# Location-Based Relay Selection in Full-Duplex Random Relay Networks
## 5 Simulation Results  
This section evaluates the performance of an FDRRN based on the proposed relay selection algorithm under various conditions. In addition, we used MATLAB for all simulations in this section. Unless otherwise specified, the system parameters listed in Table 1 were used for the simulation. In the simulation, candidate relay nodes and interfering nodes were uniformly distributed according to their spatial densities within a cell with a radius of 300 m. In addition, a normalized transmission power of 1 was used for all transmitting nodes. For reliable FD transmission, a SIC level of approximately \(-110\) dB is required, so we set \(I_{SI}\) to \(-110\) dB [22]. Figure 2 depicts the potential relay locations for different residual SI values. As discussed in Remark 1, the potential relay location shifts closer to the transmitter as the residual SI increases. This is due to the fact that as the residual SI increases, the performance \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(\alpha\) & 4 & \(\tau\) & 3 \\ \hline \(\lambda_{1}\), \(\lambda_{2}\) & \(10^{-4}\) & \(\lambda_{\mathrm{R}}\) & \(10^{-3}\) \\ \hline \(D_{\mathbf{xy}}\) & \(10\) m & Cell radius & 300 m \\ \hline \(I_{SI}\) & \(-110\) dB & \(P_{\mathrm{I}}\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. of the first relay hop degrades. Consequently, to compensate for the degraded performance of the first hop, the potential relay location moves toward the transmitter. In other words, when the capability of SIC in the relay node is not reliable, it is desirable to select the relay node near the transmitter. Figure 3 illustrates the outage probability of an FDRRN as a function of the spatial density of the interference when the relay node positioned at the potential relay location \(\mathbf{x}_{t}^{*}\) is selected. The numerical and simulation results are represented by blue circles and red lines, respectively. As shown in the figure, the numerical results show a similar trend to the simulation results, with only a negligible difference. Moreover, we can see that as the spatial density of the interfering node at each relay hop increases, the overall performance of the FDRRN decreases due to increased interference. Figure 4 displays the outage probability of an FDRRN as a function of the density of the candidate relay nodes for different residual SI values. It can be observed that as the  
Figure 3: The outage probability of an FDRRN as a function of the spatial interference density, including both the numerical and simulation results. The spatial density of interference is the same for each relay hop, i.e., \(\lambda_{1}=\lambda_{2}\). Figure 2: The potential relay locations of an FDRRN as a function of the residual SI. The residual SI increases from \(-45\) dB to \(-110\) dB. residual SI increases, the outage probability increases. In Figure 4, we can also see that as the density of the relay nodes increases, the outage probability decreases. This is attributed to the fact as the number of candidate relay nodes increases, the probability of a relay node being positioned closer to the potential relay location also increases. Consequently, the selected relay node is more likely to provide reliable communication. Figure 5 shows the outage probability of an FDRRN for the proposed, _max-min_, and optimal relay selection algorithms at different densities of candidate relay nodes. We can observe the performance differences among the various relay selection algorithms. While the performance of the proposed algorithm is slightly degraded compared to the _max-min_ and optimal algorithms due to the limited information available for relay node selection, it is worth noting that the proposed algorithm still achieves comparable performance with reduced information. Figure 4: The outage probability of an FDRRN as a function of the density of the candidate relay nodes for different residual SI values, \(I_{SI}\).