  Reconfigurable intelligent surface (RIS) has drawn considerable attention
from the research society recently, which creates favorable propagation
conditions by controlling the phase shifts of the 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 the 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 the finite-sized RIS. Based on the reflection-dominated one-hop
propagation model between the BS and users via the RIS, a hybrid beamforming
scheme is proposed and the sum-rate maximization problem is formulated.
Specifically, the 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 a good
sum-rate performance by setting a reasonable size of RIS and a small number of
discrete phase shifts.
