## 3 System Model
\[PL_{\textit{LoS}}=42.6+26 logd+20 logf \tag{13}\]  
For the UAV-BS to provide a high-quality communication service to users, the UAV-BS goes through an SINR-based ranking and selects the best links to ensure QoS as well as macrocells. The network of UAV-BSs is defined by the number of congested macrocells and the number of users in the coverage radius of the macrocells. First, it is necessary to calculate the distance between UAV-BS and the user competing for the service defined in Equation (14). \[d_{v}=\sqrt{R^{2}+h^{2}} \tag{14}\]  
where \(d_{v}\) is the distance between UAV-BS and the user, \(R^{2}\) is the radius of the UAV-BS coverage area, and \(h^{2}\) is the height from UAV-BS to the ground. The formed angle between the UAV-BS and the user can be calculated using Equation (15). \[\theta=tan^{-1}\bigg{(}\frac{h}{R}\bigg{)} \tag{15}\]  
Unlike the Cost Walfisch-Ikegami model, the dispersion model for UAVs considers the average relationship between the two equations (\(LoS\)) and (\(NLoS\)). The propagation model used to predict the path loss of UAV-BS is the air-to-ground channel model [40, 41], which can be calculated for \(LoS\) using Equation (16) and for \(NLoS\) using Equation (17). \[PL_{LoS}=20 log\bigg{(}\frac{4\pi f_{c}d_{v}}{c}\bigg{)}+\phi_{LoS} \tag{16}\]  
\[PL_{NLoS}=20 log\bigg{(}\frac{4\pi f_{c}d_{v}}{c}\bigg{)}+\phi_{NLoS} \tag{17}\]  
where \(f_{c}\) is the carrier frequency, \(c\) is the speed of light, and \(\phi_{LoS}\) and \(\phi_{NLoS}\) are average additional losses for the propagation loss in free space, which depends on the environment. The probability of obtaining a \(LoS\) link at an angular increase \(\theta\) is calculated in Equation (18):  
\[P(LoS)=\frac{1}{1+\phi\exp\Bigl{(}-\beta\Bigl{[}\frac{180}{\pi}\theta-\phi \Bigr{]}\Bigr{)}} \tag{18}\]  
where \(\phi\) and \(\beta\) are considered constant values that depend on the environment, such as urban, rural, etc. Similarly, the probability of \(NLoS\) can be found in Equation (19):  
\[P(NLoS)=1-P(LoS) \tag{19}\]  
Therefore, the average propagation loss results from the altitude and the coverage radius of the UAV-BS, calculated in Equation (20):  
\[PL(R,h)=P(LoS)PL_{LoS}+P(NLoS)PL_{NLoS} \tag{20}\]  
Signal power is a ratio between the power of the macrocell or UAV-BS and the user device calculated using the propagation model. We can assume that \((U)\) is the set of users denoted by \(U=\{1,2,...,U_{u}\}\) and that \((V)\) is the set of UAV-BS denoted by \(V=\{1,2,...,V_{v}\}\). Knowing that \(U\) is the set of users, \(M\) is the set of macrocells, where \(m\) is the total number of macrocells and \(v\) is the total number of UAV-BSs, we can calculate the received reference signal power \(PRX\) (in dB) for user \(i\in U\) from macrocell \(j\in M\) or from UAV-BS \(j\in V\), denoted by \(PRX_{i,j}\)[42, 43]. The received signal power is calculated in Equations (21) and (22). If \(j\) is a macrocell:  
\[PRX_{i,j}=PTX_{m}-PL_{m} \tag{21}\]  
If \(j\) is a UAV-BS:  
\[PRX_{i,j}=PTX_{v}-PL_{v} \tag{22}\]  
where \(PTX_{m}\) is the power transmitted by the macrocell, \(PL_{m}\) is the path loss between the macrocell and the user device, just as \(PTX_{v}\) is the power transmitted by UAV-BS, and \(PL_{v}\) is the propagation loss between UAV-BS and the user. Finally, we can calculate the signal-to-interference-plus ratio (SINR) presented in [42, 43, 36, 44] and given in Equation (23). \[d_{v}=\sqrt{R^{2}+h^{2}} \tag{14}\]0  
Here, \(SINR_{i,j}\) is the result of the ratio between the user equipment and the macrocell and \(\sigma\) is the power noise. To calculate the \(SINR\), \(PRX\) and \(\sigma\) are expressed in linear form [42; 43]. The throughput is used as a constraint to allocate users in the macrocell, where \(SINR_{i,j}\) is the main variable. The calculation is based on the channel capacity formulation presented in [36; 42; 43] and can be found in Equation (24).