Simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) has gradually been considered as a promising technology in the wireless communication networks. Besides, non-orthogonal multiple access (NOMA) is also the key technology in the sixth-generation (6G) wireless communication system. In this work, we study a multiple input single output (MISO) STAR-RIS assisted NOMA downlink network and investigate the energy efficiency (EE) maximization to achieve the tradeoff between the sum rate and the power consumption. The original formulated problem is non-convex due to the coupled beamforming vectors of the users and phase shifts of the STAR-RIS. To efficiently solve the problem, we split the original nonconvex problem into the phase shift and beamforming optimization problems and then solve them alternatively. In the phase shift optimization, fractional programming (FP) is applied to transform the sum rate maximum problem to convex semidefinite relaxation (SDR) one with the rank-one constraint. After this, a novel sequential rank-one constraint relaxation (SROCR) is proposed to convert the rank-one constraint into a convex one, which can effectively overcome the inadequacy of Gaussian randomization, i.e., quality of the solutions and computational complexity. Similarly, FP is applied to solve the beamforming problem by transforming it to SDR problem. It turns out that the optimal solution of the SDR beamforming optimization problem can be guaranteed to be rank-one by the mathematical proof and experiments. The simulation results demonstrate the STAR-RIS NOMA system can achieve the superior performance in EE.

Reconfigurable intelligent surface (RIS) assisted non-orthogonal multiple access transmission can effectively improve the energy/spectrum efficiency in wireless networks. This paper designs a low-complexity scheme to achieve the balanced tradeoff between the sum-rate and power consumption in a RIS-assisted NOMA system, which can be measured by energy efficiency. To solve the formulated problem effectively, the original non-convex problem is first decomposed into two subproblems, i.e., beamforming optimization and phase shift optimization. Alternating optimization is proposed to solve these two subproblems iteratively. In particular, successive convex approximation (SCA) is utilized to convert the non-convex constraints to convex ones. The provided simulation results demonstrate that the proposed scheme can achieve superior performance on energy efficiency compared to the random phase shifts scheme.