Max-Min SINR Optimization for RIS-aided Uplink Communications with Green Constraints

Smart radio environments aided by reconfigurable intelligent surfaces (RIS) have attracted much research attention recently. We propose a joint optimization strategy for beamforming (BF), RIS phases, and power allocation to maximize the minimum signal-to-noise ratio (SINR) of an uplink RIS-aided communication system. The users are subject to constraints on their transmit power. We derive a closed-form expression for the BF vectors and a geometric programming-based solution for power allocation. We propose two solutions for optimizing the phase shifts at the RIS, one based on the matrix lifting method and one using an approximation for the minimum function. We also propose a heuristic algorithm for optimizing quantized phase shift values. The proposed algorithms are of practical interest for systems with constraints on the maximum allowable electromagnetic field exposure. For instance, considering 16-element RIS, 4-antenna base station, and 2 users, numerical results show that the proposed algorithm achieves a gain close to 300% in terms of minimum SINR compared to a scheme with random RIS phases.