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Considering intelligent reflecting surface (IRS), we study a multi-clustermultiple-input-single-output (MISO) non-orthogonal multiple access (NOMA)downlink communication network. In the network, an IRS assists thecommunication from the base station (BS) to all users by passive beamforming.Our goal is to minimize the total transmit power by jointly optimizing thetransmit beamforming vectors at the BS and the reflection coefficient vector atthe IRS. Because of the restrictions on the IRS reflection amplitudes and phaseshifts, the formulated quadratically constrained quadratic problem is highlynon-convex. For the aforementioned problem, the conventional semidefiniteprogramming (SDP) based algorithm has prohibitively high computationalcomplexity and deteriorating performance. Here, we propose an effectivesecond-order cone programming (SOCP)-alternating direction method ofmultipliers (ADMM) based algorithm to obtain the locally optimal solution. Toreduce the computational complexity, we also propose a low-complexityzero-forcing (ZF) based suboptimal algorithm. It is shown through simulationresults that our proposed SOCP-ADMM based algorithm achieves significantperformance gain over the conventional SDP based algorithm. Furthermore, whenthe number of passive reflection elements is relatively high, our proposedZF-based suboptimal algorithm also outperforms the SDP based algorithm.

Joint Beamforming Design in Multi-Cluster MISO NOMA Intelligent Reflecting Surface-Aided Downlink Communication Networks