## 2 System Model and Problem Formulation
### Aerial Channel Model  
In this study, we adopt an air-to-ground (A2G) Rician fading channel by considering the characteristic nature of the aerial channel in practical scenarios, where the channel statistics depend on the UAV altitude [11; 12; 13; 30; 31]. A Rician fading channel consists of a deterministic line-of-sight (LoS) component as well as a random multipath component, i.e., Rayleigh-distributed non-LoS (NLoS). Thus, the A2G Rician fading channel model characterizes the aerial channel by taking into account the dominant LoS channel and the multiplicative effect of both large- and the small-scale fading. The channel vector between the UAV and the \(u\)-th EHD, denoted by \(\mathbf{h}_{u}\in\mathbb{C}^{N\times 1}\), is modeled as [14; 30; 31]. \[\mathbf{h}_{u}=\sqrt{\beta_{0}d_{u}^{-a_{u}}}\bigg{(}\sqrt{\frac{\mathcal{K}_{ u}}{\mathcal{K}_{u}+1}}\mathbf{a}_{u}+\sqrt{\frac{1}{\mathcal{K}_{u}+1}}\mathbf{h}_{u}^{ \text{NLoS}}\bigg{)} \tag{3}\]  
where \(\beta_{0}\) is the path loss at the reference distance; \(d_{u}\) and \(\alpha_{u}\) denote the distance and path loss exponent between the UAV and \(u\)-th EHD, respectively. \(\mathbf{a}_{u}\in\mathbb{C}^{N\times 1}\) is the deterministic LoS component; \(\mathbf{h}_{u}^{\text{NLoS}}\in\mathbb{C}^{N\times 1}\) is the NLoS component distributed with \(\mathbf{h}_{u}^{\text{NLoS}}\sim\mathcal{CN}(\mathbf{0},\mathbf{I}_{N})\); \(\mathcal{K}_{u}\) denotes the Rician factor which reflects the power ratio of the LoS component and NLoS component. Assuming there is a uniform linear array (ULA) at the UAV, the LoS component is represented by  
\[\mathbf{a}_{u}=\big{[}1,e^{-2\pi\frac{d_{u}}{\mathcal{K}_{c}}\sin(\phi_{u})}, \ldots,e^{-2\pi(N-1)\frac{d_{u}}{\mathcal{K}_{c}}\sin(\phi_{u})}\big{]}^{T} \tag{4}\]  
Figure 1: Illustration of our system model. where \(\lambda_{c}\) is the carrier wavelength, \(d_{a}\) is the space between adjacent antennas, and \(\phi_{u}\) is the angle of departure (AoD) [30; 31; 14]. Since the propagation characteristics of the A2G channel, such as obstacle density and link quality, are affected by the altitude of the UAV [8; 9; 10; 11; 12; 13], we model not only the probability of a link having a LoS component but also the values of the path loss exponent and Rician factor as a function of UAV altitude, as follows. First, the distance and elevation angle (in radians) between the UAV and \(u\)-th EHD are respectively given by  
\[d_{u} =\sqrt{r_{u}^{2}+h^{2}}, \tag{5}\] \[\theta_{u} =\arctan\Big{(}\frac{h}{r_{u}}\Big{)}. \tag{6}\]  
Then, the LoS probability can be modeled as a function of the elevation angle [11; 12; 13; 14]:  
\[P_{\text{LoS}}(\theta_{u})=\frac{1}{1+a_{1}\exp\Big{(}-b_{1}\big{(}\frac{180} {\pi}\theta_{u}-a_{1}\big{)}\Big{)}} \tag{7}\]  
where \(a_{1}\) and \(b_{1}\) are positive parameters that are determined by environmental characteristics, i.e., suburban, urban, dense urban, and highrise urban [8; 9; 10]. The value of the path loss exponent is typically proportional to the LoS probability, so \(\alpha_{u}\) can be modeled as [11; 12; 13; 14]  
\[\alpha_{u}=a_{2}P_{\text{LoS}}(\theta_{u})+b_{2}. \tag{8}\]  
In (8), the coefficients of \(a_{2}\) and \(b_{2}\) are given by  
\[a_{2} =\big{(}\alpha_{\frac{\pi}{2}}-\alpha_{0}\big{)}\frac{1+a_{1} \exp(a_{1}b_{1})}{a_{1}\exp(a_{1}b_{1})} \tag{9}\] \[b_{2} =\alpha_{0}-\frac{a_{2}}{1+a_{1}\exp(a_{1}b_{1})} \tag{10}\]  
where \(\alpha_{0}\) and \(\alpha_{\frac{\pi}{2}}\) are the path loss exponents of the ground and aerial links, which are determined through measurement [10; 11; 12]. Here, \(a_{2}<0\) and \(b_{2}>0\), and \(a_{2}\cong\alpha_{\frac{\pi}{2}}-\alpha_{0}\) and \(b_{2}\cong\alpha_{0}\), where the approximations come from \(P_{\text{LoS}}(0)\to 0\) and \(P_{\text{LoS}}\big{(}\frac{\pi}{2}\big{)}\to 1\). In addition, with respect to \(\theta_{u}\), \(\alpha_{u}\) is a monotonic function decreasing from \(\alpha_{0}\) to \(\alpha_{\frac{\pi}{2}}\). In addition, the Rician factor depends on the LoS probability and is thus characterized by the elevation angle of the UAV.