## 2 Problem Statement
### Transmission Model  
Assume that the UAV hovers at a designated altitude to deliver services to users, denoted \(h\) meters. Within a given time duration, the UAV functions as a flying base station, employing frequency-division multiple access (FDMA) to provide users with content transmission and charging services. Additionally, to enhance system efficiency, NOMA technology is introduced among users, partitioning users within the coverage area into multiple NOMA user pairs. Consequently, we adopt a communication approach where NOMA is utilized within user pairs and FDMA is employed between user pairs.  
Assume that \(N_{m}\in\{N_{1},N_{2},\ldots,N_{M}\}\) is the number of users on channel \(m\), \(m=1,2,\ldots M\), the user \(n\) occupying channel \(m\) is denoted \(UE_{n,m}\), where \(n=1,2,\ldots,N_{M}\), and thus the total bandwidth \(B\) is divided equally into \(M\) channels to provide communication services for \(M\) user pairs, respectively, and the bandwidth of each channel is denoted \(B_{c}=B/M\). In the scenario where each NOMA pair consists of two users, denoted \(N_{m}=2\), the magnitude of the relationship of channel gains for users \(UE_{1,m}\) and \(UE_{2,m}\) utilizing channel \(m\) is represented by \(\left|h_{1,m}\right|^{2}\geq\left|h_{2,m}\right|^{2}\), along with the corresponding magnitude of the relationship of signal transmit powers \(p_{1,m}\leq p_{2,m}\). Due to the implementation of successive interference cancellation (SIC), the SINR of \(UE_{n,m}\) can be represented as \(r_{n,m}=\frac{p_{n,m}\left|h_{n,m}\right|^{2}}{\frac{\rho_{n}^{2}}{\rho_{n}^{2} +\sum_{i=1}^{n}P_{i,m}\left|h_{n,m}\right|^{2}}}\). By normalizing the channel gain \(\left|h_{n,m}\right|^{2}\) by the noise power \(\delta_{m}^{2}\), i.e., setting \(T_{n,m}=\frac{\left|h_{n,m}\right|^{2}}{\delta_{m}^{2}}\), the SINRs of \(UE_{1,m}\) and \(UE_{2,m}\) are given by \(r_{1,m}=p_{1,m}\Gamma_{1,m}\) and \(r_{2,m}=\frac{p_{2,m}\Gamma_{2,m}}{1+p_{1,m}\Gamma_{2,m}}\), respectively.  
According to [PERSON]'s theorem, the information rates of users \(UE_{1,m}\) and \(UE_{2,m}\) on channel \(m\) can be expressed as follows:  
\[R_{1,m}=B_{c}\log(1+p_{1,m}\Gamma_{1,m}) \tag{7}\]  
\[R_{2,m}=B_{c}\log(1+\frac{p_{2,m}\Gamma_{2,m}}{1+p_{1,m}\Gamma_{2,m}}) \tag{8}\]  
To address the challenge of limited energy supply for mobile terminals, WPT technology is introduced. By maneuvering the UAV proximally to users, establishing \(LoS\) links with ground users, and deploying radio frequency (RF) energy transmitters on the UAV, RF signal energy can be transferred to devices to meet the energy supply demands of devices with constrained energy requirements. Therefore, the energy consumption of a UAV providing services to users can be expressed as follows:  
\[E_{\text{uav}}=E_{trans}+E_{char} \tag{9}\]  
where \(E_{trans}\) is the energy consumption of the transmission service for the UAV, denoted \(E_{trans}=\sum\limits_{m=1}^{M}\sum\limits_{n=1}^{N_{m}}p_{n,m}\tau_{n,m}\), and \(\tau_{n,m}\) is the delay for user \(UE_{n,m}\) on channel \(m\) to receive the requested file. \(E_{char}\) is the energy consumption of the charging service provided by the UAV, denoted \(E_{char}=P_{char}(1-\mu)T\), \(P_{char}\) is the RF power for charging the UAV, and in cases of all users requesting the file at the same time, the total transmission delay \(\mu T\) on \(M\) channels can be denoted \(\mu T=\max\limits_{m=1,\dots,M}\{\tau_{1,m},\tau_{2,m}\}\). Therefore, the energy consumption incurred by the UAV while providing services to users can be precisely delineated as follows:  
\[E_{\text{uav}}=\sum_{m=1}^{M}\sum_{n=1}^{N_{m}}p_{n,m}\tau_{n,m}+P_{char}\bigg{(} T-\max\limits_{m=1,\dots,M}\{\tau_{1,m},\tau_{2,m}\}\bigg{)} \tag{10}\]