Simultaneous transmission and reflection-reconfigurable intelligent surface (STAR-RIS) can provide expanded coverage compared with the conventional reflection-only RIS. This paper exploits the energy efficient potential of STAR-RIS in a multiple-input and multiple-output (MIMO) enabled non-orthogonal multiple access (NOMA) system. Specifically, we mainly focus on energy-efficient resource allocation with MIMO technology in the STAR-RIS assisted NOMA network. To maximize the system energy efficiency, we propose an algorithm to optimize the transmit beamforming and the phases of the low-cost passive elements on the STAR-RIS alternatively until the convergence. Specifically, we first decompose the formulated energy efficiency problem into beamforming and phase shift optimization problems. To efficiently address the non-convex beamforming optimization problem, we exploit signal alignment and zero-forcing precoding methods in each user pair to decompose MIMO-NOMA channels into single-antenna NOMA channels. Then, the Dinkelbach approach and dual decomposition are utilized to optimize the beamforming vectors. In order to solve non-convex phase shift optimization problem, we propose a successive convex approximation (SCA) based method to efficiently obtain the optimized phase shift of STAR-RIS. Simulation results demonstrate that the proposed algorithm with NOMA technology can yield superior energy efficiency performance over the orthogonal multiple access (OMA) scheme and the random phase shift scheme.

翻译：同时透射与反射可重构智能表面（STAR-RIS）相比传统仅反射式RIS能够提供更广的覆盖范围。本文探讨了STAR-RIS在多输入多输出（MIMO）赋能非正交多址接入（NOMA）系统中的能效优化潜力。具体而言，我们主要聚焦于STAR-RIS辅助NOMA网络中基于MIMO技术的能效资源分配问题。为最大化系统能量效率，我们提出一种算法，通过交替优化发射波束成形和STAR-RIS上低成本无源元件的相位直至收敛。具体地，我们首先将构建的能效优化问题分解为波束成形和相移优化两个子问题。为有效处理非凸的波束成形优化问题，我们利用信号对齐和迫零预编码方法对每个用户对进行MIMO-NOMA信道分解，将其转化为单天线NOMA信道。随后采用Dinkelbach方法和对偶分解技术优化波束成形向量。针对非凸的相移优化问题，我们提出基于逐次凸近似（SCA）的方法高效获取STAR-RIS的优化相移。仿真结果表明，所提算法结合NOMA技术相比正交多址接入（OMA）方案和随机相移方案具有更优的能效性能。