A Low Complexity Passive Beamforming Design for Reconfigurable Intelligent Surface (RIS) in 6G Networks

Reconfigurable intelligent surface (RIS) emerged as a promising technology for programming the wireless propagation environment, ushering wireless networks into a new era of high connectivity, and better spectrum and energy efficiency. Research has gained momentum over the past few years to study the gains of RIS and the optimal configuration of its elements. This paper is concerned with the optimal configuration of RIS elements; we consider a single base station (BS) serving multiple single-antenna users and formulate the problem of minimizing the total transmit power while jointly optimizing the allocated power to users and the RIS phase shifts. In line with the existing literature, the problem is decomposed into power control and RIS phase shift sub-problems. The power control sub-problem is the conventional power problem which is solved optimally through closed-form expression. Then, we tackle the problem of RIS passive beamforming optimization and propose two solutions leveraging a linear transformation and element-wise Karush-Kuhn-Tucker (KKT), respectively. The main idea of the linear transformation approach is to reduce the number of optimization variables to the number of users associated with the RIS from the number of its elements which is, in general, very large. On the other hand, the main idea of the element-wise KKT-based approach is to obtain a closed-form expression for the RIS phase shifts for a multi-user scenario, similar to the single-user case. Simulation results show that the proposed schemes have performance in total transmitted power close to the numerical solution and have much lower computational complexity than the baseline solutions. Moreover, simulation results show that the proposed solutions have a competitive performance in terms of optimality and complexity for large-scale RIS. Hence, our approach represents a general framework for configuring RIS elements in real scenarios.