## 3 Performance Simulation and Analysis
### VCM Transmission Efficiency  
The VCM system simplifies the atmospheric attenuation at different elevation angles to a fixed value [1] and needs to ensure that the link is available at the minimum 5\({}^{\circ}\) elevation angle. Only the change of free space loss caused by the change of distance between satellite and G/S is considered, and it is used as the basis for MCS switching.  
For different initial minimum MCS of VCM system, the theoretical range of elevation angle corresponding to different set of MCSs can be calculated from Figure 5. In Figure 5, starting from the upper seven maximum allowable atmospheric attenuation values with 5\({}^{\circ}\) elevation angle, seven straight lines parallel to the horizontal axis are drawn and the intersections with the existing curves which correspond to the switching elevation angles of adjacent MCS are found out. For example, when the initial minimum MCS is 1, the switching elevation angles of adjacent MCS are shown in Figure 6. The results are independent of G/S locations and shown in Table 6.  
The simulation results of VCM TEF of Kashgar G/S, Beijing G/S and Sanya G/S with different initial minimum MCS are shown in Table 5. It can be seen that:  
1. For a specific G/S, the VCM TEF increases with the increase of initial minimum MCS, mainly because of the larger system spectral efficiency for larger MCS. However, compared with the lower initial minimum MCS, the outage period is longer for higher initial minimum MCS.
2. For a specific initial minimum MCS, the VCM TEF decreases in the order of Kashgar G/S, Beijing G/S and Sanya G/S, mainly due to the differences of rainfall.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**MCS**} & \multicolumn{6}{c}{**Initial Minimum MCS**} \\ \cline{2-9}  & **1** & **3** & **6** & **12** & **14** & **20** & **25** & **28** \\ \hline
1 & [5, 10.84] & - & - & - & - & - & - & - \\
3 & [10.84, 22.42] & [5, 15.06] & - & - & - & - & - & - \\
6 & [22.42, 39.34] & [15.06, 28.21] & [5, 15.06) & - & - & - & - & - \\
12 & [39.34, 60.42] & [28.21, 41.73] & [15.06, 23.88] & [5, 11.93] & - & - & - & - \\
14 & [60.42, 90] & [41.73, 90] & [23.88, 47.1) & [11.93, 26.97] & [5, 17.49) & - & - & - \\
20 & - & - & [47.1, 90] & [26.97, 48.85] & [17.49, 32.82] & [5, 15.75] & - & - \\
25 & - & - & - & [48.85, 90] & [32.82, 48.85] & [15.75, 24.75] & [5, 11.93) & - \\
28 & - & - & - & - & [48.85, 90] & [24.75, 90] & [11.93, 90] & [5, 90] \\ \hline \hline \end{tabular}
\end{table}
Table 6: Theoretical range of elevation angle corresponding to different MCS in VCM system (\({}^{\circ}\)).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**MCS**} & \multicolumn{3}{c}{**CCM**} & \multicolumn{3}{c}{**VCM**} & \multicolumn{3}{c}{**ACM**} \\ \cline{2-10}  & **Kashgar** & **Beijing** & **Sanya** & **Kashgar** & **Beijing** & **Sanya** & **Kashgar** & **Beijing** & **Sanya** \\ \hline
1 & 294.11 & 291.84 & 275.32 & 501.12 & 497.04 & 469.05 & 2671.21 & 2644.63 & 2468.56 \\
3 & 473.56 & 468.85 & 439.32 & 666.96 & 659.87 & 618.64 & 2671.15 & 2639.80 & 2450.48 \\
6 & 793.16 & 783.31 & 722.22 & 989.98 & 977.43 & 901.88 & 2671.02 & 2634.28 & 2412.24 \\
12 & 1067.63 & 1050.97 & 949.74 & 1327.71 & 1306.82 & 1181.04 & 2670.80 & 2626.65 & 2364.68 \\
14 & 1336.30 & 1311.58 & 1165.47 & 15952.52 & 1565.33 & 1392.04 & 2670.58 & 2619.44 & 2320.68 \\
20 & 1898.02 & 1850.08 & 1584.30 & 2143.19 & 2089.15 & 1789.49 & 2669.88 & 2601.79 & 2225.59 \\
25 & 2368.12 & 2286.82 & 1869.23 & 2530.34 & 2443.33 & 1997.30 & 2668.63 & 2576.91 & 2105.92 \\
28 & 2667.01 & 2552.31 & 1982.68 & - & - & - & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 5: CCM, VCM and ACM TEF (Mbps).