Shortest Path in LEO Satellite Constellation Networks: An Explicit Analytic Approach

The Shortest Distance Path (SDP) problem is a critical routing issue in communication networks, particularly in satellite networks. Typically, SDP is solved by graph-based iterative algorithms, while an explicit or analytic approach is challenging. However, considering the orbit dynamics and topology regularity, this paper proposes, for the first time, an explicit analytic phase-based algorithm STEPCLIMB to directly solve the SDP in low-Earth orbit (LEO) satellite networks. Based on the relationship between satellite phase and inter-satellite link distance, the SDP is modeled with the satellite phase, and SDP problem is converted into a total phase offset problem through theoretical derivations. Then STEPCLIMB is derived in two cases, respectively. Monte-Carlo simulations verify STEPCLIMB's accuracy, which has zero error in the mono-valley case and has less than 0.1% error in the bi-valley case. The algorithm performs better in larger-scale constellations and can save over 99.4% computational cost compared to Dijkstra algorithm. Further, the SDP pattern and features in Starlink constellation are analyzed. The model proves that most inter-plane hops in the SDP occur successively, and the simulations further indicate that these hops prefer satellites in the higher latitude regions.