## 3 System Model
\tag{2}\]  
Here, \(L_{0}\) represents free space loss, \(L_{\text{rts}}\) represents diffraction and scattering loss between the roof and the street, and \(L_{\text{ms}}\) represents diffraction loss between multiple screens. The free space loss is given in Equation (3). \[L_{0}=32.4+20 logd+20 logf \tag{3}\] \begin{table}
\begin{tabular}{l l} \hline \hline
**Symbols** & **Definition** \\ \hline \(M\) & Macrocell \\ \(U\) & Users \\ \(V\) & UAV-BS \\ \(M_{\text{s}}\) & Overloaded macrocell set \\ \(d_{m}\) & Distance between the macrocell and the ground user \\ \(d_{v}\) & Distance between the UAV-BS and the ground user \\ PL & Average path loss (PL) for line of sight (LOS) and non-line of sight (NLOS) \\ \(\theta\) & Elevation angle (in radians) of UAV-BS with \\  & respect to the ground user is given by \\ \(PRX\) & Received signal power \\ \(SINR\) & Signal-to-interference-plus ratio \\ \(T_{ij}\) & Throughput \\ \(\mu_{j}\) & Required backhaul throughput \\ \(Loc_{(i,j)}\) & Reduced coverage area user set \\ \(Q_{v}\) & Number of UAV-BSs defined by the strategies \\ \(Vn_{i,j}\) & Is the number of UAV-BSs for each \\  & macrocells overloaded in the naive strategy? \\ \(Vo_{i,j}\) & Is the number of UAV-BSs for each \\  & macrocells overloaded in the optimized strategy? \\ \(C_{i,j}\) & Set of cluster centroid \\ \(P_{uav}\) & Ideal position set for UAV-BSs \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main symology. where \(d\) is the radio link length (in km) and \(f\) is the radio frequency (in MHz). The loss due to diffraction and scattering from the roof to the road is calculated in Equation (4). \[L_{\textit{rts}}=-16.9-10 logW+10 logf+20 log\bigtriangleup h_{u}+L_{\textit{ori}} \tag{4}\]  
Here, \(W\) is the road width and \(\bigtriangleup h_{u}\) is calculated in Equation (5). \[\bigtriangleup h_{u}=h_{r}-h_{u} \tag{5}\]  
where is the difference between the height of the rooftop \(h_{r}\) and the height of the user's device \(h_{u}\), similar to \(L_{\textit{ori}}\) calculated in Equation (6). \[L_{\textit{ori}}= \begin{cases}-10+0.354\phi&0^{\circ}\leq\phi<35^{\circ}\\ 2.5+0.075(\phi-35)&35^{\circ}\leq\phi<55^{\circ}\\ 4.0+0.114(\phi-55)&55^{\circ}\leq\phi<90^{\circ}\end{cases}  \tag{6}\]  
Here, \(\phi\) is the angle of incidence concerning the direction of the road. It is then shown that the loss is caused by the multiscreen diffraction calculated in Equation (7). \[L_{\textit{ms}}=L_{\textit{bsh}}+k_{a}+k_{d}\;logd+k_{f}\;logf-9 logB \tag{7}\]  
Here, \(B\) is the distance between buildings along the signal path and \(L_{\textit{bsh}}\), and \(k_{a}\) represents the increase in path loss due to a lower height of the macrocell antenna. Using the abbreviation in Equation (8),  
\[\bigtriangleup h_{m}=h_{m}-h_{r} \tag{8}\]  
where the height of the base antenna above the rooftops \(h_{m}\) is represented, we find that \(L_{\textit{bsh}}\) and \(k_{a}\) are passed through in Equations (9) and (10). \[L_{\textit{bsh}}= \begin{cases}-180 log(1+\bigtriangleup h_{m})&h_{m}>h_{r}\\ 0&h_{m}\leq h_{r}\end{cases}  \tag{9}\]  
\[K_{a}= \begin{cases}54&h_{r}>h_{m}\\ 54-0.8\bigtriangleup h_{m}&d\geq 0.5\;km\end{cases} \quad\text{and}\quad \begin{cases} h_{r}\leq h_{m}\\ h_{r}\leq h_{m}\end{cases}  \tag{10}\]  
The expressions \(K_{d}\) and \(K_{f}\) control the dependence of the diffraction loss of the multiple screens on distance and operating frequency, respectively. The distance factor \(K_{d}\) is given in Equation (11). \[K_{d}= \begin{cases}18-15(\bigtriangleup h_{m}/h_{r})&h\leq h_{m}\\ 18&h>h_{m}\end{cases}  \tag{11}\]  
The factor \(k_{f}\) is given in Equation (12):  
\[K_{f}=-4+ \begin{cases}0.7\Big{[}\frac{f}{925}-1\Big{]}&\text{medium sized and suburban}\\ 1.5\Big{[}\frac{f}{925}-1\Big{]}&\text{metropolitan center}\end{cases}  \tag{12}\]  
For line of sight condition, the total attenuation \(PL_{\textit{LoS}}\) is given in Equation (13).