# Design of Mega-Constellations for Global Uniform Coverage with Inter-Satellite Links
## 4 Simulation and Results
### Simulation Studies and Results on Mega-Constellation Design  
The probability density function of the sub-satellite points density \(f_{k}\) is the key variable in the mega-constellation design method proposed in this paper. During the constellation design process, we regard it as a variable that only relates to the satellite's orbital elements, not interested in constellation parameters. By default, Walker constellations with the same other parameters but different numbers of satellites have the same \(f_{k}\). To verify that the statement is reasonable, this paper conducts a simulation analysis on the distribution characteristics of \(f_{k}\). Figure 6 shows the simulation results about the \(f_{k}\). The parameters are set as follows: \(e=0\), \(H=600\ km\), \(\omega=0\). The number of orbital planes is equal to the total number of satellites in the [PERSON] constellation (\(F=1\)). These parameters apply to all subgraphs in Figure 6. The four groups of figures respectively represent the distribution of sub  
Figure 5: Pseudo-code for Dijkstra’s algorithm. satellite points density of Walker constellation under different orbit inclinations. The three subgraphs of each group compare the distribution of \(f_{k}\) when all other parameters are the same but for the total number of satellites, and show the deviation rate between the two. By comparing the four groups of figures, it can be seen that the \(f_{k}\) distributions corresponding to different orbit inclination vary considerably. In Figure 6a, the distribution of \(f_{k}\) is almost identical whether the total number of satellites in the Walker constellation is 300 or 500. The deviation rate between the two sets of data is kept within 2%. Therefore, it can be concluded that the total number of satellites makes almost no difference to \(f_{k}\). The same conclusion can be drawn for the other three sets of figures. To sum up, it is reasonable to assume that the distribution of \(f_{k}\) is independent of the total number of satellites in the Walker constellation as a precondition for the mega-constellation design in this paper. Figure 6: _Cont._  
Simulations are carried out according to the mega-constellation design method proposed in this paper. The orbit altitude of all satellites is set to 600 km. The simulation duration is one orbital period, i.e., 96.69 min, and the time step is 1 min. A latitude zone is divided every 2\({}^{\circ}\). The total number of satellites in the initial sub-constellation with the maximum orbit inclination (90\({}^{\circ}\)) is set to 150. After iterative calculations, an LEO mega-constellation composed of 45 sub-Walker constellations with 5686 satellites is finally achieved. Table 1 records the results of the mega-constellation configuration obtained by the method proposed in this paper. \begin{table}
\begin{tabular}{c c c c} \hline
**Sub-Constellation** & \(i\,NP\) & **Sub-Constellation** & \(i\,NP\) \\
**Number** & & **Number** & \(i\,NP\) \\ \hline Cons\_1 & 90\({}^{\circ}\) 150 15 & Cons\_24 & 44\({}^{\circ}\) 138 23 \\ Cons\_2 & 88\({}^{\circ}\) 183 3 & Cons\_25 & 42\({}^{\circ}\) 131 131 \\ Cons\_3 & 86\({}^{\circ}\) 184 23 & Cons\_26 & 40\({}^{\circ}\) 126 9 \\ Cons\_4 & 84\({}^{\circ}\) 190 19 & Cons\_27 & 38\({}^{\circ}\) 123 3 \\ Cons\_5 & 82\({}^{\circ}\) 196 14 & Cons\_28 & 36\({}^{\circ}\) 118 59 \\ Cons\_6 & 80\({}^{\circ}\) 188 47 & Cons\_29 & 34\({}^{\circ}\) 112 14 \\ Cons\_7 & 78\({}^{\circ}\) 184 23 & Cons\_30 & 32\({}^{\circ}\) 104 13 \\ Cons\_8 & 76\({}^{\circ}\) 194 97 & Cons\_31 & 30\({}^{\circ}\) 98 7 \\ Cons\_9 & 74\({}^{\circ}\) 184 23 & Cons\_32 & 28\({}^{\circ}\) 95 5 \\ Cons\_10 & 72\({}^{\circ}\) 195 13 & Cons\_33 & 26\({}^{\circ}\) 90 9 \\ \hline \end{tabular}
\end{table} 
Table 1: Simulation results of the mega-constellation configuration. Figure 6: Distribution of sub-satellite points density along latitude zones with the variation of the total number of satellites and the orbital inclination.