# Laser Inter-Satellite Link Visibility and Topology Optimization for Mega Constellation
###### Abstract  
In this paper, we begin by describing the Starlink constellation's configuration plan, treating each satellite as a network node, naming and numbering the various nodes, and then classifying the laser interstellar links (LISLs) according to their orbital alignment and whether they are permanently visible. Whereupon, the method for calculating the respective theoretical interstellar distances required for establishing LISLs under two distinct orbital scenarios, co-orbital and hetero-orbital are analyzed, and the optimal phasing factors are proposed by solving an optimization algorithm for the shortest distance. The OneWeb and Starlink constellations, as well as the constellation states of various phasing factors are simulated, respectively. The Starlink constellation with F = 11 obtains the best coverage between 60\({}^{\circ}\) north and south latitudes predicated upon the analysis of the constellation N Asset Coverage. Following that, the first phase of the Starlink constellation deployment was modeled in order to analyze and count the number of permanent LISLs in orbit, adjacent to, and nearby. Subsequently, the characteristics of azimuthal, elevation, and range (AER) were subsequently analyzed to ascertain their variation law and to compile the number of permanent and temporary LISLs that could be established at various inter-distance ranges. Finally, predicated on the simulation results, the optimal LISLs connection strategy for the Starlink constellation is evaluated and a static topology for the constellation is constructed. Laser interstellar links; Starlink constellation; phasing factors; N Asset Coverage; visibility analysis 20221122322114 June 202214 July 202211 July 20  
Table 1 outlines the parameters of several typical international LEO constellation systems. It is evident that microsatellite technology tends to be practical, and the fact that a large number of mature commercial-grade components are used to construct microsatellites leads to its short development cycle and low cost [6]. The LEO constellation system has reached its pinnacle of development due to the high demand for high-capacity, low-latency satellite communications [7]. For the development of the next LEO mega-constellations, it is thus crucial to synthesize the variation laws of LISLs in different situations and optimize the static topology of the constellation. This paper examines, from a topological standpoint, the use of satellites as network nodes and wireless links as network edges, both of which can connect users in the three fields of sea, land, and air through inter-satellite and satellite-ground links [8]. To optimize the topology of OISLs for future navigation satellites, for instance, [PERSON] et al. proposed the multi-objective discrete binary particle swarm optimization algorithm, which fully took into account the complex constraints of inter-satellite links [9]. Through the analysis of ISL paths, [PERSON] et al. sought to offer insights into the topology and routing design of Mega-constellation networks; numerical results reveal the superiority of optimizing the constellation phasing factor [10]. Consequently, it is worthwhile to investigate the static topology of satellite networks, as well as the optimal phasing factor and connection strategies for LISLs in varying states. While many researchers have studied and found sufficient performance with the topology design of LEO constellation networks, they frequently base their findings on the assumption that the total number of satellites would not exceed 100, as is the case with the optimal Walker constellation's topology design [11]. As a result, the previously proposed topology algorithms are incompatible with large constellations, and a new link allocation strategy is necessary to re-propose the inter-satellite links in large-scale LEO satellite constellations so as to design an appropriate topology and minimize inter-satellite communication delay [12].