## 4 Proposed CB-FBC and Genetic Approach
### Optimization of \(P_{tj_{i}S}(t)\) and \(B_{Sj_{i}}(t)\)
\(C\) is the computational complexity of the fitness function given in (16) which is equal to \(\mathcal{O}(2N)\). \(U\), \(O\), and \(S\) are the computational complexities of the mutation, crossover, and selection functions used by the \"GA\" algorithm. For simplicity, we can ignore the effect of \"GA\" algorithm functions as they typically have constant complexity and are lower than the fitness function complexity. Thus, the computational complexity of the envisioned \"GA\" algorithm equals \(\mathcal{O}(4000N^{2})\). To sum up, the total computational complexity of the proposed approach, i.e., \"CB-FP\" + \"GA\" algorithms, will be in the range of \(\mathcal{O}\big{(}N^{2}\big{)}\). Thus, the improved performance of the proposed approach over the naive algorithms and that proposed in [23] comes with a slight increase in its computational complexity. However, as the algorithm will be run on the power supply feed terrestrial GBS, this will not be a big issue for the proposed approach. ## 6 Conclusions

In summary, this study suggests a new approach for aerials' deployment in post-disaster areas using LEO-Sat assistance, aiming to maximize the accessible sum rate of aerials simultaneously with achieving fairness in cluster coverage based on UDs' densities and considering the finite existing resources of both LEO-Sat and aerials. The approach utilizes the \"CB-FBC\" algorithm to distribute aerials eventually while considering fairness in the clusters' coverage and the aerials' battery capacity. A \"GA\" was also used to optimize the allocation of aerials' TX powers and LEO-Sat's bandwidths. The study conducted extensive numerical analysis, which shows that the proposed approach outperforms naive

Figure 6: LEO-SAT bandwidth utilization ratio against the numbers of aerials. benchmark schemes like nearest- and random-based selections regarding total system rate, aerials' batteries' consumption, aerials' TX powers allocation, and LEO-Sat bandwidth utilization. Overall, this study opens opportunities for using LEO-aerial integration in different 6G network scenarios. All authors contributed equally to this paper. All authors have read and agreed to the published version of the manuscript. The authors extend their appreciation to Prince Sattam Bin Abdulaziz University for funding this research work through the project number (PSAU/2023/01/24766). Data Availability StatementData are available upon request to the authors. The authors declare no conflict of interest. ## References

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