# Sum Rate Optimization Scheme of UAV-Assisted NOMA under Hardware Impairments
## 2 System Model and Problem Formulation  
The NOMA-based UAV communication model with HIs is shown in Figure 1. We consider a UAV half-duplex relaying NOMA networks consisting of a BS and a rotor-wing UAV work in the amplify-and-forward (AF) mode, which assists data transmission from BS to downlink users. All communication nodes are equipped with a single antenna. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Objective** & **HIs** & **Model** & **UAV Relay** & **Article** \\ \hline Sum Rate & \(\times\) & Los & \(\times\) & [9] \\ Performance Analysis & \(\times\) & Rician & ✓ & [13] \\ Sum Rate & \(\times\) & Los & \(\times\) & [14] \\ Achievable Rate & \(\times\) & LoS & \(\times\) & [15] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the related UAV’s works. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Objective** & **HIs** & **Model** & **UAV Relay** & **Article** \\ \hline Max-min Rate & \(\times\) & Rician & \(\times\) & [16] \\ Sum Rate & \(\times\) & LoS & \(\times\) & [17] \\ Total Transmit Energy & \(\times\) & Los & ✓ & [19] \\ Energy Efficiency & \(\times\) & LoS\&NLoS & \(\times\) & [20] \\ Performance Analysis & ✓ & Nakagami-m & ✓ & [23] \\ Performance Analysis & ✓ & Nakagami-m & ✓ & [25] \\ Max-min Rate & ✓ & LoS\&NLoS & ✓ & [26] \\ Average Request Delay & \(\times\) & LoS\&NLoS & \(\times\) & [10] \\ Max-min Rate & \(\times\) & LoS & ✓ & [11] \\ Coverage probability & \(\times\) & LoS\&NLoS & \(\times\) & [12] \\ Sum rate & ✓ & LoS & ✓ & This Work \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._The ground users \(U_{n}\), \(n\in\{1,2,\ldots,N\}\) are located at \(\mathbf{I}_{n}=\left[\mathbf{w}_{n}{}^{T},0\right]^{T}\), where the horizontal coordinates are represented by \(\mathbf{w}_{n}=[x_{n},y_{n}]^{T}\). The coordination of BS is \(\mathbf{I}_{BS}=\left[\mathbf{w}_{s}{}^{T},0\right]^{T}\); similarly, \(\mathbf{w}_{s}=[x_{s},y_{s}]^{T}\). The UAV flies on the horizontal plane at a fixed height \(H\). \(\mathbf{I}_{r}=\left[\mathbf{w}_{r}{}^{T},H\right]^{T}\) denotes the horizontal coordinate of UAV, where \(\mathbf{w}_{r}=[x,y]^{T}\). According to the 3 GPP report, the LoS probability is nearly 100% when the drone is above 100\(m\) height from the ground in the urban macro scenario [27,28]. Thus, a free-space path loss model is considered between the UAV and ground users due to channels being dominated by line-of-sight (LoS) links. Note that this model has been adopted in recent literature such as [29,30]. Hence, the channel gain can be modeled as:  
\[h_{sr}=\sqrt{\beta_{0}d_{sr}^{-2}}=\sqrt{\frac{\beta_{0}}{H^{2}+(x-x_{s})^{2}+ (y-y_{s})^{2}}}, \tag{1}\]  
\[h_{rn}=\sqrt{\beta_{0}d_{rn}^{-2}}=\sqrt{\frac{\beta_{0}}{H^{2}+(x-x_{n})^{2}+ (y-y_{n})^{2}}}, \tag{2}\]  
where \(h_{sr}\) and \(h_{rn}\) are the channel coefficients between BS to UAV and UAV to the user \(n\) respectively; \(\beta_{0}\) denotes the channel gain at the reference distance, \(d_{sr}\) and \(d_{rn}\) is the distance from BS to UAV and UAV to the user \(n\) respectively. The direct link between the base station and ground users is not considered to be due to a severe shadow effect or building block. The communication process is divided into a two-time slots. In the first slot, the BS sends a superimposed signal \(y=\sum_{n=1}^{N}\sqrt{p_{n}}\theta_{n}\) to UAV.