Hybrid Beamforming for Reconfigurable Intelligent Surface based Multi-User Communications: Achievable Rates with Limited Discrete Phase Shifts

Reconfigurable intelligent surfaces (RISs) have drawn considerable attention from the research community recently. RISs create favorable propagation conditions by controlling the phase shifts of reflected waves at the surface, thereby enhancing wireless transmissions. In this paper, we study a downlink multi-user system where the transmission from a multi-antenna base station (BS) to various users is achieved by an RIS reflecting the incident signals of the BS towards the users. Unlike most existing works, we consider the practical case where only a limited number of discrete phase shifts can be realized by a finite-sized RIS. A hybrid beamforming scheme is proposed and the sum-rate maximization problem is formulated. Specifically, continuous digital beamforming and discrete RIS-based analog beamforming are performed at the BS and the RIS, respectively, and an iterative algorithm is designed to solve this problem. Both theoretical analysis and numerical validations show that the RIS-based system can achieve good sum-rate performance by setting a reasonable size of the RIS and a small number of discrete phase shifts.