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.

中文翻译：

---

折射 RIS 辅助混合卫星-陆地中继网络：联合波束成形设计和优化

可重构智能表面（RIS）被视为构建传播信道的可重构无线电环境并通过智能地协调无源元件在RIS处的相移来提高接收信号功率的有前景的解决方案。受这种新兴技术的启发，本文重点关注 RIS 辅助混合卫星-地面中继网络的联合波束成形设计和优化，其中从卫星和基站 (BS) 到多个用户的链路被阻塞。具体来说，折射 RIS 与 BS 合作，后者作为半双工解码和转发中继运行，以增强阻塞用户的所需卫星信号。考虑到板载电源有限，设计目标是在保证用户速率要求的同时，最小化卫星和基站的总发射功率。由于卫星和基站的优化波束赋形权向量和RIS上的移相器是耦合的，导致数学上难以解决的优化问题，我们提出了一种交替优化方案，利用奇异值分解和上下行对偶性来优化波束赋形权向量，并使用泰勒展开和罚函数方法迭代优化移相器。最后，通过仿真结果验证了所提方案与基准方案相比的优越性。导致数学上难以解决的优化问题，我们提出了一种交替优化方案，通过利用奇异值分解和上行链路-下行链路对偶性来优化波束形成权向量，并使用泰勒展开和惩罚函数方法来迭代优化移相器。最后，通过仿真结果验证了所提方案与基准方案相比的优越性。导致数学上难以解决的优化问题，我们提出了一种交替优化方案，通过利用奇异值分解和上行链路-下行链路对偶性来优化波束形成权向量，并使用泰勒展开和惩罚函数方法来迭代优化移相器。最后，通过仿真结果验证了所提方案与基准方案相比的优越性。