## 6 Simulation and Analysis
### Simulation Results  
The system energy efficiency performance for different \(\alpha\) values is shown in Figure 3 under three schemes (FD dual-antenna energy harvesting, FD single-antenna energy harvesting, and HD) and fixed \(P_{S}=[30\ dB,20\ dB,10\ dB]\). According to Figure 3, under the different transmission powers, the energy efficiency trend under the three schemes is the same, specifically that it monotonically increases first, then monotonically decreases with the time-switching factor, because the energy collected in this short period of time is insufficient to satisfy the second stage of information transmission. At this time, the larger the time allocation factor, the greater the system energy efficiency. When the time-switching factor is greater than 0.6, the energy efficiency curve of the FD single antenna and the FD single-antenna energy harvesting system are almost identical, and they all gradually decrease as the time allocation factor increases. As a result, long periods of energy harvesting can degrade system performance. According to Figure 3, the optimal time allocation factor of the FD dual antenna is smaller than that of HD and the optimal time allocation factor of HD is smaller than that of the FD single antenna. This is because the extra antenna reduces the energy collection time. Figure 4 shows how the energy efficiency varies with time allocation factors in three cases (FD dual-antenna, FD single antenna, and HD). The energy conversion efficiencies are 0.7, 0.5, and 0.3, respectively. We set \(P_{s}/N_{0}=10 dB\). According to Figure 4, the energy efficiency of the FD relay system is much better than the HD relay system. The energy efficiency of the FD dual-antenna energy harvesting system is better than that of the single antenna. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Energy conversion efficiency & 0.75 \\ Noise at three nodes & 1 \\ Circuit power consumption & 6 dB \\ Power amplifier efficiency & 1 \\ Coefficient of self-interference between antennas & \(-80\) dB \\ Source nodes transmit power & 0-30 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. In wireless power communication systems, the increase of \(P_{s}/N_{0}\) not only has a positive impact on system performance, but also a certain negative impact on system performance. Figure 5 shows the variation of system energy efficiency with \(P_{S}/N_{0}\) in three cases (FD dual-antenna, FD single-antenna, and HD) when the time factor is optimal and the energy conversion efficiency \(\eta\) is 0.7. According to Figure 5, the system energy efficiency of HD dual antennas for energy harvesting is greater than that of HD single-antenna energy harvesting system at the same transmission power, especially at low \(SINR\). Because of the same transmitted power, the FD dual-antenna energy harvesting system obtains more energy per unit time for information transmission. However, with the gradual increase of the transmitting power, an antenna obtains enough energy, and excessive energy harvesting causes greater loopback interference, which reduces the performance of the system. Therefore, when the transmission power is large, the effect of the extra antenna on the system energy efficiency gradually reduces. At this time, the effects of the FD dual-antenna and FD single-antenna schemes on the system energy efficiency are not much different, and the curves almost coincide. At the same time, regardless of whether the signal-to-noise ratio is high or low, the system energy efficiency of the FD system is always greater than that of the HD system. FD significantly improves the performance of the system. Figure 4: The system energy efficiency versus \(\alpha\) with \(\eta=\{0.7,0.5,0.3\}\) and \(P_{S}=~{}10 dB\). Figure 3: The system energy efficiency versus \(\alpha\) with \(P_{S}=\{30 dB,20 dB,10 dB\}\). The energy conversion efficiency determines how much power the relay can actually receive.