Non-Hermitian Random Matrix Theory for MIMO Channels

Abstract

The propagation mechanism of signals for multiple input multiple output (MIMO) channels can be explained via a random matrix. Random matrix theory is a very powerful tool to understand behaviour of such channels and analyse their performance measure of MIMO systems. In this work we study: The asymptotic eigenvalue distribution and the mutual information of a multiuser (MU) multiple-input multiple output (MIMO) channel with a certain fraction of users experiencing line-of-sight. It shows that the AED of the channel matrix decomposes into two separate bulks for practically relevant parameter choices and differs very much from the common assumption of independent identically distributed (iid) entries which induces the quarter circle law. This happens even without antenna correlation at either side of the channel. In order to tackle this problem the paper makes use of recent developments in free probability theory which allow to deal with complex-valued eigenvalue distributions of non-Hermitian matrices. Moreover to understand behaviour of MIMO channels we derived asymptotic complex-valued eigenvalue distributions of practically relevant channels models by means of their respective square equivalent and singular equivalent of channel matrices. Finally we derived an explicit mutual information formula which allows us calculate the mutual information (in general) analytically in high signal-to noiseratio (SNR) regime for numerous practical important scenarios. Furthermore the numerical result shows that, high-SNR approximation draws reliable portrait even for quite moderate SNR level.