## 2 System Model
### Covert Wireless Communication with UAV  
In this paper, we adopt the Cartesian coordinate system to describe the position, where the coordinates of U1, U2, and Willie are \(q_{j}=[x_{j},y_{j}],j=u_{1},u_{2},w\). In addition, the coordinates of the best position for UAV communication are \(q_{i}=[x_{i},y_{i}]\), and the altitude of UAV is denoted by \(H\), \(H_{\text{min}}\leq H\leq H_{\text{max}}\). Let \(h_{j},j\in\{u_{1},u_{2},w\}\) be the channel fading from the UAV to the users, where \(u_{1},u_{2}\), and \(w\) denote U1, U2, and Willie, respectively.  
The air-to-ground channel model between the UAV and the users is provided by 3 GPP specifications. Accordingly, the path loss depends on the line-of-sight (LOS) and non-line  
Figure 1: UAV-assisted covert communication system deployed in a hydropower plant consisting of several zones, denoted as Zone I, Zone II, Zone III, and Zone IV, where Zone I is used for production, Zone II for schedule, Zone III for management, and Zone IV for other aspects.  
of-sight (NLoS) links. For low-altitude UAVs and short-range LoS communication, the UAV-ground channels are mostly been dominated by the LoS link. For example, the authors of [22] proposed a secure communication scheme for the NOMA-based UAV-MEC system towards a flying eavesdropper. The channels are assumed to be well modeled by the quasi-static block fading LoS links and follow the distance-dependent path loss model. In addition, ref [23] proposed a UAV-assisted multi-user communication system based on NOMA, which uses the line of sight air-to-ground communication. Therefore, according to [18; 24], the communication between the UAV and a ground user is modeled as an LoS link, and thus we can obtain the expression  
\[h_{j}=\sqrt{\frac{\beta}{\left\|q_{i}-q_{j}\right\|^{2}+H^{2}}},j=u_{1},u_{2},w \tag{1}\]  
Since \(h_{w}\) is known to [PERSON], as additional power is received from the UAV, [PERSON] can determine that covert communications exist. To avoid being detected by [PERSON], the transmit power of the UAV is random. For the communication between UAV and U1, a random power transmission scheme is adopted, where the transmit power follows a uniform distribution over \(\left[0,P_{u_{1}}^{\max}\right]\). Accordingly, the probability density function of \(P_{u_{1}}\) is given in Equation (2)  
\[f_{P_{u_{1}}}(x)=\left\{\begin{array}{ll}\frac{1}{P_{u_{1}}},&\text{if }0\leq x \leq P_{u_{1}}^{\max},\\ 0,&\text{otherwise},\end{array}\right. \tag{2}\]  
where \(P_{u_{1}}^{\max}\) is the maximum transmit power of the UAV to U1.  
When the UAV transmits signals to U1 and U2, the received signals can be expressed as  
\[\mathbf{y}_{u_{1}}[k]=\sqrt{P_{u_{1}}}h_{u_{1}}\mathbf{x}_{u_{1}}[k]+\sqrt{P_{ u_{2}}}h_{u_{1}}\mathbf{x}_{u_{2}}[k]+\mathbf{n}_{u_{1}}[k], \tag{3}\]  
and  
\[\mathbf{y}_{u_{2}}[k]=\sqrt{P_{u_{1}}}h_{u_{2}}\mathbf{x}_{u_{1}}[k]+\sqrt{P_ {u_{2}}}h_{u_{2}}\mathbf{x}_{u_{2}}[k]+\mathbf{n}_{u_{2}}[k], \tag{4}\]  
where \(k=1,2,\ldots,N\), \(x[k]\) is denoted as the signal transmitted by the UAV in the \(k\)-th covert channel. \(P_{u_{1}}\) and \(P_{u_{2}}\) denote the transmit power of the UAV communicating with U1 and U2, respectively. \(\mathbf{n}[k]\) is the received Gaussian white noise with the variance, denoted by \(\sigma_{u_{1}}^{2}\), being 0. In the proposed CCS with NOMA, the transmission between the UAV and U1 can provide a cover for the covert transmission of U2. Since \(P_{u_{1}}>P_{u_{2}}\), by using the SIC decoder, we can express the received signal-to-interference plus noise ratio (SINR) of U1 as  
\[\gamma_{u_{1}}=\frac{P_{u_{1}}h_{u_{1}}^{2}}{P_{u_{1}}h_{u_{1}}^{2}+\sigma_{u _{1}}^{2}}. \tag{5}\]  
The received SINR of U2 is  
\[\gamma_{u_{2}}=\frac{P_{u_{2}}h_{u_{2}}^{2}}{\sigma_{u_{2}}^{2}}. \tag{6}\]  
Then, with the obtained channel model, we can analyze the performance of the system with finite LTMB.