# Forward Link Optimization for the Design of VHTS Satellite Networks
## 5 Case Studies
### Scenario 2  
Following the proposed methodology, the average \(CINR_{b}\) for scenario 2 for different user \(G\)/\(T\) is represented in Figure 10a. As expected, when the user \(G\)/\(T\) increases, the optimal number of beams decreases, and the tradeoff motivated by the increase in cochannel interference for large number of beams appears. Figure 10b shows the capacity per beam for scenario 2, with a non-monotonic behavior with the number of beams. Figure 11 shows the reduction in the cost per Gbps in orbit with the increase in the optimal number of beams for different user \(G\)/\(T\) for scenario 2. Compared to the first scenario, the optimal number of beams and the total cost of the system is reduced, as it corresponds to a system with lower capacity requirements and reduced service area. Figure 8: Service area percentage for different ModCods (CCM) of Scenario 1 (159 beams and a user G/\(T\) of 17 dB/K). Figure 9: VCM map (DVB-S2X), scenario 1, 159 beams, and a user \(G\)/\(T\) of 17 dB/K (availability 99.9%). The decision factors of the first step of the methodology are presented in Table 3. The minimum feasible user \(G\)/\(T\) in scenario 2 is 15 dB/K. There is a trade-off again because the \(\mathit{CINR}_{b}\), the capacity per beam, and the cost per Gbps in orbit decrease, but the number of gateways, the total cost of the system, and total capacity of the system increase. Figure 11: Variation of the Cost per Gbps in orbit for different optimal numbers of beams depending on the user \(G\)/\(T\). Scenario 2. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{\(G\)/\(T\) [dB/K]} & \multirow{2}{*}{
\begin{tabular}{c} **Optimal** \\ **Number** \\ **of Beams** \\ \end{tabular} } & \multirow{2}{*}{\(\begin{array}{c} **CINR\textsubscript{b}** \\ **[dB]** \\ \end{array}\)} & \multirow{2}{*}{\(\begin{array}{c} **Gbps Per** \\ **Beam** \\ **[dB]** \\ \end{array}\)} & \multirow{2}{*}{\(\begin{array}{c} **Ideal** \\ **Satellite** \\ **Capacity** \\ **[Gbps]** \\ \end{array}\)} & \multirow{2}{*}{\(\begin{array}{c} **Satellite** \\ **Mass [kg]** \\ \end{array}\)} & \multirow{2}{*}{\(\begin{array}{c} **Number of** \\ **Gateways** \\ **Cost [M]** \\ \end{array}\)} & \multirow{2}{*}{\(\begin{array}{c} **Total** \\ **Gbps in** \\ **Cbit [M€** \\ \end{array}\)} \\ \hline
15 & 97 & 15.9491 & 1.3336 & 129.3588 & 6.2769e3 & 5 & 374.9645 & 2.8986 \\
17 & 87 & 16.8955 & 1.4104 & 122.7081 & 6.2279e3 & 5 & 356.9645 & 2.9911 \\
20 & 71 & 18.2139 & 1.5180 & 107.7803 & 6.1392e3 & 4 & 324.0916 & 3.0070 \\
23 & 55 & 19.4923 & 1.6228 & 89.2558 & 6.0327e3 & 3 & 291.2187 & 3.2627 \\
25 & 44 & 20.3663 & 1.6947 & 74.5661 & 5.9440e3 & 3 & 271.4187 & 3.6400 \\
27 & 32 & 21.285 & 1.7704 & 56.6513 & 5.8240e3 & 2 & 245.7458 & 4.3379 \\ \hline \end{tabular}
\end{table} 
Table 3: Analysis in clear sky conditions for Scenario 2. Figure 10: Analysis in clear sky conditions in scenario 2. **(a)** variation of the \(\mathit{CINR}_{b}\) depending on the numbers of beams and the user \(G\)/\(T\); **(b)** variation of the \(C_{b}\) depending on the numbers of beams and the user \(G\)/\(T\). In scenario 2, when the user \(G\)/\(T\) is 15 dB/K and the number of beams is 97, a minimum possible cost of 2.8986 M\(\mathrm{\SIUnitSymbolCelsius}\) per Gbps in orbit is obtained, which exceeds the specified system cost in 25 M\(\mathrm{\SIUnitSymbolCelsius}\) (see Table 1). For this reason, the minimum possible cost per Gbps in orbit that meets with all the requirements is 2.9091 M\(\mathrm{\SIUnitSymbolCelsius}\) per Gbps, achieved for a user \(G\)/\(T\) of 17 dB/K and 87 beams. For scenario 2, the percentage of the service area that meets the requirements for 17 dB/K, 87 beams, and different availabilities in case of using CCM is shown in Figure 12. It is observed that in scenario 2, it is feasible to use 64 APSK 11/15 up to an availability of 99.7%. When using 32 APSK 2/3-L, 16 APSK 7/9, or 16 APSK 3/5, 99.9% is the maximum link availability that meets the minimum service area percentage.