  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.
