Refracting RIS-Aided Hybrid Satellite-Terrestrial Relay Networks: Joint Beamforming Design and Optimization

Reconfigurable intelligent surface (RIS) has been viewed as a promising solution in constructing reconfigurable radio environment of the propagation channel and boosting the received signal power by smartly coordinating the passive elements' phase shifts at the RIS. Inspired by this emerging technique, this article focuses on joint beamforming design and optimization for RIS-aided hybrid satellite-terrestrial relay networks, where the links from the satellite and base station (BS) to multiple users are blocked. Specifically, a refracting RIS cooperates with a BS, where the latter operates as a half-duplex decode-and-forward relay, in order to strengthen the desired satellite signals at the blocked users. Considering the limited onboard power resource, the design objective is to minimize the total transmit power of both the satellite and BS while guaranteeing the rate requirements of users. Since the optimized beamforming weight vectors at the satellite and BS, and phase shifters at the RIS are coupled, leading to a mathematically intractable optimization problem, we propose an alternating optimization scheme by utilizing singular value decomposition and uplink–downlink duality to optimize beamforming weight vectors, and using Taylor expansion and penalty function methods to optimize phase shifters iteratively. Finally, simulation results are provided to verify the superiority of the proposed scheme compared to the benchmark schemes.