  Reconfigurable intelligent surface (RIS) provides a promising way to build
the programmable wireless transmission environments in the future. Owing to the
large number of reflecting elements used at the RIS, joint optimization for the
active beamforming at the transmitter and the passive reflector at the RIS is
usually complicated and time-consuming. To address this problem, this paper
proposes a low-complexity joint beamforming and reflecting algorithm based on
fractional programing (FP). Specifically, we first consider a RIS-aided
multi-user communication system with perfect channel state information (CSI)
and formulate an optimization problem to maximize the sum rate of all users.
Since the problem is nonconvex, we decompose the original problem into three
disjoint subproblems. By introducing favorable auxiliary variables, we derive
the closed-form expressions of the beamforming vectors and reflecting matrix in
each subproblem, leading to a joint beamforming and reflecting algorithm with
low complexity. We then extend our approach to handle the case when
transmitter-RIS and RIS-receiver channels are not perfect and develop
corresponding low-complexity joint beamforming and reflecting algorithm with
practical channel estimation. Simulation results have verified the
effectiveness of the proposed algorithms as compared to various benchmark
schemes.
