## 4 Proposed CB-FBC and Genetic Approach
### Optimization of \(P_{tj_{i}S}(t)\) and \(B_{Sj_{i}}(t)\)
The handover process between the LEO-Sat and both GBS and aerials can be conducted smoothly, and its impact on network performance will be investigated in future studies. The total bandwidth allocated for the aerial is 40 MHz, and for the LEO-Sat, it is 100 MHz. For the \"GA\" algorithm, the number of populations is 20, the maximum number of generations is 50, the percentage of mutation is 0.3, the percentage of crossover is 0.3, and the percentage of creation function is 0.1. Other simulation parameters are provided in Table 1. For performance comparisons, we compare the proposed approach with a basic UCB MAB algorithm given in [19] for cluster selection. Also, the GA is used for the aerials' TX power and LEO-Sat bandwidth optimization for fair comparisons. In the UCB-based clusters selection, the clusters that maximize the upper confidence criterion are selected by the survival GBS for aerial deployment without any fairness guarantee, where the super arm selection is carried out based on the following equation [19]:

\[A(t)=\underset{A(t)\subset\mathcal{M}}{\arg\max}\sum_{i\in A(t)}\left(\tau_{i }(t)+\sqrt{\frac{2 ln(t)}{h_{i}(t)}}\right),|A(t)|\leq N, \tag{14}\]

where \(A(t)\) is the group of selected clusters, \(\mathcal{M}\) is the space of all available clusters, \(h_{i}(t)\) is the number of times cluster \(i\) was selected just before time \(t\), and \(\bar{\tau}_{i}(t)\) is the average data rate of cluster \(i\) just before time \(t\). Also, naive benchmarks like nearest and random approaches are involved in the comparisons. In the \"Nearest\" approach, the aerials always select their nearest clusters without collisions, i.e., no aerials cover the same cluster. If the same cluster is the nearest for two or more aerials, it will be covered by the nearest one of them. The other aerials will cover their second or third nearer cluster, and so on. Also, aerials operate at their maximum TX power values, i.e., \(P_{Vmax}\), while the LEO-Sat bandwidth is equally allocated between the LEO-aerial links. Regarding the \"Rand\" approach, the clusters are selected randomly, the aerials operate at their maximum TX powers, and the LEO-Sat bandwidth is randomly allocated within the LEO-aerial links. ### Performance Analysis

Figure 2 adjusts the number of GA generations, where the average total system rate is evaluated against different numbers of GA generations ranging from 10 to 100. In this simulation, the number of aerials is set to 14 to cover 36 clusters. From this figure, as the number of generations increases from 10 to 50, the average total system rate increases by 28%, while it only increases by 4% when increasing the number of generations from \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline \(B_{Smax}\), \(B_{V}\) & 100 MHz [26], 40 MHz [24] \\ \hline \(P_{i\backslash f_{i}}\), \(P_{Vmax}\) & 1 Watt, 10 Watt [26] \\ \hline \(K_{i}\) & Uniformly random in the range [1, 100] \\ \hline \(f_{V}\), \(f_{S}\) & 2 GHz [24], 2.4 GHz [26] \\ \hline \(\sigma^{2}(dBm)\) & \(-174\) + 10 log10(W) + 10 [30] \\ \hline \(P_{f}\), \(P_{h}\) & 4, 2 Watt [31] \\ \hline \(\tau\) and \(\varepsilon\) & 1000 and 1.38 \(\times\) 10\({}^{-23}\)[26] \\ \hline \(\rho^{LOS}\) and \(\rho^{NLOS}\) & 0.1 dB and 21 dB [24] \\ \hline UD data load & 5 Gbit \\ \hline \(T\), \(\Omega\) & 1000, 0.01 \\ \hline \(G_{ij}\), \(G_{GS}\) & 15 dB [26] \\ \hline \(a\), \(b\) & 4.88, 0.429 [24] \\ \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. 50 to 100. This means that the average total system rate starts to saturate after 50 number of generations. Considering that the complexity of the GA algorithm increases linearly with an increase in the number of generations, we selected 50 generations to trade off complexity and performance as aforementioned. Figure 3 displays the average total system rate versus distinct numbers of aerials. As the number of aerials increases, so does the mean total system rate for all compared schemes due to a greater coverage area.