Capacity Analysis of LEO Mega-Constellations with Quasi-Torus Topologies

The network topology is a typical element that affects the network capacity of low Earth orbit (LEO) mega-constellations. Considering the relative relationship between satellites, most mega-constellations with inclined orbits adopt the classic torus-like topology in which each satellite establishes four inter-satellite links (ISLs) with neighboring satellites. However, do we need so many ISLs to achieve the required capacity? In this paper, we provide an in-depth capacity analysis for quasi-torus topologies in which each satellite is connected by fewer than four ISLs. Based on the topological regularity and constellation scale, we first introduce the models of typical quasi-torus topologies. Considering that all the satellites are not symmetrical, we divide a quasi-torus topology into the same regions exhibiting axial symmetry. Combining the uniform traffic distribution and the symmetry of each region, we derive the closed-form formulae of network capacity by determining the maximum traffic load among ISLs. The formulae provide insights into the impact of ISL distribution and the constellation scale. Simulation results validate the theoretical analysis and show that the quasi-torus topology with fewer ISLs can achieve high capacity comparable to the torus-like topology. The theoretical analysis obtained is instrumental to the topology design of mega-constellations.