The Riemann Sum Method for the SOC-Based Simulation of 3D MIMO Fading Channels

The Riemann sum method (RSM) was introduced almost two decades ago as an efficient parameterization method for the design of mobile fading channel simulators based on the sum-of-cissoids (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 multipath propagation in two-dimensional (2D) scenarios. This assumption imposes an important limitation, as the mobile communication systems are evolving to provide three-dimensional (3D) connectivity, such as that required to connect ground-level terminals with small-cell towers and drones. In this paper, we present a generalized version of the RSM that enables the SOC-based simulation of multiple-input multiple-output (MIMO) narrowband mobile fading channels under 3D propagation conditions. Simulation results presented here demonstrate that the proposed method provides an excellent approximation to the time autocorrelation function and to the spatial cross-correlation function of the reference 3D MIMO channel model.