Reconfigurable Intelligent Surface for MISO Systems with Proportional Rate Constraints

This paper investigates the spectral efficiency (SE) in reconfigurable intelligent surface (RIS)-aided multiuser multiple-input single-output (MISO) systems, where RIS can reconFigure the propagation environment via a large number of controllable and intelligent phase shifters. In order to explore the SE performance with user proportional fairness for such a system, an optimization problem is formulated to maximize the SE by jointly considering the power allocation at the base station (BS) and phase shift at the RIS, under nonlinear proportional rate fairness constraints. To solve the non-convex optimization problem, an effective solution is developed, which capitalizes on an iterative algorithm with closed-form expressions, i.e., alternatively optimizing the transmit power at the BS and the reflecting phase shift at the RIS. Numerical simulations are provided to validate the theoretical analysis and assess the performance of the proposed alternative algorithm.