This paper considers downlink of reconfigurable intelligent surface (RIS) assisted cooperative non-orthogonal multiple access (CNOMA) systems. Our objective is to minimize the total transmit power by jointly optimizing the active beamforming vectors, transmit-relaying power, and RIS phase shifts. The formulated problem is a mixed-integer nonlinear programming (MINLP) problem. To tackle this problem, the alternating optimization approach is utilized to decouple the variables. In each alternative procedure, the optimal solutions for the active beamforming vectors, transmit-relaying power and phase shifts are obtained. However, the proposed algorithm has high complexity since the optimal phase shifts are solved by integer linear programming (ILP) whose computational complexity is exponential in the number of variables. To strike a good computational complexity-optimality trade-off, a low-complexity suboptimal algorithm is proposed by invoking the iterative penalty function based semidefinite programming (SDP) and the successive refinement approaches. Numerical results illustrate that: i) the proposed RIS-CNOMA system, aided by our proposed algorithms, outperforms the conventional CNOMA system. ii) the proposed low-complexity suboptimal algorithm can achieve the near-optimal performance. iii) whether the RIS-CNOMA system outperforms the RIS assisted non-orthogonal multiple access (RIS-NOMA) system depends not only on the users' locations but also on the RIS' location.

中文翻译：

---

可重构智能表面辅助协作非正交多路访问系统

本文考虑了可重构智能表面（RIS）辅助的协作式非正交多路访问（CNOMA）系统的下行链路。我们的目标是通过共同优化有效波束形成矢量，发射中继功率和RIS相移来最大程度地降低总发射功率。拟定的问题是混合整数非线性规划（MINLP）问题。为了解决这个问题，交替优化方法被用来解耦变量。在每个替代程序中，将获得有效波束成形矢量，发射中继功率和相移的最佳解决方案。然而，由于最优相移是通过整数线性规划（ILP）求解的，该整数线性规划（ILP）的计算复杂度在变量数量上是指数级的，因此该算法具有很高的复杂度。为了达到良好的计算复杂度-最优平衡，通过调用基于迭代罚函数的半定规划（SDP）和逐次细化方法，提出了一种低复杂度次优算法。数值结果表明：i）在我们提出的算法的帮助下，提出的RIS-CNOMA系统优于常规的CNOMA系统。ii）所提出的低复杂度次优算法可以实现近乎最优的性能。iii）RIS-CNOMA系统是否优于RIS辅助非正交多路访问（RIS-NOMA）系统，不仅取决于用户的位置，还取决于RIS的位置。通过调用基于迭代罚函数的半定规划（SDP）和逐次精细化方法，提出了一种低复杂度次优算法。数值结果表明：i）在我们提出的算法的帮助下，提出的RIS-CNOMA系统优于常规的CNOMA系统。ii）所提出的低复杂度次优算法可以实现近乎最优的性能。iii）RIS-CNOMA系统是否优于RIS辅助非正交多路访问（RIS-NOMA）系统，不仅取决于用户的位置，还取决于RIS的位置。通过调用基于迭代罚函数的半定规划（SDP）和逐次精细化方法，提出了一种低复杂度次优算法。数值结果表明：i）在我们提出的算法的帮助下，提出的RIS-CNOMA系统优于常规的CNOMA系统。ii）所提出的低复杂度次优算法可以实现近乎最优的性能。iii）RIS-CNOMA系统是否优于RIS辅助非正交多路访问（RIS-NOMA）系统，不仅取决于用户的位置，还取决于RIS的位置。