Resource Allocations for Active RIS Empowered Satellite-Terrestrial RSMA Networks

This paper studies an active reconfigurable intelligent surface (ARlS) empowered multiple-input single-ou+-tput (MISO) downlink satellite-terrestrial network (STN) with a rate splitting multiple access (RSMA) scheme. The system comprises a satellite (SAT) equipped with multiple antennas, an ARIS with multiple reflecting elements, and multiple users adopting a power splitting architecture. Aiming to maximize the system spectral efficiency (SE), this paper focuses on the joint optimization of active beamforming of SAT, active phase shift matrix of ARlS, and power-splitting (PS) ratio of multiple terrestrial users. The formulated SE maximization problem is non-convex due to these coupled variables. To deal with it, we first propose an alternating optimization (AO) algorithm to jointly design active beamformers of SAT and ARlS, as well as PS ratio. Specifically, the AO framework decomposes the original problem into two subproblems. One subproblem optimizes the active beamformers of SAT and PS ratio while keeping the phase shifts of ARIS fixed, which can be efficiently solved by convex optimization techniques. The other subproblem optimizes the active phase shift matrix of ARIS with fixed SAT beamformers and PS ratio, which is tackled using semi-definite relaxation (SDR). Finally, numerical results are presented to verify the performance of the proposed algorithm.