Phase Shift Optimization Algorithm for Achievable Rate Maximization in Reconfigurable Intelligent Surface-Assisted THz Communications

Terahertz (THz) band communications are considered a crucial technology to support future applications, such as ultra-high bit rate wireless local area networks, in the next generation of wireless communication systems. In this work, we consider an ultra-massive multiple-input multiple-output (UM-MIMO) THz communication system operating in a typical indoor scenario where the direct link between the transmitter and receiver is obstructed due to surrounding obstacles. To help establish communication, we assume the aid of a nearby reconfigurable intelligent surface (RIS) whose phase shifts can be adjusted. To configure the individual phase shifts of the RIS elements, we formulate the problem as a constrained achievable rate maximization. Due to the typical large dimensions of this optimization problem, we apply the accelerated proximal gradient (APG) method, which results in a low complexity algorithm that copes with the non-convex phase shift constraint through simple element-wise normalization. Our numerical results demonstrate the effectiveness of the proposed algorithm even when considering realistic discrete phase shifts' quantization and imperfect channel knowledge. Furthermore, comparison against existing alternatives reveals improvements between 30% and 120% in terms of range, for a reference rate of 100 Gbps when using the proposed approach with only 81 RIS elements.