surface (RIS) is useful to effectively im...
research
03/04/2023

Derivatives of mutual information in Gaussian channels

We derive a general formula for the derivatives of mutual information be...
research
04/11/2023

Breakdown of a concavity property of mutual information for non-Gaussian channels

Let S and S̃ be two independent and identically distributed random varia...
research
01/19/2019

Ergodic MIMO Mutual Information: Twenty Years After Emre Telatar

In the celebrated work of Emre Telatar in the year 1999 (14274 citations...

Please sign up or login with your details

Forgot password? Click here to reset