Reconfigurable Intelligent Surface-Assisted Multi-Satellite Cooperative Downlink Beamforming

As a vital enabler for ubiquitous connectivity in space-air-ground integrated networks, the satellite-terrestrial communication system has been envisioned to be a crucial complement to terrestrial networks because of its superior capability of providing wide coverage. However, there are many practical limitations that degrade system performance, including on-board power constraints, severe path loss, high delay, and Doppler frequency shift. Reconfigurable intelligent surface (RIS), an attractive candidate technology for future networks, has been expected to be a promising solution to tackle these challenges. In this paper, we propose an RIS-assisted multi-satellite cooperative downlink transmission scheme, where an RIS is deployed near the terrestrial receiver to enhance the communication via joint design of beamforming vectors at satellites and phase shift optimization at RIS. Specifically, we first optimize the channel gain of the proposed transmission scheme under the continuous-time propagation model. Then, we formulate the problem as a maximization optimization of the received signal power during the duration of multi-satellite communication service, and we apply an alternating optimization (AO) algorithm to solve the non-convex problem. To reduce computational complexity, we further propose a low-complexity optimization algorithm under line-of-sight (LoS) transmission conditions and a scalable distributed optimization algorithm without the need to share the multi-satellite individual channel state information. Simulation results validate the superiority of our proposed transmission scheme and demonstrate that the low-complexity algorithm and the distributed algorithm can achieve system performance comparable to that of the AO algorithm under LoS channel conditions.