A Game-Theoretic Approach for Satellites Beam Scheduling and Power Control in a Mega Hybrid Constellation Spectrum Sharing Scenario

A mega hybrid constellation of low-Earth orbit (LEO) and geosynchronous orbit (GEO) satellites represents a typical architecture for future space networks. However, the emergence of such large constellations exacerbates the shortage of spectrum resources. To address this issue, this article investigates a hierarchical optimization method for beam scheduling and power control of LEO satellites, aiming to extend the available spectrum by sharing the downlink spectrum of GEO satellites. In the upper layer optimization, a many-to-one matching game model is constructed to achieve optimal matching of LEO satellite beams and LEO users (LUs). A distributed beam matching learning algorithm (DBMLA) is designed to find a stable matching solution for the model, with the convergence of the algorithm theoretically proven. In the lower layer optimization, an LEO beam power level optimization game model is developed for discrete LEO beam power levels. This model is demonstrated to be an exact potential game with at least one Nash equilibrium (NE). To solve this NE, a dynamic power allocation logarithmic learning algorithm (DPALLA) is proposed. Simulation results verify that the proposed DBMLA-DPALLA hierarchical optimization scheme effectively balances convergence time and accuracy compared to traditional independent optimization strategies. By leveraging the combined effects of the two optimization strategies, it better mitigates the co-channel interference experienced by GEO satellites and improves the average network satisfaction of the LUs.