A Coalition Formation Game-Based Beam Scheduling Method for LEO Satellites in Mega Hybrid Constellations

A mega hybrid constellation comprising low Earth orbit (LEO) and geostationary orbit (GEO) satellites represents a prevalent architecture for future space-based networks. However, the emergence of mega constellations has exacerbated the shortage of spectrum resources. To address this issue, this paper investigates a method for LEO satellites within such constellations to expand their available spectrum by sharing the downlink spectrum of GEO satellites. Firstly, to avoid interference with GEO satellites and optimize the beam coverage for LEO user (LU), a coalition formation game model for LU based on cooperation criteria is constructed, and the existence of a stable coalition structure is proven. Secondly, to determine this stable coalition structure, a coalition formation game algorithm based on the best response (BR) is proposed, and its convergence is theoretically validated. Additionally, to more efficiently determine the beam radius and center covering the LU in the coalition, an improved algorithm for solving the outer circle of LU in the coalition using a K-dimensional tree is presented. Simulation results demonstrate that the proposed method effectively balances convergence time and accuracy. Without affecting GEO satellite communications, LEO satellites can share the downlink spectrum of GEO satellites, thereby enhancing the utilization of spectrum resources within the hybrid constellation.