Joint Resource Scheduling and Energy-Efficient Beamformer Design for Multisatellite Networks Empowered by RIS

In this article, we propose a framework for energy efficiency (EE) design in reconfigurable intelligent surface (RIS)-assisted multisatellite Internet of Things (IoT) networks, taking into account the imperfect channel state information (CSI). In this framework, the multisatellite network is used to enhance communication capabilities, while the RIS is deployed to further improve EE performance. Our objective is to maximize the EE of the proposed network by jointly optimizing the active beamforming and scheduling of the satellites and the phase shifts of RIS under the transmit power constraint for each satellite, the elevation angle constraints, and the phase shift constraints of the RIS. To handle this nonconvex and NP-hard optimization problem, we propose two efficient algorithms, i.e., the dinkelbach-bigM-successive-penalty (DBSP) algorithm and the Lagrangian dual majorization (LDM) algorithm. The DBSP algorithm is based on the alternating optimization (AO) approach, which can effectively solve the formulated nonconvex optimization problem with multiple dual and complex optimization variables. Specifically, we first employ the Dinkelbach method, successive convex approximation (SCA), big-M formulation, and semidefinite relaxation (SDR) method to optimize the active beamforming and the scheduling of the satellites. In addition, the penalty convex-concave procedure (P-CCP) approach is utilized to design the phase shifts of RIS. To reduce the complexity and improve computational efficiency, we propose the LDM algorithm and derive an analytical solution for active beamforming and phase shifts by exploiting the Lagrangian dual transform, quadratic transform (QT), and majorization-minimization (MM) algorithms. Numerical simulations are conducted to demonstrate the efficiency and convergence behavior of the proposed algorithms. Moreover, it is also demonstrated that the proposed algorithms are superior to other benchmarks, corroborating the benefits of deploying an RIS in the multisatellite network.