A Random Matrix Model for mmWave MIMO Systems

Random matrices are nowadays classical tools for modeling multiantenna wireless channels. Scattering phenomena typical of cellular frequencies and channel reciprocity features led to the adoption of matrices sampled either from the Gaussian Unitary Ensemble (GUE) or from more general Polynomial Ensembles (PE). Such matrices can be used to model the random impairments of the radio channel on the transmitted signal over a wireless link whose transmitter and receiver are both equipped with antenna arrays. The exploitation of the millimeter-wave (mmWave) frequency band, planned for 5G and beyond mobile networks, prevents the use of GUE and PE elements as candidate models for channel matrices. This is mainly due to the lack of scattering richness compared to microwave-based transmissions. In this work, we propose to model mmWave Multi-Input–MultiOutput (MIMO) systems via products of random Vandermonde matrices. We illustrate the physical motivation of our model selection, discuss the meaning of the parameters and their impact on the spectral properties of the random matrix at hand, and provide both a list of results of immediate use for performance analysis of mmWave MIMO systems, as well as a list of open problems in the field