Random Matrix Products in Wireless (Multiantenna) Sytems

Modeling a multiantenna wireless channel via a product of independent random matrices captures the main geometrical and electromagnetic features of the communication link. Upon a proper tuning of the various parameters (e.g. marginal distribution of each matrix entry, size of each matrix factor, etc.) the product model, early introduced by Mu ̈ller [1], is suitable to model different scenarios, across several generations of wireless systems. Among the various applications of random matrix theory in the performance analysis of wireless systems represented by product models, we focus hereinafter on a finite-blocklength setting. Specifically, we evaluate the so-called channel dispersion, a metric useful to determine the impact of channel dynamics and antenna selection rules on the communication rate, for an isotropic (i.e. unitarily invariant in law) channel. Then, we provide the statistics of the mutual information corresponding to non-isotropic product channels, paving the way to the characterization of the dispersion in more realistic scenarios.