Nakagami-$m$ MIMO Channel Model

Nakagami-$m$ is a widely adopted generalized channel model as it fits closely to the majority of measured fading radio channels. As well, the mathematical model for Nakagami-$m$ is more analytically tractable than other well-known fading channels, which attracted considerable interest among the research community. Original channel model was proposed mainly for single–input single–output (SISO) systems, where the envelope follows the Nakagami distribution while the phase is assumed to be uniformly distributed. However, such model is shown previously to be inaccurate for multiple–input multiple–output (MIMO) systems accomplishing multiplexing gains such as spatial multiplexing (SMX) and space modulation techniques (SMTs). As such, a different Nakagami-$m$ MIMO channel model was suggested and shown to correctly models the behavior of the channel parameters under different conditions. Yet, it is revealed in this study that the previously advised model is imprecise as the phase distribution was not accurately modeled. As well, the previous model was only realizable for integer values of the Nakagami $m$ parameter. Thereby, an altered accurate model is suggested and thoroughly analyzed in this article. Also, the new model is shown to be applicable for arbitrary values of $m$ (i.e., not necessarily integers or half integers). The paper also presents the modified conditions under which the analytical formulation is correct as compared to Monte-Carlo Simulation. For illustration purposes, space shift keying (SSK), quadrature spatial modulation (QSM) and SMX MIMO systems are considered in this study.