  Considering intelligent reflecting surface (IRS), we study a multi-cluster
multiple-input-single-output (MISO) non-orthogonal multiple access (NOMA)
downlink communication network. In the network, an IRS assists the
communication from the base station (BS) to all users by passive beamforming.
Our goal is to minimize the total transmit power by jointly optimizing the
transmit beamforming vectors at the BS and the reflection coefficient vector at
the IRS. Because of the restrictions on the IRS reflection amplitudes and phase
shifts, the formulated quadratically constrained quadratic problem is highly
non-convex. For the aforementioned problem, the conventional semidefinite
programming (SDP) based algorithm has prohibitively high computational
complexity and deteriorating performance. Here, we propose an effective
second-order cone programming (SOCP)-alternating direction method of
multipliers (ADMM) based algorithm to obtain the locally optimal solution. To
reduce the computational complexity, we also propose a low-complexity
zero-forcing (ZF) based suboptimal algorithm. It is shown through simulation
results that our proposed SOCP-ADMM based algorithm achieves significant
performance gain over the conventional SDP based algorithm. Furthermore, when
the number of passive reflection elements is relatively high, our proposed
ZF-based suboptimal algorithm also outperforms the SDP based algorithm.
