# Wireless Energy Harvesting with Cooperative Relaying under the Best Relay Selection Scheme
## 5 Numerical Results  
In this section, numerical results are performed to validate the proposed theoretical analysis. \(N\)-wireless energy harvesting (WEH) relays are considered based on the BRS scheme. Numerical examples are investigated. System parameters are shown in Table 1. To study the relays location on the performance, normalized distances are applied. In the following, numerical results of outage probability for different WEH relaying are shown. In addition, the impact of using WEH relaying on the power splitting ratio, the distance between source and relays will be analyzed. The spectral efficiency and energy efficiency of EH-AF scheme is presented and compared with a different number of \(N\)-WEH relays. Finally, the comparison between conventional AF relaying and WEH-AF relaying is illustrated by understanding the trade-off between SE and EE. It is assumed that the relays are close to the source compared to the destination with normalized distances. Since the distance from the source to relay is increasing, the energy harvested and received signal power at the relay decreases due to the path loss. Figure 3 represents the effect of the power-splitting ratio on the SE for a single relay at 20 dB SNR. The maximum SE result is about 1.6 bits/s/Hz. Figure 3 illustrates the importance of optimizing the power-splitting ratio to achieve the best SE of the overall system using WEH relaying. When the splitting ratio is too small, only a limited amount of energy is harvested, and this can directly affect the SE performance. in contrast, when the splitting ratio is large, the energy harvested at the relay exceeds the required level, thereby decreasing the SE level. Figure 4 shows the outage probability corresponding to average SNR with different values of \(N\). When \(N\) increases, the outage probability is enhanced; for example, at 20 dB SNR, the outage probability for \(N=2\) is about \(10^{-4}\), versus about \(10^{-5}\) at \(N=5\). \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value** \\ \hline SNR threshold \(\Gamma^{th}\) & 5 dB \\ Energy conversion efficiency \(\eta\) & 0.6 \\ Path loss exponent \(n\) & 2 \\ Normalized distance from S to relay \(i\), \(d_{1}\) & 0.3 m \\ Normalized distanc from S to relay \(i\), \(d_{2}\) & 0.7 m \\ Normalized distanc from S to D \(d_{3}\) & 1 m \\ Maximum energy at the source \(E_{s}^{max}\) & 3 J \\ Maximum energy at the selected relay \(E_{i}^{max}\) & 3 J \\ Number of relays \(N\) & 2, 3, 5 \\ Bit error rate-target \(BERT\) & \(10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Parameters. Figure 3: Spectral Efficiency (SE) at 20 dB versus the power splitting ratio. Figure 5 shows the outage probability results with the PS ratio for different values of \(N\) under the 5 dB SNR threshold. A portion of the power that should be received at the destination is consumed at the EH relays. Thus, the signal level that is fed to the information processing decreases with the increase in PS, which decreases the outage probability. Figure 6 illustrates the outage probability with respect to the EH relays locations. The outage probability is constant with respect to relay locations. This occurs because at a high SNR, the outage probability becomes independent of the location of the relays. Figure 4: Outage probability versus signal to noise ratio (SNR) for EH relaying. Figure 5: Outage probability versus power splitting ratio (\(\bar{\gamma}=20\) dB, \(\Gamma^{th}=5\) dB). Figure 7 shows the SE for conventional (non-WEH) relaying and WEH relaying. Cooperative WEH relaying causes degradation in SE compared with the conventional CR. For example, at 20 dB SNR and \(N=2\), the SE for WEH relaying is approximately 1.3 bits/s/Hz; a loss of approximately 0.4 bits/s/Hz is observed compared with the conventional CR, which translates to a 23% degradation in SE. On the other hand, increasing the number of relays enhances SE for both conventional and WEH-AF relays.