# A Deep Learning Approach for Maximum Activity Links in D2D Communications
## 3 System Model  
We considered that D2D communications occur within a single cell of a cellular system and share the system's downlink resources. In this scenario, a cellular device may suffer interference phenomena introduced by D2D communication activities. D2D transmitters can also interfere with the eNB. Due to the strong interference management capability of the eNB, it is necessary to schedule links in order to allow downlink connectivity for cellular device communications. In the proposed system model, D2D devices are randomly distributed under the coverage of the same eNB. As shown in Figure 1, the heterogeneous network consists of a single eNB for serving cellular devices and \(M\) D2D-capable devices. Let \(V=\{V_{1},V_{2},\cdots,V_{M}\}\) denote the set of D2D users in the network. To make full use of available spectrum resources, we allowed multiple D2D devices to simultaneously use the same downlink channel of cellular devices. Two D2D devices (a D2D pair) can establish no more than a direct communication. According to the SINR model, the SINR involving a single D2D sender-receiver pair \((i,j)(i,j\in V)\) in the presence of a cellular device \(C\) connected to an eNB operating in the same cell is:  
\[SINR_{D}=\frac{P_{i}g_{ij}}{P_{B}g_{C}+\eta} \tag{1}\]where \(\mathbf{P_{i}}\) is the transmit power characterizing the D2D sender \(i\), \(g_{ij}\) denotes the propagation attenuation (link gain) modeled as \(g_{ij}=d_{ij}{}^{-\alpha}\) (\(d_{ij}\) denotes the distance between D2D pair and \(\alpha\geq 1\) is a constant path-loss exponent), \(\mathbf{P_{B}}\) is the transmission power of the eNB, \(g_{C}\) is the gain of a cellular device \(C\) connected to the eNB concurrent to \(i\), and \(\mathbf{\eta}\) is the ambient noise. Clearly, the signal power transmitted by the eNB to \(C\) is perceived at \(i\) as interference. Let \(\gamma_{C}\) and \(\gamma_{D}\) denote the minimum SINR threshold of the cellular device and D2D device, respectively. If the condition \(\mathbf{\dot{SIN}_{D}}\geq\gamma_{D}\) is held, the D2D receiver \(j\) successfully receives a message from D2D sender \(i\) (the D2D pair of devices communicate successfully). We denote the set of \(N\) pairs \(A\) that are able to successfully perform D2D communication as \(A=\{A_{1},A_{2},\cdots,A_{N}\}\). The notation used in this paper is shown in Table 1.  
There are four conditions in the model: (1) Any D2D terminal device can communicate with another within the same cell; (2) a node can be a sender or receiver, but a node can send to at most one receiver or receive from at most one sender; (3) the D2D receiving user can estimate the link state information (channel state information, CSI) according to the received signal; and (4) the eNB controls channel resource allocation in a centralized way.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Meaning** \\ \hline \(V\) & Sets of D2 Ds \\ \(A\) & Sets of D2D pairs \\ \(C\) & Cellular user \\ \(\eta\) & Ambient noise \\ \(\alpha\) & Path-loss exponent \\ \(P_{i}\) & Transmit power of D2D \(i\) \\ \(P_{B}\) & Transmit power of the eNB \\ \(P_{C}\) & Transmit power of cellular user \\ \(g_{ij}\) & Channel gain between two D2D (\(i\) and \(j\)) \\ \(g_{C}\) & Channel gain between the eNB to cellular user \\ \(d_{ij}\) & Transmission distance of two D2D (i and \(j\)) \\ \(d_{iC}\) & Transmission distance between D2D i to cellular user \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of notation.  
Figure 1: System model.