## 4 Simulation Results
### Capacity Performance  
The joint optimization of the hovering radius with a different number of users in the target area is shown in Figure 4 The radius of the target region in Figure 4a,b is 1500 m and 2000 m respectively. As the number of iterations increases, the hovering radius of UAV converges gradually. As shown, the optimal solution of the algorithm generally does not change after the fourth and fifth iterations, which also shows the effectiveness and stability of the algorithm. In addition, a different number of users \(N\) in the area leads to different results of each iteration. The algorithm eventually converges to a value, which is the optimal hovering radius of the UAV in this scenario. The change process of fairness performance with the number of iterations is shown in Figure 5. The vertical axis of the figure is the fairness metric, which is \(\sum\limits_{i~{}=~{}1}^{N}\sum\limits_{n~{}=~{}1}^{N}u_{i}[n](SNR_{\max}- SNR_{i}[n])^{2}\), as defined above; and the fairness metric is the objective function in ACA-GA. The radius of the target region in Figure 5a,b is 1500 m and 2000 m, respectively. Although the number of users does not affect the convergence of the hovering radius, it does affect the convergence of fairness performance. The fairness performance decreases as the number of user increase. It becomes more difficult to assign each user the time slot that maximizes fairness performance as the number of users increases. Figure 3: The Iterative process of the Genetic Algorithm (GA). Figure 2: The Iterative process of the Ant Colony Algorithm (ACA). The result, shown in Figure 6, is the network capacity in three different optimization methods. The horizontal line in the figure represents the performance of the system when the UAV is fixed at the regional origin. In this case, no optimization is required, and the total network capacity can be calculated directly from the location of each user, and the result is a fixed value. We can see that when the only genetic algorithm is used to optimize the hovering radius of the UAV without optimizing user scheduling, the performance of the network is lower than that in the case that the UAV is fixed at a point. The reason is that the user is randomly connected to the network during the hovering of the UAV without optimizing user scheduling, and there is no guarantee that each user will have access within the appropriate time slot. Then we investigate the variation of the throughput with the iteration number in three different optimization methods. We calculate the sum of the transmission rates \(C_{sum}\) based on the SNR of the user \(SNR_{i}[n]\) and user scheduling, to represent the throughput of the network. Therefore, \(C_{sum}\) can be written as \(C_{sum}\ =\ \sum\limits_{i\ =\ 1}^{N}\sum\limits_{n\ =\ 1}^{N}u_{i}[n]\cdot W\log(1+SNR_{i}[n])\). \(W\) is the bandwidth and we assume \(W\ =\ 1\) MHz. As shown in Figure 7, the ACA-GA joint optimization has a significant improvement in the throughput of the network, compared with the case that without optimization and only use GA to optimize radius. ACA-GA converges when the iteration number is 10, while GA converges when the iteration number is about 60. The ACA-GA joint optimization approach has better network capacity and better convergence than either of the above two methods. Figure 4: The iterative process of hovering radius in joint optimization. \(R_{\text{o}}\) is 1500 m (**a**) and 2000 m (**b**). Figure 5: The iterative process of fairness performance in joint optimization. \(R_{\text{o}}\) is 1500 m (**a**) and 2000 m (**b**). In order to compare with the ground mobile base station, we consider the situation that the ground mobile base station provides service for users when it moves with a circular trajectory.