Channel Modelling of MU-MIMO Systems by Quaternionic Free Probability

This paper studies the asymptotic eigenvalue distribution (AED) 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 by means of quaternions.