Optimal phase shift design for fair allocation in RIS aided uplink network using statistical CSI

Reconfigurable intelligent surface (RIS) can be crucial in next-generation communication systems. However, designing the RIS phases according to the instantaneous channel state information (CSI) can be challenging in practice due to the short coherent time of the channel. In this regard, we propose a novel algorithm based on the channel statistics of massive multiple input multiple output systems rather than the CSI. The beamforming at the base station (BS), power allocation of the users, and phase shifts at the RIS elements are optimized to maximize the minimum signal to interference and noise ratio (SINR), guaranteeing fair operation among various users. In particular, we design the RIS phases by leveraging the asymptotic deterministic equivalent of the minimum SINR that depends only on the channel statistics. This significantly reduces the computational complexity and the amount of controlling data between the BS and RIS for updating the phases. This setup is also useful for electromagnetic fields (EMF)-aware systems with constraints on the maximum user's exposure to EMF. The numerical results show that the proposed algorithms achieve more than 100% gain in terms of minimum SINR, compared to a system with random RIS phase shifts, with 40 RIS elements, 20 antennas at the BS and 10 users, respectively.