## 4 Numerical Results and Discussion  
Like in previous studies [33; 34; 35; 36], we conducted Monte Carlo simulations to verify analytical expressions of the OP and EC of the proposed system in the above section. In addition, we investigated the effect of the primary system parameter on the system performance in terms of OP and EC. All other simulation parameters are listed in Table 1.  
Figure 3a,b plots the influence of P\({}_{s}\)/N\({}_{0}\) on the OP and EC of the proposed system. In Figure 3, the main parameters are as follows: K = 2, R = 0.5, and \(\rho\) = 0.2 and 0.6. In this figure, the OP of the case \(\rho\) = 0.2 and 06 and the maximum capacity are also proposed for comparison. It is observed that the simulation values of the OP match the values from the mathematical analysis. In connection with the effect of \(\rho\), the OP decreases, and EC increases as \(\rho\) varies from 0.2 to 0.6. When P\({}_{s}\)/N\({}_{0}\) increases from 0 to 20 dB, the OP decreases and EC significantly increases. Furthermore, the higher the value of \(\rho\) is, the faster the OP decreases and the EC increases. In addition, we can see that the OP and EC of the model system in the maximum capacity case are better in comparison with the other cases, with other values of \(\rho\). This can be observed based on the mathematical analysis in Equations (17) and (20). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Name** & **Values** \\ \hline \(\eta\) & Energy harvesting efficiency & 0.8 \\ \hline \(\lambda_{sr}\) & Mean of \(|h_{sr}|^{2}\) & 0.5 \\ \hline \(\lambda_{rd}\) & Mean of \(|h_{rd}|^{2}\) & 0.5 \\ \hline \(m_{\gamma_{1}}\) & Nakagami m-factor & 3 \\ \hline z & \(SNR\) threshold & 1 \\ \hline P\({}_{s}\)/N\({}_{0}\) & Source power to noise ratio & 0–20 dB \\ \hline R & Source rate & 0.5 bit/s/Hz \\ \hline K & Number of users & 1–6 \\ \hline m & Pathloss exponent & 3 \\ \hline \(d_{sr}=d_{i}\) &
\begin{tabular}{c} the distance of S-R link and \\ R-D link, respectively \\ \end{tabular} & 0.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 4a,b depicts the effect of P\({}_{\rm{s}}\)/N\({}_{0}\) on the OP and the EC. We set R = 0.5 bps, \(\rho\) = 0.5, and K = 1, 3, and 6 in Figure 4a and R = 0.5 bps, \(\rho\) = 0.5, and K = 1, 3, and 6, respectively. From Figure 4a, the OP decreases when P\({}_{\rm{s}}\)/N\({}_{0}\) increases from 0 to 20 dB, and OP decreases faster with a higher K. On the other hand, the EC increases significantly, while P\({}_{\rm{s}}\)/N\({}_{0}\) rises from 0 to 20 dB. Furthermore, the EC is higher with the higher K value. In all research results, the simulation and analytical results are the same. Moreover, Figure 5a,b plots the influence of the ratio P\({}_{\rm{s}}\)/N\({}_{0}\) on the OP and the EC of the model system. Here, the cases Ray-Ray, Naka-Ray in the non-maximize and maximize modes are compared with each other in the same system condition. In the simulation, we set the ratio P\({}_{\rm{s}}\)/N\({}_{0}\) increased from 0 to 20 dB, \(\rho\) = 0.2, and K = 2 for the OP and \(\rho\) = 0.4 and K = 3 for the EC, respectively. Figure 5a shows that the OP decreases faster in the Naka-Ray case with maximum capacity compared with other cases. In the same way, the EC increases faster in the Ray-Ray case with non-maximum capacity in Figure 5b. Here we can see that the system performance in the maximum capacity case is better than in the non-maximum capacity case. Furthermore, the simulation results agreed with the mathematical analysis of the above section. Figure 4: The outage probability (**a**) and ergodic capacity (**b**) versus P\({}_{\rm{s}}\)/N\({}_{0}\) while \(\rho\) = 0.5. Figure 3: The outage probability (**a**) and ergodic capacity (**b**) versus P\({}_{\rm{s}}\)/N\({}_{0}\) while K = 2. Figure 6 illustrates the OP versus the system factors \(\eta\). In this case, we set \(\mathrm{P_{s}/N_{0}}=10\) dB, \(\rho=0.3\), and K = 1 and 4 in each case.