## 5 Numerical and Simulation Results
### Multiple SWIPT Relaying Systems  
Table 2 shows the channel model used for the multiple SWIPT relaying system and the corresponding link channel power. In Table 2, Ch. \(\text{Model}=[1,X,1]\) indicates the environment in which the RD link channel power can be different according to \(R\). Also, Ch. \(\text{Model}=[1,1,X]\) provides the SR link channel power-varying environment. Table 3 shows the relationship between the meaning, equation number, and symbols of the legend used in the resulting figures.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Ch. Model** & **Link** & **Ch. Power** & **R** \\ \hline \multirow{5}{*}{\([1,1,X]\)} & SD & \(\Omega_{\text{sd}}=1\) & \\ \cline{2-4}  & SR & \(\Omega_{\text{sr}}\in\{1\}\) & \\ \cline{2-4}  & & \(\Omega_{\text{rd}_{r}}\in\{1\}\) & 1 \\  & RD & \(\Omega_{\text{rd}_{r}}\in\{1,2\}\) & 2 \\  & & \(\Omega_{\text{rd}_{r}}\in\{1/4,1,4\}\) & 3 \\  & & \(\Omega_{\text{rd}_{r}}\in\{1/2,1,2,4\}\) & 4 \\ \hline \multirow{5}{*}{\([1,X,1]\)} & SD & \(\Omega_{\text{sd}}=1\) & \\ \cline{2-4}  & & \(\Omega_{\text{rd}_{r}}\in\{1\}\) & 1 \\ \cline{2-4}  & SR & \(\Omega_{\text{sr}_{r}}\in\{1,2\}\) & 2 \\ \cline{2-4}  & & \(\Omega_{\text{sr}_{r}}\in\{1/4,1,4\}\) & 3 \\ \cline{2-4}  & & \(\Omega_{\text{sr}_{r}}\in\{1/2,1,2,4\}\) & 4 \\ \cline{2-4}  & RD & \(\Omega_{\text{rd}_{r}}\in\{1\}\) & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Channel models for multiple SWIPT relaying system.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**At** & **Legend** & **Symbol** & **Equation** & **Comment** \\ \hline \multirow{3}{*}{Figures 6 and 7} & Theory, Exact & \(P_{S,\text{sd}},P_{S,\text{id}},P_{S,\text{cb}}\) & (32) & Exact MGF \\  & Theory, Up & \(P_{S,\text{id}}^{\text{UP}},P_{S,\text{cb}}^{\text{UP}}\) & (33) & Upper Bounded MGF \\  & Theory, Asym & \(P_{B,\text{id}}^{\text{Asym}},P_{B,\text{cb}}^{\text{Asym}}\) & (35) & Asymptotic Bound \\ \hline \multirow{3}{*}{Figures 6 and 7} & Theory, AF-App & \(P_{S,\text{id}}^{\text{AF-App}},P_{S,\text{cb}}^{\text{AF-App}}\) & (41) & AF-Approximation \\  & \(P_{B,\text{id}}^{\text{AF-App}},P_{B,\text{cb}}^{\text{AF-App}}\) & (42) & \\ \hline \multirow{3}{*}{Figures 8 and 9} & Theory, Exact & \(P_{\text{out,sd}}\) & (45) & Exact only for SD \\  & Theory, AF-App & \(P_{\text{out,id}}^{\text{AF-App}},P_{\text{out,cb}}^{\text{AF-App}}\) & (44) & AF-Approximation \\ \hline \multirow{3}{*}{Figures 10–13} & Theory, Exact & \(C_{\text{sd}}\) & (46) & Exact only for SD \\  & Theory, AF-App & \(C_{\text{id}}^{\text{AF-App}},C_{\text{cb}}^{\text{AF-App}}\) & (48) and (49) & AF-Approximation \\ \hline \hline \end{tabular}
\end{table}
Table 3: Legend description for multiple SWIPT relaying system.  
Figure 8: Outage Probability Comparison with respect to SNR (BPSK, \(\eta=1.0\), \(\rho_{r}=\rho_{\text{opt}}\), Ch. Model \(=[1,1,X]\)): (a) \(R\in\{1,2\}\), (b) \(R=3\), and (c) \(R=4\).  
Figure 6: BER performance comparison with respect to SNR (BPSK, \(\eta=1.0\), \(\rho_{r}=\rho_{\text{opt}}\), Ch. Model \(=[1,1,X]\)): (a) \(R\in\{1,2\}\) and (b) \(R\in\{3,4\}\).  
Figure 10: Channel capacity comparison with respect to SNR (BPSK, \(\eta=1.0\), \(\rho_{r}=\rho_{\text{opt}}\), Ch. Model \(=[1,1,X]\)): (**a**) \(R=1\), (**b**) \(R=2\), (**c**) \(R=3\), and (**d**) \(R=4\).  
Figure 11: Channel capacity comparison with respect to SNR (BPSK, \(\eta=1.0\), \(\rho_{r}=\rho_{\rm opt}\), \(R\in\{1,2,3,4\}\), Ch. Model \(=[1,1,X]\)): (**a**) Indirect link and (**b**) combined link.