Reconfigurable intelligent surfaces (RIS) is a promising solution to build a programmable wireless environment via steering the incident signal in fully customizable ways with reconfigurable passive elements. In this paper, we consider a RIS-aided multiuser multiple-input single-output (MISO) downlink communication system. Our objective is to maximize the weighted sum-rate (WSR) of all users by joint designing the beamforming at the access point (AP) and the phase vector of the RIS elements, while both the perfect channel state information (CSI) setup and the imperfect CSI setup are investigated. For perfect CSI setup, a low-complexity algorithm is proposed to obtain the stationary solution for the joint design problem by utilizing the fractional programming technique. Then, we resort to the stochastic successive convex approximation technique and extend the proposed algorithm to the scenario wherein the CSI is imperfect. The validity of the proposed methods is confirmed by numerical results. In particular, the proposed algorithm performs quite well when the channel uncertainty is smaller than 10%.
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