# Social-Aware Relay Selection for Cooperative Multicast Device-to-Device Communications
## 4 Numerical Results  
In this section, we provide numerical results concerning the performance of the proposed D2D multicast social relaying method. In the considered scenario, a single D2D source device with \(R_{j}\) neighbor relay devices, where \(j=1...N\), and \(D_{i}\) destination devices, where \(i=1...M\), are located in a single cell with radius \(C\), which guarantees a reserved channel for the control communications among these devices. Destination devices are distributed in a restricted area to form a cluster with radius \(r\) and \(0\leq r\leq C\). Within the D2D multicast area, the \(i\)th device is at the location \((d_{i},\theta_{i})\) with \(-r\leq d_{i}\leq r\) and \(0\leq\theta_{i}\leq 2\pi\), and the distance between two nodes is defined as \(d_{j,i}=\sqrt{d_{j}^{2}+d_{i}^{2}-2d_{j}d_{i}cos(\theta_{j}-\theta_{i})}\). We assume that the distance between the source and the destinations is larger than the distance between any two devices in the multicast group and among the relay and devices and is heavily attenuated because of obstacles, building, and so on. Therefore, the direct link between the source and the destinations does not exist, and communications can be established only via relay. We consider a transmission channel model often assumed in literature [17], including both the large scale path loss, shadowing variations and zero-mean AWGN. We assume the frequency of non-selective Rayleigh block fading according to a complex Gaussian distribution with zero mean and variance \(\sigma_{j,i}^{2}\) for the \(i\)th to \(j\)th link, that is, constant during one transmission period and changing independently from one period to another. The channel gains \(|h_{j,i}|^{2}\) are exponentially distributed, as in [17; 10]. The average SNR for the signal received by a generic D2D destination device from the D2D source device is defined as \(\gamma_{SD}\), and the standard deviation is defined as \(\sigma_{sd}^{2}\). To simulate an urban environment, we set the \(\gamma_{SD}\) value in the region of 0 dB. This choice considers that the direct path has a heavier attenuation, as a result, for example, of obstacles, buildings, and so on, in a generic real multicast D2D communication scenario. The average SNR for the signal received by a D2D destination device from one of the D2D relays is defined as \(\gamma_{RD}\), and the average SNR for the signal received by a generic \(j\)th D2D relay from the D2D source device is \(\gamma_{SR}\). Table 1 shows the values of the main parameters. The value of \(\beta_{j}\), as described in the system model, varies depending of the friendship level. If the D2D relay has a friendship connection, it sets its \(\beta\) value equal to 1; instead, if it has no friendship connection, it reduces the value 10-fold. We suppose that each relay and the D2D source device have the complete knowledge of friendship relations and channel state in terms of the SNR. For a comparative perspective, the throughput normalized with respect to the throughput of direct source-destination transmissions, that is, without the use of relays, is shown in Figure 3 for the number of relays increasing. First, a comparison of the normalized throughput of our method with social and physical information with respect to the stopping approach [18] is shown in the top of Figure 3, for which the direct transmission is added to the source-relay transmission at the receiver, highlighting similar performance. \begin{table}
\begin{tabular}{l l} \hline \hline
**Bandwidth** & **10 MHz** \\ \hline Path-loss coefficient & 4 \\ Cell radius & 1 Km \\ Cluster radius & 0.03 Km \\ Number of destinations, \(M\) & 10 \\ Number of relays, \(N\) & 5:15 \\ \(\gamma_{SD}\) & 3 dB \\ \(\gamma_{RD}\) & 13-18 dB \\ Friendship probability & 20\% \\ \(\beta_{j}\) for a friend source & 1 \\ \(\beta_{j}\) for a non-friend source & 0.1 \\ \(\sigma_{sd}\) & 1 dB \\ \(\sigma_{rd}\) & 9 dB \\ User distribution & Uniform \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main Simulation Parameters.