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The mutual information (MI) of Gaussian multi-input multi-output (MIMO)channels has been evaluated by utilizing random matrix theory (RMT) and shownto asymptotically follow Gaussian distribution, where the ergodic mutualinformation (EMI) converges to a deterministic quantity. However, withnon-Gaussian channels, there is a bias between the EMI and its deterministicequivalent (DE), whose evaluation is not available in the literature. This biasof 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, whichis further extended to compute the bias for the linear spectral statistics(LSS). Then, we apply the above results on non-Gaussian MIMO channels todetermine 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 isutilized to modify the central limit theory (CLT) and calculate the outageprobability. Numerical results show that the modified CLT significantlyoutperforms previous methods in approximating the distribution of the MI andimproves the accuracy for the outage probability evaluation.

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