Optimization Design of Beamforming, Phase Shifts, and Power Allocation for RIS-Assisted AF Relay Network

In this letter, we investigate an optimization design for reconfigurable intelligent surface (RIS)-assisted amplify-and-forward relay network. Specifically, we formulate an energy-efficiency (EE) maximization problem by simultaneously optimizing the beamforming, phase shifts, and transmit power. To solve this problem, we design an alternative optimization algorithm based on successive convex approximation (SCA) and Dinkelbach transformation. Firstly, through the SCA and Dinkelbach transformation, we can obtain the optimal beamforming. Then, with the optimal beamforming, we use the semi-definite relaxation and Gaussian randomization to obtain the optimal phase shifts. Subsequently, with the optimal beamforming and phase shifts, we further apply the Karush-Kuhn-Tucker conditions to obtain the optimal transmit power. Simulation results illustrate that our optimization design can effectively enhance the network EE.