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Analytical Framework for Full-Dimensional Massive MIMO With Ray-Based Channels

The performance of baseband beamforming in multi-user multiple-input multiple-output (MU-MIMO) systems has been extensively studied for simplified statistical channel models where no angular parameters are taken into account. In contrast, there is little performance analysis with ray-based models, which are more physically motivated, feature prominently in standardization and have been experimentally validated. Thus, unlike previous studies, we present a mathematical framework to analyze the performance of zero forcing (ZF) and minimum mean-squared error (MMSE) combining. Using a central result for averaging in the angular domain, we derive tight approximations for the uplink signal-to-noise ratio and signal-to-interference-and-noise ratio (SINR) for ZF and MMSE processing, respectively, and the resulting spectral efficiencies. The remarkably simple expressions offer the following insights into the effects of the propagation environment. We demonstrate an improvement in performance when moving from vertical uniform rectangular array (URA) to horizontal URA to uniform linear array (ULA) antenna configurations. There is also a corresponding increase in the robustness of the performance to propagation scenarios. We demonstrate that under specific conditions increasing the angular spread can decrease the SINR for a ULA - an unexpected behavior which we link to the effects of end-fire radiation. Furthermore, our results allow us to investigate the impact of different array configurations and system parameters on the rate of convergence to favorable propagation conditions. Finally, we evaluate the spatial correlation properties intrinsically present in ray-based models, and compare them to the commonly used simple exponential model which yields equal, fixed correlation characteristics for each user.