Topological Design and Optimization of ISLs in LEO Constellations Using Covering Space and Generator

The rapid development of low Earth orbit (LEO) satellite constellations in global communications, navigation, and remote sensing has significantly increased the demand for efficient intersatellite link (ISL) solutions. However, traditional methods face numerous challenges due to the complexity of topological structures and the ambiguity of link formation rules, often relying on empirical experience for design. To address these issues, this article proposes an ISL design methodology grounded in topological principles. By introducing concepts, such as covering spaces, group actions, and generators, a unified link description framework is established, transforming the time-varying physical topology into a stationary logical one, applicable to homogeneous constellation topologies. Based on this framework, a generator-based design approach is developed, where binary decision variables define link states to enable configuration and optimization of ISL topologies. Simulation results show that this method enables further optimization of classical designs and supports the construction of advanced connectivity schemes. The proposed strategy provides a systematic perspective for scalable topological link design in LEO satellite networks.