Energy-Aware Scheduling and Beamforming for Simultaneous Wireless Information and Power Transfer in Low-Earth-Orbit Satellite and UAV Networks Using Lyapunov Optimization, Successive Convex Approximation, and WMMSE

The integration of low-Earth-orbit (LEO) satellites with unmanned aerial vehicles (UAVs) promises high-throughput and flexible wireless connectivity, yet it faces critical challenges in simultaneously guaranteeing data rates and long-term energy harvesting under mobility and imperfect channel state information (CSI). Additionally, the rate–energy trade-off imposed by simultaneous wireless information and power transfer (SWIPT) further complicates per-slot resource allocation. In this paper, we propose a Lyapunov-based scheduling framework that stabilizes UAV data and virtual energy queues while maximizing weighted throughput. The framework employs a custom inner solver combining successive convex approximation (SCA) and weighted minimum mean-square error (WMMSE) optimization to efficiently compute per-slot beamformers and power-splitting ratios. Our approach explicitly accounts for UAV mobility, Rician fading channels with Doppler, and circuit nonlinearities in energy harvesting, ensuring feasible and energy-aware SWIPT operation. A LEO satellite–UAV integrated communication system is considered, where multiple satellites provide wireless connectivity to energy-constrained UAVs operating in a dynamic three-dimensional environment. The satellites employ multi-antenna transmission, while the UAVs rely on energy harvesting mechanisms to sustain their operation. The communication links are characterized by dominant line-of-sight propagation conditions, and UAV trajectories are adaptively optimized to improve network performance and energy efficiency. Simulation results demonstrate that the proposed Lyapunov-based SCA-WMMSE framework significantly outperforms a fixed baseline approach, providing substantial improvements in signal quality, achievable data rates, and harvested energy. Moreover, the proposed method maintains stable energy management behavior and guarantees long-term energy sustainability for the UAVs.