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Reconfigurable intelligent surface (RIS) has drawn considerable attentionfrom the research society recently, which creates favorable propagationconditions by controlling the phase shifts of the reflected waves at thesurface, thereby enhancing wireless transmissions. In this paper, we study adownlink multi-user system where the transmission from a multi-antenna basestation (BS) to various users is achieved by the RIS reflecting the incidentsignals of the BS towards the users. Unlike most existing works, we considerthe practical case where only a limited number of discrete phase shifts can berealized by the finite-sized RIS. Based on the reflection-dominated one-hoppropagation model between the BS and users via the RIS, a hybrid beamformingscheme is proposed and the sum-rate maximization problem is formulated.Specifically, the continuous digital beamforming and discrete RIS-based analogbeamforming are performed at the BS and the RIS, respectively, and an iterativealgorithm is designed to solve this problem. Both theoretical analysis andnumerical validations show that the RIS-based system can achieve a goodsum-rate performance by setting a reasonable size of RIS and a small number ofdiscrete phase shifts.

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