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Intelligent reflecting surface (IRS) is a promising solution to build a programmable wireless environment for future communication systems, in which the reflector elements steer the incident signal in fully customizable ways by passive beamforming. This work focuses on the downlink of an IRS-aided multiuser multiple-input single-output (MISO) system. A practical IRS assumption is considered, in which the incident signal can only be shifted with discrete phase levels. Then, the weighted sum-rate of all users is maximized by joint optimizing the active beamforming at the base-station (BS) and the passive beamforming at the IRS. This non-convex problem is firstly decomposed via Lagrangian dual transform, and then the active and passive beamforming can be optimized alternatingly. In addition, an efficient algorithm with closed-form solutions is proposed for the passive beamforming, which is applicable to both the …