This paper focuses on the research of anti-jamming issues for Low Earth Orbit (LEO) satellite constellations. Initially, the anti-jamming problem is modeled as a Local Interaction Markov Game (LIMG) and proven to be an Exact Potential Game (EPG), with at least one pure strategy Nash Equilibrium (NE) existing. Secondly, based on the theoretical analysis and the ”offline training and online execution” architecture, a Distributed Multi-Agent Deep Reinforcement Learning-based anti-jamming (DMDRLA) scheme is proposed, and its convergence and asymptotic optimality are theoretically analyzed. Finally, simulations validate that the proposed DM-DRLA scheme can effectively balance the training costs and performance optimization of the anti-jamming model, making it suitable for anti-jamming issues in resource-constrained LEO satellite networks.

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.

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.

Large-scale satellite constellations lead to a scarcity of spatial spectrum resources, especially for the overlapped spectrum between Low Earth Orbit (LEO) and Geostationary Orbit (GEO)satellites in hybrid constellations. Hence, based on game theory, a distributed spectrum-sharing method is proposed for downlink spectrum sharing in large-scale hybrid satellite constellations. Specifically, the system cycle is divided into equal-spaced topological periods, and the beams ofLEOsatellites are assigned toLEOground stations (LGS) during every topological period. A system model based on game theory is also developed to describe the mutual interference of links established betweenLEOsatellites andLGS. Subsequently, the formulated game is proven to be an exact potential game, with at least one pure strategic Nash equilibrium (NE). Along the line, to obtain the NE solution, a dynamic channel allocation algorithm is proposed based on stochastic learning theory, and the convergence is proven. Finally, the simulation results demonstrate the proposed DCASLA’s effectiveness, which can balance the convergence speed and overall network satisfaction.