## 2 System Model
### Path Loss Exponent and Rician Factor Modeling  
Unlike simplified models that assume a fixed LoS or complete blockage, the Rician factor in the proposed scheme is dynamically changed based on the UAV altitude, the elevation angle between the UAV and users. Intuitively, when the altitude of the UAV decreases, the channels suffer severe fading due to the obstacles between the UAV and the users. In addition, the elevation angle of the UAV relative to the ground user is identified as a key factor in determining the Rician factor [14]. Therefore, by introducing the non-decreasing function \(KE(\theta_{X})\), where \(X\in\left\{t,r,G\right\}\) and \(\theta_{X}\in\left[0,\frac{\pi}{2}\right]\), the Rician factor is modeled as a function of the elevation angle \(K_{X}=KE(\theta_{X})\). The elevation angles between the UAV and the ground users are denoted as \(\theta_{r}\) and \(\theta_{t}\), and the elevation angle between the UAV and the BS is \(\theta_{G}\). In fact, a large \(\theta_{X}\) leads to a higher LoS contribution and less multipath scatters at the receiver, resulting in a larger \(K_{X}\)[15]. According to [14], the Rician factors can be modeled by the following function:  
\[K_{X}=KE(\theta_{X}), \tag{3a}\] \[KE(\theta_{X})=a_{1}^{X}\cdot e^{\eta^{2}\theta_{X}},\] (3b) \[a_{1}^{X}=\kappa_{0}^{X},\quad b_{1}^{X}=\frac{2}{\pi}\ln\left( \frac{\kappa_{\pi/2}^{X}}{\kappa_{0}^{X}}\right),\] (3c) \[X\in\left\{t,r,G\right\},\theta_{X}\in\left[0,\frac{\pi}{2}\right]. \tag{3d}\]  
where \(\kappa_{0}^{X}=KE(\theta_{X})\) is the minimum Rician factor for \(\theta_{X}=0\) and \(\kappa_{\pi/2}^{X}=KE(\theta_{X})\) is the maximum Rician factor for \(\theta_{X}=\frac{\pi}{2}\). \(\kappa_{0}^{X}\) and \(\kappa_{\pi/2}^{X}\) are fixed values related to the environment, and as the environmental parameters change, the shape of \(KE(\theta_{X})\) will also vary accordingly. Furthermore, (3b) reflects the influence of the elevation angle on the LoS component and the reduction in multipath effects as \(\theta_{X}\) increases.  
Similarly, the path loss exponent is affected by the elevation angle, with \(\varepsilon\) potentially decreasing as the UAV's elevation angle \(\theta_{X}\) increases. In this approach, \(e_{0}^{X}\) represents the maximum path loss exponent at \(\theta_{X}=0\), while \(\varepsilon_{\pi/2}^{X}\) denotes the minimum path loss exponent at \(\theta_{X}=\frac{\pi}{2}\). Generally, denser environments, with more obstacles between the transmitter and receiver, typically result in higher path loss exponents. To account for this, function \(\varepsilon_{X}(\theta_{X})\) is described based on the LoS function, \(P_{\text{LoS}}(\theta_{X})\), between the UAV and the ground user [16], which is given by the following:  
\[\varepsilon_{X}(\theta_{X})=a_{2}^{X}\cdot\mathcal{P}_{\text{LoS} }(\theta_{X})+b_{2}^{X}, \tag{4a}\] \[\mathcal{P}_{\text{LoS}}(\theta_{X})=\frac{1}{a_{3}^{X}e^{-b_{3} ^{X}\theta_{X}}+1},\] (4b) \[X\in\left\{t,r,G\right\},\theta_{X}\in\left[0,\frac{\pi}{2}\right]. \tag{4c}\]  
where the parameters \(a_{2}^{X},b_{2}^{X},a_{3}^{X}\), and \(b_{3}^{X}\) are influenced by the environmental conditions and the transmission frequency. \(a_{2}^{X}\) and \(b_{2}^{X}\) can be modeled as below  
\[a_{2}^{X}=\frac{\varepsilon_{\pi/2}^{X}-\varepsilon_{0}^{X}}{ \mathcal{P}_{\text{LoS}}\left(\frac{\pi}{2}\right)-\mathcal{P}_{\text{LoS}}(0 )}\cong e_{\pi/2}^{X}-\varepsilon_{0}^{X}, \tag{5a}\] \[b_{2}^{X}=e_{0}^{X}-a_{2}^{X}\cdot\mathcal{P}_{\text{LoS}}(0) \cong\varepsilon_{0}^{X},\] (5b) \[X\in\left\{t,r,G\right\}. \tag{5c}\]  
where the approximations arise from the fact that \(\mathcal{P}_{\text{LoS}}(0)\to 0\) and \(\mathcal{P}_{\text{LoS}}(\pi/2)\to 1\), with detailed proofs provided in [15].