  Power-domain non-orthogonal multiple access (NOMA) has become a promising
technology to exploit the new dimension of the power domain to enhance the
spectral efficiency of wireless networks. However, most existing NOMA schemes
rely on the strong assumption that users' channel gains are quite different,
which may be invalid in practice. To unleash the potential of power-domain
NOMA, we will propose a reconfigurable intelligent surface (RIS)-empowered NOMA
network to introduce desirable channel gain differences among the users by
adjusting the phase shifts at RIS. Our goal is to minimize the total transmit
power by jointly optimizing the beamforming vectors at the base station and the
phase-shift matrix at the RIS. To address the highly coupled optimization
variables, we present an alternating optimization framework to decompose the
non-convex bi-quadratically constrained quadratic problem into two rank-one
constrained matrices optimization problems via matrix lifting. At the same
time, to accurately detect the feasibility of the non-convex rank-one
constraints and improve performance by avoiding early stopping in the
alternating optimization procedure, we equivalently represent the rank-one
constraint as the difference between nuclear norm and spectral norm. A
difference-of-convex (DC) algorithm is further developed to solve the resulting
DC programs via successive convex relaxation, followed by establishing the
convergence of the proposed DC-based alternating optimization method. We
further propose an efficient user ordering scheme with closed-form expressions,
considering both the channel conditions and users' target data rates.
Simulation results will validate the effectiveness of deploying an RIS and the
superiority of the proposed DC-based alternating optimization method in
reducing the total transmit power.
