Random Matrix Systems with Block-Based Behavior and Operator-Valued Models

A model to estimate the asymptotic isotropic mutual information of a multiantenna channel is considered. Using a block-based dynamics and the angle diversity of the system, we derived what may be thought of as the operator-valued version of the Kronecker correlation model. This model turns out to be more flexible than the classical version, as it incorporates both an arbitrary channel correlation and the correlation produced by the asymptotic antenna patterns. A method to calculate the asymptotic isotropic mutual information of the system is established using operator-valued free probability tools. A particular case is considered in which we start with explicit Cauchy transforms and all the computations are done with diagonal matrices, which make the implementation simpler and more efficient.