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The joint optimization of user pairing, beamforming and phase shifting in a Non-Orthogonal Multiple Access (NOMA) network assisted by Intelligent Reflecting Surface (IRS) is studied in this paper. In the system, each pair is assigned with one beam and the intra-group successive interference cancellation in the signal detection is adopted. A user pairing strategy independent of transmit beamforming and IRS phase shift is proposed, so the user pairing is separated from the joint optimization and the difficulty and complexity in the solving of the optimization is significantly reduced. Then, the transmit beamforming, power allocation and IRS phase shift are jointly optimized to minimize the total transmission power of the base station. The original optimization problem is non-convex. By using the methods such as slack variables, successive convex approximation, semidefinite relaxation and alternative optimization, the …