The combination of non-orthogonal multiple access (NOMA) and intelligent reflecting surface (IRS) is an efficient solution to significantly enhance the energy efficiency of the wireless communication system. In this paper, we focus on a downlink multi-cluster NOMA network, where each cluster is supported by one IRS. We aim to minimize the transmit power by jointly optimizing the beamforming, the power allocation and the phase shift of each IRS. The formulated problem is non-convex and challenging to solve due to the coupled variables, i.e., the beamforming vector, the power allocation coefficient and the phase shift matrix. To address this non-convex problem, we propose an alternating optimization based algorithm. Specifically, we divide the primal problem into the two subproblems for beamforming optimization and phase shifting feasiblity, where the two subproblems are solved iteratively. Moreover, to guarantee the feasibility of the beamforming optimization problem, an iterative algorithm is proposed to search the feasible initial points. To reduce the complexity, we also propose a simplified algorithm based on partial exhaustive search for this system model. Simulation results demonstrate that the proposed alternating algorithm can yield a better performance gain than the partial exhaustive search algorithm, OMA-IRS, and NOMA with random IRS phase shift.
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