On Some Unifications Arising from the MIMO Rician Shadowed Model

TL;DR

This paper introduces a unifying MIMO Rician shadowed model that encompasses various SISO and MIMO fading models, providing new analytical expressions for key statistical functions relevant to wireless communication performance analysis.

Contribution

The paper derives the moment generating function, CDF, and PDF of the maximum eigenvalue for the MIMO Rician shadowed model, unifying multiple fading models under a common framework.

Findings

Unified MIMO and SISO fading models using Rician shadowed framework

Derived tractable expressions for MIMO channel matrix statistics

Showed that existing models are special cases of the proposed model

Abstract

This paper shows that the proposed Rician shadowed model for multi-antenna communications allows for the unification of a wide set of models, both for multiple-input multiple output (MIMO) and single-input single output (SISO) communications. The MIMO Rayleigh and MIMO Rician can be deduced from the MIMO Rician shadowed, and so their SISO counterparts. Other SISO models, besides the Rician shadowed proposed by Abdi et. al., are included in the model, such as the $\kappa$-$\mu$ defined by Yacoub, and its recent generalization, the \mbox{$\kappa$-$\mu$} shadowed model. Moreover, the SISO \mbox{$\eta$-$\mu$} and \mbox{Nakagami-$q$} models can be seen as particular cases of the MIMO Rician shadowed. The literature already presents the probability density function (pdf) of the Rician shadowed Gram channel matrix in terms of the well-known gamma-Wishart distribution. We here derive its moment generating function in a tractable form. Closed-form expressions for the cumulative distribution function and the pdf of the maximum eigenvalue are also carried out.