## 6 Simulation Analyses
### Beneficial Region and Transmission Power Requirement  
We study the conditions when the flying base station becomes beneficial over the stationary base station, i.e., \(\mathcal{G}>0\), and call it the _beneficial region_ when such conditions are met. Figure 4: Flying base station channel capacity per bandwidth with respect to path loss exponent \(\gamma\). Figure 3: Flying base station channel capacity per bandwidth with respect to the stationary base station’s SNR, SNR\({}_{SU}\). The flying base station's transmission power affects the communication channel performance and determines if the flying base station is operating within the beneficial region, in which the cellular service operator would want to deploy the flying base station (in addition to the existing stationary base station) so that the user can connect to the flying base station over the stationary base station. We, therefore, analyze the \(\eta\) dependency for the beneficial region while varying the stationary base station's channel condition in SNR, SNR\({}_{SU}\). Figure 5 plots the beneficial region threshold so that the flying base station is beneficial if its transmission power capability \(\eta\) exceeds the threshold and \(\eta\) is above the plotted curve. Figure 5a provide the results of many simulation scenarios varying, SNR\({}_{SU}\), \(\gamma\), and whether the flying base station is full-duplex capable or not. Figure 5b focuses on one of those cases when \(\gamma=2\) and when the flying base station does not support full-duplex capability (i.e., half-duplex capable) and corresponds to the \"Half Duplex (\(\gamma=2\))\" in Figure 5a. Although Figure 5b provides the threshold behaviors for fewer scenarios, it provides an alternative visualization of the beneficial region by coloring the beneficial region; if (SNR\({}_{SU}\),\(\eta\)) falls under the colored beneficial region, then the half-duplex flying base station provides capacity gain over the stationary base station. The beneficial region threshold behavior is drastically different for the two cases when the flying base station has full-duplex capability or not/half-duplex. The beneficial region threshold behaves much differently when comparing full-duplex vs. half-duplex from the previous capacity performance analyses in Sections 6.1 and 6.2 where the full-duplex simply doubles the capacity performances of the half-duplex. If the flying base station has full-duplex capability, then it is beneficial as long as \(\eta\) is greater than a fixed threshold independent of the stationary base station's SNR. These correspond to the horizontal lines in Figure 5a. If \(\gamma=2\), the flying base station is beneficial as long as \(\eta>0.25\) or the flying base station's transmission power is at least as great as 0.25 times the stationary base station's transmission power. If \(\gamma=3\) and \(\gamma=4\), respectively, the flying base station is beneficial if \(\eta>0.125\) and \(\eta>0.0625\). Thus, if flying base station power per user is greater than a quarter (0.25\(\times\)) of the transmission power of the stationary base station per user, i.e., \(\eta=1\), then flying base station is beneficial for wireless communications which typically have \(\gamma>2\). In urban environment with greater path attenuation (e.g., physical barriers), \(\gamma\) increases and can reach or exceed 4, and the \(\eta\) threshold for beneficial region decreases, requiring smaller transmission power on the flying base station compared to that of the stationary base station. In the half-duplex case, the \(\eta\) requirement for the beneficial region depends on and varies with SNR\({}_{SU}\), as shown in Figure 5a. The greater the SNR between the stationary  
Figure 5: Beneficial region showing the \(\eta\) threshold with respect to SNR\({}_{SU}\). (**a**) Beneficial region varying SNR\({}_{SU}\) and \(\gamma\). If \(\eta\) is greater than the threshold (the line in the plot), the flying base station is beneficial. (**b**) Beneficial region varying SNR\({}_{SU}\) given half-duplex capability and \(\gamma=2\).