Uplink Ergodic Capacity of Reconfigurable Intelligent Surface-Aided Multi-User MISO Communications With Statistical CSI

Reconfigurable intelligent surface (RIS) is a promising solution to build a programmable wireless environment with reconfigurable passive elements, which can achieve high spectral and energy efficiency. In this paper, we investigate the ergodic capacity of RIS-assisted multi-user multiple-input single-output (MISO) wireless systems in uplink scenario. Unlike most of prior works, where instantaneous channel state information (CSI) is assumed, we consider the realistic scenario with only statistical CSI. Specifically, we first present an analytical expressions for the ergodic sum capacity of the system. Based on which, the joint power control and phase shift design problem maximizing the ergodic sum capacity is formulated. Simulation results are presented to validate the accuracy of the analytical ergodic sum capacity expressions and evaluate the impact of key system parameters such as CSI and Rician
$K$
factor. The findings suggest that the proposed statistical CSI design achieves decent performance compared with the instantaneous CSI based design.