Since reconfigurable intelligent surface (RIS) is considered to be a passive reflector for rate performance enhancement, a RIS-aided amplify-and-forward (AF) relay network is presented. By jointly optimizing the beamforming matrix at AF relay and the phase shifts matrices at RIS, two schemes are put forward to address a maximizing signal-to-noise ratio (SNR) problem. Firstly, aiming at achieving a high rate, a high-performance alternating optimization (AO) method based on Charnes-Cooper transformation and semidefinite programming (CCT-SDP) is proposed, where the optimization problem is decomposed to three subproblems solved by CCT-SDP and rank-one solutions can be recovered by Gaussian randomization. While the optimization variables in CCT-SDP method are matrices, which leads to extremely high complexity. In order to reduce the complexity, a low-complexity AO scheme based on Dinkelbachs transformation and successive convex approximation (DT-SCA) is put forward, where matrices variables are transformed to vector variables and three decoupled subproblems are solved by DT-SCA. Simulation results verify that compared to two benchmarks (i.e. a RIS-assisted AF relay network with random phase and a AF relay network without RIS), the proposed CCT-SDP and DT-SCA schemes can harvest better rate performance. Furthermore, it is revealed that the rate of the low-complexity DT-SCA method is close to that of CCT-SDP method.

翻译：由于可重构智能表面（RIS）被视为一种用于提升速率性能的无源反射器，本文提出了一种RIS辅助的放大转发（AF）中继网络。通过联合优化AF中继处的波束赋形矩阵和RIS处的相移矩阵，提出了两种方案来解决最大化信噪比（SNR）问题。首先，为实现高速率，提出了一种基于Charnes-Cooper变换与半定规划（CCT-SDP）的高性能交替优化（AO）方法，其中优化问题被分解为三个子问题，通过CCT-SDP求解，并利用高斯随机化恢复秩一解。然而，CCT-SDP方法中的优化变量为矩阵形式，导致复杂度极高。为降低复杂度，提出了一种基于Dinkelbach变换与逐次凸近似（DT-SCA）的低复杂度AO方案，其中矩阵变量被转换为向量变量，并通过DT-SCA求解三个解耦的子问题。仿真结果验证了，与两种基准方案（即随机相位的RIS辅助AF中继网络和无RIS的AF中继网络）相比，所提出的CCT-SDP和DT-SCA方案能够获得更优的速率性能。此外，结果表明低复杂度DT-SCA方法的速率接近CCT-SDP方法的速率。