Multi-Layer Low Earth Orbit Constellation Capacity Fundamental.

Multi-layer low Earth orbit constellations (ML-LEOs) have become a pivotal trend in the development of satellite network systems, where their layered orbital architecture improves system performance by strategically deploying satellites in distinct orbital layers. However, two critical issues remain open: how does the configuration of ML-LEO affect its performance, and how many layers are required to achieve optimal performance? This paper first investigates the impact of the number of layers L on the capacity of ML-LEOs. By analyzing the distribution of inter-layer inter-satellite links (ISLs) and the flow count on bottleneck links, we derive a closed-form mathematical expression for ML-LEO capacity under different values of L. In particular, we show that when each layer adopts an identical constellation topology and the number of satellites per orbit equals the number of orbits, the capacity of the ML-LEO is L times that of a single-layer low Earth orbit constellation (SL-LEO). Furthermore, we present the optimal parameter configuration for ML-LEOs: the number of orbits per layer should equal the number of satellites per orbit, the number of layers should be half the number of satellites per orbit, and the optimal number of inter-layer ISLs is twice the product of the number of orbits per layer and the number of layers. Finally, extensive simulations are carried out to thoroughly verify the accuracy of the analytical results. Our analysis reveals the performance benefits of multi-layer topology and establishes a theoretical framework for parameter optimization in ML-LEO.