Abstract: The use of a reconfigurable intelligent surface (RIS) in the enhancement of the rate performance is considered to involve the limitation of the RIS being a passive reflector. To address this issue, we propose a RIS-aided amplify-and-forward (AF) relay network in this paper. By jointly optimizing the beamforming matrix at AF relay and the phase-shift matrices at RIS, two schemes are put forward to address a maximizing signal-to-noise ratio (SNR) problem. First, 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 into three subproblems solved using CCT-SDP, and rank-one solutions can be recovered using Gaussian randomization. However, the optimization variables in the CCT-SDP method are matrices, leading to extremely high complexity. To reduce the complexity, a low-complexity AO scheme based on Dinkelbachs transformation and successive convex approximation (DT-SCA) is proposed, where the variables are represented in vector form, and the three decoupling subproblems are solved using DT-SCA. Simulation results verify that compared to three benchmarks (i.e., a RIS-assisted AF relay network with random phase, an AF relay network without RIS, and a RIS-aided network without AF relay), 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 the CCT-SDP method.

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