## 2 Path Loss Profile Additionally, Modeling for UAV Swarm  
The section describes the UAV's air-to-air link for swarm UAVs, whereas the communication channel is considered a line of sight (LOS), as shown in Figure 2. The Doppler frequency drift is taken as a dominant effect in the aerial link between the swarm of UAVs, and the effects increase with the moving speed of the swarm. Additionally, the Doppler effect can also be observed through a large-scale fading model, as shown below [20]. \[RSS(dB)=P_{t}+G_{UAV1}+G_{UAV2}+10\log_{10}\left(\frac{\lambda_{0}}{4\pi d_{0}} \right)^{a_{0}} \tag{1}\]  
In Equation (1), the received signal strength is RSS, \(P_{t}\) is taken as transmitted power and \(\lambda_{0}\) is the wavelength. The distance between the UAVs is \(d_{0}\), and the antenna gains of UAVs are \(G_{UAV1}\) and \(G_{UAV2}\). Referring to Equation (1), the \(P_{t}\) and distance \(d_{0}\) are constant for all swarm elements. The RSS vs. \(d_{0}\) is plotted and shown in the Figure 3[21]. However, there is a need to improve the gain of the antenna array in order to receive the \(P_{r}\) from other UAVs. On the other hand, the relative velocities of swarm elements are assumed to be zero for the simplicity of the model. According to the reference [22], the Doppler effect of moving UAVs can be shown as below. \[P_{L}(dB)=P_{L}(d_{0})+10\alpha_{o}\left(\log_{10}\frac{d}{d_{0}}\right)-\log _{10}\left(\frac{\delta h}{h_{opt}}\right)+C_{p}+10x\log_{10}\frac{f_{c}+ \delta f}{f_{c}}+\varsigma \tag{2}\]  
where frequency-dependent path-loss is represented by \(x\) and \(\delta f\) is considered as frequency drift [23]. One can understand that the aforementioned formula does not take antenna  
Figure 2: UAV master-and-slave configuration to operate in emergency scenarios such as wild fires, floods and road accidents. gain into account. During the flight of the swarm, the path-loss is calculated through [24]. Similarly, the power loss (\(PL\)) and \(RSS\) vs. \(d_{0}\) are shown in Figure 3.  
The wireless channels (small-scale fading-model) are also taken into consideration to reflect the influences of the multi-path components while assessing the effectiveness of the deployed antenna design which was previously stated. Since the 3 GPP/ITU model is the foundation for the 3D channel model created in [24; 25], it is taken into consideration. The model provides information on the received multipath components such as amplitude, phase, time delay, angle of arrival (AoA) and angle of departure (AoD) in elevation and azimuth domains. As a result, the wireless channel matrix may be modeled using Equation (3). Table 1 provides a detailed list of the variables used in the equation below. \[ \begin{split} G_{u,g,n}(t_{0})=\sqrt{P_{n}}\sum_{m=1}^{M}\left[ \begin{array}{cc}E_{tx0,s,V_{t}}((\theta_{i},\phi_{i})_{n,m,AOA})\\ E_{tx0,s,H_{t}}((\theta_{i},\phi_{i})_{n,m,AOA})\end{array}\right]^{T}\left[ \begin{array}{cc}e^{i\varphi_{t,m}^{\mathrm{spie}}}&\sqrt{\kappa_{n,m}}e^{i \varphi_{t,m}^{\mathrm{spie}}}\\ \sqrt{\kappa_{n,m}}e^{i\varphi_{t,m}^{\mathrm{spie}}}&e^{i\varphi_{t,m}^{ \mathrm{spie}}}\end{array}\right]\\ \left[\begin{array}{cc}E_{rx0,u,V_{t}}((\theta_{i},\phi_{i})_{n,m,AOD})\\ E_{rx0,u,H_{t}}((\theta_{i},\phi_{i})_{n,m,AOD})\end{array}\right]^{T}e^{i \omega_{t}}e^{i\omega_{t}}e^{2j\pi v_{n,m}t}\end{split}  \tag{3}\]  
The dataset of path loss and \(RSS\) was extracted from Figure 3[21]. For this purpose, the plot digitization technique (plot to CSV) was used and preprocessed in Python (Jupyter notebook). Thereafter, the supervised machine-learning algorithm known as random forest (RF) was applied to train the model based on available data points with (n_estimators = 10, random_state = 0). Accordingly, the prediction plots of path loss and \(RSS\) has been