# Machine Learning-Based Methods for Enhancement of UAV-NOMA and D2D Cooperative Networks
## 2 System Model
### Achievable Rates Analysis  
As the SINR expressions of the strong GMT\({}_{i}\) and the weak GMT\({}_{j}\) for each pair \(k\) have been determined, it is straightforward to compute the corresponding achievable rates. The theoretical achievable rate of each GMT\({}_{l}\), when we consider a conventional UAV-OMA transmission scheme, can be mathematically expressed as:  
\[R_{l}^{o}=\frac{B_{u}}{2K}\log_{2}(1+P_{u}\Gamma_{l}^{u}), \tag{15}\]  
In contrast, in the case of a UAV-NOMA scheme, the maximum downlink NOMA achievable rates which succeed by the strong GMT\({}_{i}\) and the weak GMT\({}_{j}\) through the A2G channel are:  
\[R_{i}^{u}=\frac{B_{u}}{K}\log_{2}(1+\gamma_{i}^{u}), \tag{16}\]  
\[R_{j}^{u}=\frac{B_{u}}{K}\log_{2}\Bigl{(}1+\gamma_{j}^{u}\Bigr{)}, \tag{17}\]respectively. Moreover, for the strong GMT\({}_{i}\), the achievable rate of the weak GMT\({}_{j}\)'s signal is equal to:  
\[R_{k}^{u}=\frac{B_{u}}{K}\log_{2}(1+\gamma_{k}^{u}). \tag{18}\]  
Also, the maximum achievable rate \(R_{k}^{d}\) concerning the established D2D link between the strong user GMT\({}_{i}\) and the weak user GMT\({}_{j}\) is expressed as:  
\[R_{k}^{d}=\frac{B_{d}}{K}\log_{2}\Bigl{(}1+\gamma_{k}^{d}\Bigr{)}, \tag{19}\]  
Since the weak GMT\({}_{j}\) can receive its signal directly from the UFBS or via the strong GMT\({}_{i}\) of the pair it belongs to utilizing the D2D communication capabilities, GMT\({}_{j}\)'s device always chooses to be served by the link that offers the highest achievable rate. Thus, it holds that the maximum achievable rate of each weak GMT\({}_{j}\) that belongs to the NOMA pair \(k\), combining the UAV-NOMA with cooperative D2D scheme, can be calculated as follows:  
\[R_{j}^{\text{COPD2D}}=\max\Bigl{(}R_{j}^{u},\Lambda_{j}\Bigr{)}, \tag{20}\]  
where \(\Lambda_{j}\) is the achievable rate through the D2D communication with the strong GMT\({}_{i}\). In fact, the weak GMT\({}_{j}\)'s signal is decoded on the strong GMT\({}_{i}\), and the D2D communication provides the channel to forward this decoded signal from the strong GMT\({}_{i}\) to the weak GMT\({}_{j}\). As a result, the weak GMT\({}_{j}\) can never receive a rate greater than \(R_{k}^{u}\), meaning that \(\Lambda_{j}\leq R_{k}^{u}\). Essentially, the quality of the D2D communication will determine whether the weak GMT\({}_{j}\) will enjoy the maximum possible rate \(R_{k}^{u}\) or less. Specifically, we can recognize the following cases:  
**Case 1.**_The D2D channel is profitable for the weak user, i.e., \(R_{k}^{d}\geq R_{k}^{u}\), and the achievable rate of the weak user is \(\Lambda_{j}=R_{k}^{u}\). This happens because the weak user can never receive a rate greater than the achievable decoding rate of its signal on the strong user._  
**Case 2.**_The D2D channel is not profitable for the weak user, i.e., \(R_{k}^{d}<R_{k}^{u}\), and the achievable rate of the weak user is equal to the transmission rate that the D2D communication can provide, i.e., \(\Lambda_{j}=R_{k}^{d}\). In this case, we observe that the achievable rate of the weak user is limited based on the capabilities of the D2D communication channel._  
Based on the above cases concerning the use of D2D communication for receiving the signal on the weak user, we observe that the minimum rate between the achievable rates \(R_{k}^{d}\) and \(R_{k}^{u}\) is always selected. Therefore, in the case where D2D communication is used, it follows that the achievable rate of the weak user is equal to \(\Lambda_{j}=\min\Bigl{(}R_{k}^{u},R_{k}^{d}\Bigr{)}\). By substituting \(\Lambda_{j}\) in (20):  
\[R_{j}^{\text{COPD2D}}=\max\Bigl{(}R_{j}^{u},\min\Bigl{(}R_{k}^{u},R_{k}^{d} \Bigr{)}\Bigr{)}. \tag{21}\]  
Utilizing the UAV-NOMA and D2D-aided scheme the total sum rate which is succeeded on each pair \(k\) is equal to:  
\[R_{k}=R_{i}^{u}+R_{j}^{\text{COPD2D}}. \tag{22}\]  
Therefore, the total system sum rate that can be achieved by utilizing the aforementioned cooperative scheme is:  
\[R_{s}=\sum_{k=1}^{K}R_{k} \tag{23}\]