## 2 The System and Channel Models for THz Band  
We consider a system model where the ground base station communicates with UAVs in the THz spectrum. According to the characteristics of the THz spectrum, UAVs closer to the base station can utilize a wider bandwidth, while those farther away have access to a narrower spectrum. In the single-user case, the quadrature amplitude modulation (QAM) strategy is applied to modulate the information for higher data rates. To characterize the UAV THz channel between the transmitter and receiver, we consider factors such as UAV mobility, altitude, and environmental interactions that are specific to UAV applications. UAVs are mobile and can operate at varying altitudes, which affects the channel characteristics, including path loss and Doppler shifts. Therefore, we include the path gain coefficient \(h_{l}\) in the UAV THz channel model. Beam misalignment, here noted by \(h_{p}\), is a critical issue in high-frequency communication, such as THz, due to the narrow beamwidths involved. Additionally, multipath fading \(h_{f}\) is a significant factor in UAV communication environments where reflections from buildings, the ground, and other obstacles can impact signal quality. By including these elements, we aim to present a more realistic and practical model of the UAV communication channel. Therefore, the total channel coefficient \(h\)[24; 30], is expressed as  
\[h=h_{l}h_{p}h_{f} \tag{1}\]  
where \(h_{l}\), \(h_{p}\), and \(h_{f}\) are the path gain coefficient, beam misalignment fading coefficient, and the multi-path fading coefficient, respectively. Specifically, the path loss gain \(h_{l}\) is calculated as [39]  
\[ \begin{split}& h_{l}=h_{s}h_{a}\\ &=\bigg{(}\frac{c}{4\pi fd}\bigg{)}^{2}G_{T}G_{R}\exp(-d(y_{1}(f, \mu)+y_{1}(f,\mu)+g(f,\mu)))\end{split}  \tag{2}\]  
where \(h_{s}\) refers to the free space spread gain coefficient caused by the attenuation experienced by the THz wave atmospheric propagation with the isotropic antenna. \(h_{a}\) denotes the absorption gain on the THz band, which is mainly caused by the water vapor molecules in the atmosphere. The parameter \(d\) is the distance between a single user and the base station. The transmit and receive antenna gains are represented by \(G_{T}\) and \(G_{R}\), respectively. The factor \(g(f,\mu)\) is an equalization factor. \(y_{1}(f,\mu)\), \(y_{2}(f,\mu)\) are the molecular absorption model at the two major absorption lines, one at about 325 GHz and second at 380 GHz. The parameters \(y_{1}\), \(y_{2}\), and \(g\) are calculated, respectively, as \(y_{1}(f,\mu^{\prime})=\frac{A(\mu^{\prime})}{B(\mu^{\prime})+\big{(}\frac{f}{ 100^{2}}-c_{1}\big{)}^{2}},y_{2}(f,\mu^{\prime})=\frac{C(\mu^{\prime})}{D(\mu^ {\prime})+\big{(}\frac{f}{100^{2}}-c_{2}\big{)}^{2}}\) and \(g(f,\mu^{\prime})=p_{1}f^{3}+p_{2}f^{2}+p_{3}f+p_{4}\). In \(y_{1}\), \(y_{2}\), and \(g\), \(\text{A}(\mu^{\prime})=0.2205\mu^{\prime}(0.1203\mu^{\prime}+0.0294)\), \(B(\mu^{\prime})=(0.4093\mu^{\prime}+0.0925)^{2}\), \(C(\mu^{\prime})=2.014\mu^{\prime}(0.1702\mu^{\prime}+0.0303)\), \(D(\mu^{\prime})=(0.537\mu^{\prime}+0.0956)^{2}\) with the volume of the mixing ratio of water vapor, \(\mu^{\prime}=\frac{p_{m}(T,p)}{p}\), where \(p_{w}(T,p)=w_{1}(w_{2}+w_{3})\exp(\frac{w_{1}T}{w_{3}+T})\), \(w_{1}=6.1121\), \(w_{2}=1.0007\), \(w_{3}=3.46\times 10^{-8}\), \(w_{4}=17.502\), \(w_{5}=240.97\), \(c_{1}=10.853\) cm\({}^{-1}\), \(c_{2}=12.664\) cm\({}^{-1}\), \(p_{1}=5.54\times 10^{-37}\) Hz\({}^{-3}\), \(p_{2}=-3.94\times 10^{-25}\) Hz\({}^{-2}\), \(p_{3}=9.06\times 10^{-14}\) Hz\({}^{-1}\)