Reconfigurable Intelligent Surface Empowered Downlink Non-Orthogonal Multiple Access

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.