# NOMA-Based Rate Optimization for Multi-UAV-Assisted D2D Communication Networks
## 2 System Model
### Communication Model  
As analyzed in Figure 1, the following interferences exist under the UAV-assisted D2D-NOMA system: (1) inter-group interference: interference from D2D transmitters in D2D groups that reuse the same subchannels; (2) intra-group interference: interference from superimposed signals to another receiver in the same D2D group; and (3) cellular interference: interference from cellular users that reuse the same subchannels. Therefore, UAV \(u\) receives a signal on subchannel \(S_{i}\in\mathcal{S}_{u}\) denoted as  
\[y_{i}^{u}=\sqrt{P_{i}^{u}}g_{i}^{u}x_{i}^{u}+\sum_{D_{j}\in\mathcal{D}_{u}}I_{i, DT_{j}}^{u}\sqrt{P_{i,D_{j}}^{u}}x_{i,DT_{j}}^{u}g_{i,DT_{j}}^{u}+\eta \tag{11}\]  
where \(P_{i}^{u}\) and \(P_{i,D_{j}}^{u}\) are denoted as the transmit power of cellular user \(C_{i}\) and D2D cluster \(D_{j}\), respectively, \(\mathcal{D}_{u}\in\mathcal{D}\) denotes the set of D2D clusters in the coverage area of UAV \(u\), and \(\eta\) is an additive Gaussian white noise with mean 0 and variance \(\sigma^{2}\). \(x_{i}^{u}\) denotes the signal of the cellular user, and \(x_{i,DT_{j}}^{u}\) is the superimposed signal of \(DT_{j}\), which can be represented by Equation (12):  
\[x_{i,DT_{j}}^{u}=\sqrt{a_{i,DR_{j,1}}^{u}}x_{i,DR_{j,1}}^{u}+\sqrt{a_{i,DR_{j,2 }}^{u}}x_{i,DR_{j,2}}^{u} \tag{12}\]  
where \(a_{i,DR_{j,1}}^{u}\) and \(a_{i,DR_{j,2}}^{u}\) denote the power allocation coefficients of the D2D receivers \(DR_{j,1}\) and \(DR_{j,2}\), respectively, and the relationship between them is \(a_{i,DR_{j,1}}^{u}+a_{i,DR_{j,2}}^{u}\leq 1\). \(x_{i,DR_{j,1}}^{u}\) and \(x_{i,DR_{j,2}}^{u}\) denote the signals of \(DR_{j,1}\) and \(DR_{j,2}\), respectively. In addition, \(I_{i,DT_{j}}^{u}\) is a binary decision variable:  
\[I_{i,DT_{j}}^{u}= \begin{cases}1,&D_{j}\in\mathcal{D}_{u}\text{ occupies }C_{i}\in\mathcal{C}_{u}\text{ channel resources},\\ 0,&\text{otherwise}.\end{cases}  \tag{13}\]  
A D2D cluster can only occupy at most one cellular user channel resource among all UAV BTSs, i.e., there is \(\sum_{u\in\mathcal{U}}\sum_{C_{i}\in\mathcal{C}_{u}}I_{i,DT_{j}}^{u}\leq 1\). In addition, the maximum number of D2D clusters associated with UAV \(u\) must satisfy \(\sum_{C_{i}\in\mathcal{C}_{u}}\sum_{D_{j}\in\mathcal{D}_{u}}I_{i,DT_{j}}^{u} \leq\xi_{u}\). Finally, the total transmit power of each channel \(S_{i}\in\mathcal{S}_{u}\) of each UAV \(u\) must not exceed \(P\) and must satisfy the total power constraint on each channel, andthere is \(P_{i}^{u}+\sum_{D_{j}\in\mathcal{D}_{u}}I_{i,DT_{j}}^{u}P_{i,D_{j}}^{u}\leq P\). Based on Equation (11), the signal-to-interference-plus-noise ratio (SINR) at UAV \(u\) corresponding to the received signal at \(C_{i}\) is  
\[r_{i}^{u}=\frac{P_{i}^{u}\left|g_{i}^{u}\right|^{2}}{\sum_{D_{j}\in\mathcal{D} _{u}}I_{i,DT_{j}}^{u}P_{i,D_{j}}^{u}\left|g_{i,DT_{j}}^{u}\right|^{2}+\sigma^ {2}} \tag{14}\]  
D2D receiver \(DR_{j,n}(n=1,2)\) receives the signal on subchannel \(S_{i}\in\mathcal{S}_{u}\), denoted as  
\[y_{i,DR_{j,n}}^{u}=\sqrt{P_{i,D}^{u}}x_{i,DT_{j}}^{u}g_{i,DT_{j},DR_{j,n}}^{u} +\sqrt{P_{i}^{u}}x_{i}^{u}g_{i,DR_{j,n}}^{u}+\eta \tag{15}\]  
Based on the principle of NOMA, the intra-group interference will be eliminated at the receiver side according to the SIC technique, where the strong users are assigned low power and the weak users are assigned high power in the superposition coding so that the weak users are less interfered with by the strong users and can demodulate their own signals on their own, whereas the strong users need to remove the signals of the weak users and then demodulate their own signals through the SIC technique.