# A Novel Multi-Cell Interference-Aware Cooperative QoS-Based NOMA Group D2D System
## 2 System Model  
Consider multi-cell cooperative relaying in Q-NOMA-enabled D2D scenario shown in Figure 1. It is assumed that each group transmitter sends data to its clustered devices using NOMA and relay nodes (\(R_{e}\)s) are supposed to send data to the adjacent cells' group transmitters using OMA. In our case, the device connected to group transmitter one (\(G_{T_{1}}\)wants to transmit data to a device present in neighboring cell connected to its group transmitter \((G_{72})\). As such, under this particular setting, the entire communication is divided into two phases. \(G_{T_{1}}\) in Phase I is responsible for transmitting the NOMA signal to all the receivers (\(r_{x}\)) in its coverage area (any receiver would act as a \(R_{e}\) in Phase II). In Phase II, the relay nodes communicate to \((G_{72})\) of the concerned receiver using OMA transmission. The signal received at the \(i\)th relay in Phase I is written as:  
\[ \begin{split} y_{R_{e},i}&=h_{i,1}\sum_{m_{1}=1}^ {M_{1}+1}\sqrt{\beta_{m_{1}}P_{G_{T_{1}}}}S_{m_{1}}+n_{i,1}+I\\ i&=1,2,\cdots,M_{1}\end{split}  \tag{1}\]  
where \(h_{i,1}=\frac{\tilde{h}_{i,1}}{\sqrt{1+d_{1}^{n}}}\) denotes the channel between \(i\)th relay and \(G_{T_{1}}\) during Phase I, \(\tilde{h}_{i,1}\) is the Rayleigh fading channel gain, \(d_{i,1}\) is the distance of the \(i\)th relay to the \(G_{T_{1}}\), \(\alpha\) is the path loss factor, \(\beta_{m_{1}}\) is the power allocation coefficient, and \(S_{m_{1}}\) is the message signal of \(m_{1}\)th receiver. \(P_{G_{T_{1}}}\) denotes the transmission power of \(G_{T_{1}}\), \(I\) is the interference, and \(n_{i,1}\) is the additive white Gaussian noise (AWGN) with zero mean and variance \(\sigma^{2}\). Any number of \(r_{x}\) near the cell edge can act as a D2D \(R_{e}\) and forward the desired data to \(G_{T_{2}}\) (group transmitter in Phase II). The relays receive \(M_{1}+1\) data streams multiplexed using NOMA and decode two data signals, one data stream being its own signal and the second stream the data that needs to be relayed \((S_{R_{e}})\). In Phase II, each \(R_{e}\) will transmit the decoded data to \(G_{T_{2}}\). The \(G_{T_{2}}\) will employ MRC and transmits the data to \(R_{x}\) using NOMA as follows:  
\[ \begin{split}\begin{bmatrix}y_{2,1}\\ \vdots\\ y_{2,i}\end{bmatrix}^{T}&=\begin{bmatrix}h_{2,1}\\ \vdots\\ h_{2,i}\end{bmatrix}^{T}S_{R_{e}}P_{R_{e}}+\begin{bmatrix}n_{2,1}\\ \vdots\\ n_{2,i}\end{bmatrix}^{T}\\ \hat{g}_{G_{T_{2}}}&=\Pi S_{R_{e}}P_{R_{e}}+\bar{n}\end{split}  \tag{2}\]  
where \(i=\{1,2,\cdots,M_{1}\}\), \(y_{2,i}\) represents the received signal at a \(G_{T_{2}}\) transmitted from \(i\)th relay, \(h_{2,i}\) and \(n_{2,i}\) are the Rayleigh fading channel gain and AWGN between \(i\)th relay and \(G_{T_{2}}\), respectively. For simplicity, we assumed that every relay transmits signal with power \(P_{R_{e}}\). After MRC, the received signal at \(G_{T_{2}}\) can be written as:  
\[ \begin{split} y_{G_{T_{2}}}&=\frac{\mathbb{H}^{H}S_{R_{e }}P_{R_{e}}+\mathbb{H}^{H}\bar{n}}{||\mathbb{H}||}\\ &=||\mathbb{H}||S_{R_{e}}P_{R_{e}}+\frac{\mathbb{H}^{H}\bar{n}}{|| \mathbb{H}||}\end{split}  \tag{3}\]  
\(G_{T_{2}}\) is responsible for delivering the message signal to all \(r_{x}\) in its cell. The received signal at \(R_{x}\) can be denoted by \(y_{R_{e}}\) and is written as:  
\[y_{R_{x}}=h_{R_{x},2}\sum_{m_{2}=1}^{M_{2}}\sqrt{\beta_{m_{2}}P_{G_{T_{2}}}}S_ {m_{2}}+n_{R_{x},2} \tag{4}\]  
After SIC, the desired signal at \(R_{x}\) can be written as follows:  
\[ \begin{split} y_{R_{x}}&=h_{R_{x},2}\bigg{(}\sqrt{ \beta_{R_{x}}P_{G_{T_{2}}}}||\mathbb{H}||S_{R_{e}}P_{R_{e}}+\frac{\mathbb{H}^{H }\bar{n}}{||\mathbb{H}||}\bigg{)}+n_{R_{x},2}\\ &=h_{R_{x},2}\bigg{(}\sqrt{\beta_{R_{x}}P_{G_{T_{2}}}}||\mathbb{H }||S_{R_{e}}P_{R_{e}})\bigg{)}+\aleph^{2}\end{split}  \tag{5}\]Here, \(\aleph=\sqrt{h_{s_{2},s}\sqrt{\beta_{x},P_{G_{T_{2}}}\left[\frac{\mathbf{H}^{H}_{R} }{||\mathbf{H}||}\right]}+n_{s_{2},2}}\).