SOC-Based Simulation of 3D MIMO Mobile-to-Mobile Fading Channels: A Riemann Sum Approach

The Riemann sum method (RSM) was introduced almost two decades ago as an efficient parameter computation method for the design of narrowband multiple-input multiple-output (MIMO) mobile fading channel simulators based on the sum-of-cisoids (SOC) principle. This method has been shown to be more accurate and less computationally expensive than other methods based on the SOC principle. However, the RSM was formulated by assuming uniform linear antenna arrays and a two-dimensional geometrical propagation environment. These assumptions impose important limitations, as the mobile communication systems are evolving to provide service in a variety of three-dimensional (3D) environments by employing different antenna array configurations. This article presents two generalized versions of the RSM that remove such limitations. One version follows the deterministic approach of the original RSM, which is specific to the design of ergodic SOC-based simulators for wide-sense stationary (WSS) channels. The other version is inspired by a stochastic approach that enables the non-ergodic simulation of WSS channels and which can be extrapolated to the simulation of non-WSS channels. Simulation results presented here demonstrate that both generalizations provide an excellent approximation to the envelope distribution and correlation properties of 3D narrowband MIMO mobile-to-mobile fading channels, regardless of the antenna array configuration and the propagation environment's geometry.