# Social-Aware Peer Selection for Device-to-Device Communications in Dense Small-Cell Networks
## 5 Simulations and Numerical Results
### Best Peer Selection  
Figures 6-8 illustrate the peer selection mechanism of the proposed scheme based on social, physical, and combined attributes, respectively. In this scenario, we maintained \(m\) as a constant (i.e., five) and run the algorithm for 10 iterations. For the results in Figure 6, we took into account the social attributes of DUEs only. We applied the algorithm formulated in Section 4.1 to compute the closeness coefficient for social attributes (i.e., \(\delta_{s}\)). We ranked the DUEs based on the value \(\delta_{s}\) and selected the best one as D2D peer. It was clear that, in each iteration, the UE with the maximum value of \(\delta_{s}\) was selected as marked with a blue circle in the figure.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Network & Small- and macro-cell \\ \hline \(m\) & 5 to 50 \\ \hline Carrier frequency & 2 GHz [25] \\ \hline Small-cell radius & 100 m [24] \\ \hline Macro-cell radius & 1000 m \\ \hline \(Q\) & 3 \\ \hline \(d_{th}\) & 50 m [26] \\ \hline \(\beta\) & 3 [1] \\ \hline \(SFI\) & 0 to 1 [17] \\ \hline \(N\) & 1 to 20 [24] \\ \hline \(T_{Tx}\) & 1 to 20 s [20] \\ \hline \(\Gamma\) & 20 s [24] \\ \hline \(\tau\) & 0.01 s [20] \\ \hline \(\varepsilon\varepsilon_{Init}\) & 1 Kbps/W [21] \\ \hline \(P_{cht}\) & 0.01 W [21] \\ \hline UE \(P_{(Tx)}\) & 23 dBm [26] \\ \hline SCBS \(P_{(Tx)}\) & 40 dBm [25] \\ \hline MCBS \(P_{(Tx)}\) & 46 dBm [26] \\ \hline Fading & Rayleigh flat fading [13] \\ \hline Number of experiments & 50 \\ \hline User distribution & Uniform \\ \hline \hline \end{tabular}
\end{table}
Table 3: Simulation Parameters.  
Figure 5: Computation time comparison of the proposed scheme with the Hungarian algorithm vs. \(m\).  
Figure 6: Selection of UE with the best \(\delta_{s}\) values.  
Figure 7: Selection of UE with the best \(\delta_{p}\) values.  
Similarly, for the results in Figure 7, we only took into account the physical attributes of the DUEs. We followed the same procedure to compute the closeness coefficient for physical attributes (i.e., \(\delta_{p}\)). We ranked the DUEs based on the value \(\delta_{p}\) and selected the best one as the D2D peer. It was clear that, in each iteration, the UE with the maximum value of \(\delta_{p}\), was selected as marked with a blue circle in the figure.  
Figure 8 shows the D2D peer selection based on the combined social and physical attributes. It can be observed that in each iteration, DUE with a maximum \(\Delta\) was selected for the D2D communication. As \(\Delta\) is obtained from the summation of \(\delta_{s}\) and \(\delta_{p}\), whose values lie between 0 and 1, the value of \(\Delta\) exceeded 1 in most of the cases. Moreover, the social and physical parameters had different impacts on the performance of D2D communications. Therefore, a DUE could have had the maximum value of \(\delta_{p}\) but was not selected as the best D2D peer because the value of \(\delta_{s}\) was smaller, and vice versa. This phenomenon was observed in the 5 th iteration, where UE5 was selected based on the highest value of \(\delta_{s}\) and UE2 was selected based on the highest value of \(\delta_{p}\) in Figures 6 and 7, respectively. However, the value of \(\Delta\) was maximum for UE1. Therefore, it was selected as the final best D2D peer. The maximum value of \(\Delta\) led to higher \(\gamma\), \(R\), and eventually the best \(\mathfrak{I}\).