# UAV Communication Recovery under Meteorological Conditions
## 3 Methods
### UAV Coverage Radius with Elevation Angle under Different Weather Conditions
#### 3.3.3. Compensated Path Loss in UAV-Ground Communications  
In this section, we explain the compensated path loss, which is denoted by \(PL_{\text{cps}}\). Based on Equation (10), we observe that introducing the specific attenuation of one type  
Figure 14: UAV optimal height versus snowfall rate in four regions. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Weather** & **Regions** & **28 GHz** & **71 GHz** \\ \hline \multirow{4}{*}{Rain (\(0<R_{\text{rain}}<100\) mm/h)} & Region 1 & 78.29 & 25.17 \\ \cline{2-4}  & Region 2 & 60.31 & 19.52 \\ \cline{2-4}  & Region 3 & 26.61 & 8.05 \\ \cline{2-4}  & Region 4 & 15.50 & 4.39 \\ \hline \multirow{4}{*}{Fog (\(0.05<R_{\text{fog}}<0.5\) g/m\({}^{3}\))} & Region 1 & 3.93 & 2.19 \\ \cline{2-4}  & Region 2 & 2.62 & 1.47 \\ \cline{2-4}  & Region 3 & 1.09 & 0.61 \\ \cline{2-4}  & Region 4 & 0.60 & 0.34 \\ \hline \multirow{4}{*}{Snow (\(0<R_{\text{snow}}<10\) mm/h)} & Region 1 & 0.96 & 6.33 \\ \cline{2-4}  & Region 2 & 0.62 & 4.45 \\ \cline{1-1} \cline{2-4}  & Region 3 & 0.26 & 1.30 \\ \cline{1-1} \cline{2-4}  & Region 4 & 0.14 & 0.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The extent of decrease in the optimal height (in m) due to increases in rainfall rate, liquid water density, and snowfall rate. Figure 13: UAV optimal height versus liquid water density in four regions. of weather (rain, fog, or snow) leads to an increase in transmission loss compared to only considering atmospheric conditions. We compensate for the propagation loss due to rain by increasing the value of \(PL_{\text{max}}\) on the left side of the equation, as shown in Equation (11). The compensated path loss can be calculated using Equation (12), where \(\mathbb{C}_{r}^{\text{gas}}\) denotes the maximum coverage radius of the UAV under atmospheric conditions only, and \(H_{opt}^{\text{gas}}\) represents the corresponding optimal UAV height. \[ \begin{split} PL_{\text{max}}+PL_{cps}&=[i\cdot \sin(j\theta+k)+l\cdot\sin(m\theta+n)]\times(\eta_{LoS}-\eta_{NLoS1})+20\log d\\ &+20\log\left(\frac{4\pi}{\lambda}\right)+\eta_{NLoS1}+\frac{( \beta+\gamma)d}{1000},(0\leq\theta\leq 70^{\circ}).\end{split}  \tag{11}\]  
\[PL_{cps}=\gamma\times\sqrt{\left(C_{r}^{\text{gas}}\right)^{2}+\left(H_{opt}^ {\text{gas}}\right)^{2}}\times 0.001. \tag{12}\]  
Based on Equation (12), the relationships between the calculated compensated path loss (\(PL_{cps}\)) and the rainfall rate, liquid water density, and snowfall rate in the four regions are illustrated in Figure 15, Figure 16, and Figure 17, respectively. In these three figures, each discrete marker point represents the compensated path loss value calculated based on each corresponding rainfall rate, liquid water density, or snowfall rate. The solid line and dashed line depict the fitting curves for the frequencies of 28 GHz and 71 GHz, respectively. From the three figures, we can find that the compensated path loss increases with the rainfall rate, liquid water density, and snowfall rate. The extents of the increases in the compensated path loss are summarized in Table 10. It can be seen from the three figures (Figures 15-17) and Table 10 that when the frequency is 28 GHz, the increases in the compensated path loss in the four regions due to rain, fog, and snow are over 3 dB, 0.1 dB, and 0.02 dB, respectively. When the frequency is 71 GHz, the increases in the compensated path loss in the four regions due to rain, fog, and snow are over 2 dB, 0.1 dB, and 0.3 dB, respectively. Therefore, when the frequency is 28 GHz, the increase in the compensated path loss caused by rain and snow is the largest and the smallest, respectively. When the frequency is 71 GHz, the increase in the compensated path loss caused by rain and fog is the largest and the smallest, respectively. Figure 15: Compensated path loss versus rainfall rate in four regions. Figure 16: Compensated path loss versus liquid water density in four regions.