Maximizing the Geometric Mean of User-Rates to Improve Rate-Fairness in Double RIS-Assisted System

This paper proposes a double reconfigurable intelligent surface (RIS)-assisted multi-user downlink communication network with two RISs deployed symmetrically about the base station (BS) for enhancing communication signals. We aim to jointly optimize the beamformers at the BS and the reflection coefficient matrices of the two RISs to maximize the geometric mean (GM) of the users’ rates. An efficient alternating descent iteration algorithm based on closed-forms is proposed to address this non-convex problem. Simulation results show that the advantages of the conceived double-RIS system and the viability of the proposed algorithm. Furthermore, our results unveil that the proposed algorithm can significantly improve rate fairness.