Capacity Maximization for Double Passive/Active RIS-Aided MISO Systems in Multiuser Scenarios

This paper addresses the problem of capacity maximization in double reconfigurable intelligent surface (RIS) -aided multiple-input single-output (MISO) systems under multi-user scenarios. A system model is proposed for double RIS-aided MISO configurations, incorporating both passive RIS (PRIS) and active RIS (ARIS). The primary objective is to maximize the minimum channel capacity across all users, and a corresponding optimization problem is formulated to achieve this goal. To overcome the challenges posed by the fractional structure of the non-convex objective function, auxiliary variables are introduced, and the bisection method is utilized. Given the highly coupled and nonconvex nature of the optimization variables, a joint alternating optimization (AO) algorithm is designed based on the bisection method and successive convex approximation (SCA), enabling iterative determination of the beamforming vectors at the base station and the reflection coefficients of RISs. The results indicate that deploying double RISs substantially enhances the system’s channel capacity through reflected links. Notably, the ARIS protocols yield higher performance gains, particularly under scenarios involving high total power and large amplification factors. In multi-user environments, the double RIS configuration significantly outperforms the single RIS setup due to the increased degrees of freedom, especially when supported by ARIS protocols. These findings underscore the substantial potential and advantages of double RIS configurations in complex communication environments.