## 3 Performance Evaluation
### Outage Probability
As observed from Figure 3, the position of the primary users has a significant impact on \(x_{\mathrm{R}}^{*}\). It is seen that, when the primary users are close to the source (\(x_{\mathrm{P}}\) is small), the value of \(x_{\mathrm{R}}^{*}\) is low and vice versa. Figure 4 compares the outage performance of H-PRS, B-ORS and C-ORS with various values of \(C_{\mathrm{th}}\). We can see that the OP of B-ORS is lowest, and the OP of H-PRS is highest. At high transmit SNR, OP of B-ORS and C-ORS rapidly decrease as \(\Delta\) is increasing. It is due to the fact that B-ORS and C-ORS obtain a higher diversity gain as compared with H-PRS. In order to investigate the impact of distances on the outage performance of the proposed protocols, we present OP as a function of the locations of the relays on the \(x\)-axis (\(x_{\text{R}}\)). Figure 5 shows that there exists an optimal position of the relays, at which the OP value of B-ORS and C-ORS is lowest. For H-PRS, its performance is similar to the performance of C-ORS when the relays are near the source. In addition, an interesting result can be observed that when the relays are near the destination, the OP value of H-PRS reaches that of B-ORS and C-ORS. This can be explained by the fact that when the relays are very close to the destination, OP of all of the protocols significantly depends on the source to relay link, thus H-PRS can be roughly approximated to B-ORS and C-ORS. However, different from B-ORS and C-ORS, the performance of H-PRS is not good as the relays are in the middle of the source and the destination, e.g., OP of H-PRS is highest when \(x_{\text{R}}\) is about 0.6. In Figure 6, we investigate the impact of the hardware impairment level \(\left(\tau_{\rm D}^{2}\right)\) on the performance of H-PRS, B-ORS and C-ORS. As we can see, the OP values rapidly increase with the increasing of \(\tau_{\rm D}^{2}\). Moreover, Figure 6 shows that all of the proposed protocols are always in outage when \(\tau_{\rm D}^{2}\) is higher than 0.55. As stated in Section 3, if \(\tau_{\rm D}^{2}\geq 0.55\), then \(1-\tau_{\rm D}^{2}\theta<0\), and hence \(\rm{OP}_{H-PRS}\)= \(\rm{OP}_{B-ORS}\)= \(\rm{OP}_{C-ORS}=1\). In Figure 7, the throughput (TP) is presented as a function of the fraction of time allocated for the EH process. As presented in the previous sections, the \(\alpha\) value plays a key role in the EH process, since it affects both the harvested power, and the transmit power of the source or the selected relay node. As we can see from this figure, there exist optimal values of \(\alpha\) at which the throughput of the proposed protocols is highest. This can be explained as follows when the \(\alpha\) value is too small: less energy can be harvested from the power beacon. Hence, the small amount of energy that the source or relay node can use for data transmission. At the other extreme, when the \(\alpha\) value is too large, a less effective transmission time is utilized to relay the data from source to destination, which leads to the decreasing of the throughput. Therefore, for practical design, the best TP performance can be obtained when \(\alpha\) reaches the optimal value. Finally, similar to the OP metric, for all \(\alpha\) values, the TP performance of B-ORS is always better than that of C-ORS, which further outperforms H-PRS. Figure 8 demonstrates TP versus the number of relays. As expected, the throughput of H-PRS, B-ORS and C-ORS can be enhanced by increasing the \(M\) value. Again, we can see that the performance of the considered protocols can be improved by assigning the value of \(\alpha\) appropriately. From Figures 4-8, it is evident that the simulation results are perfectly consistent with our derived theoretical values, and the gap between the exact and asymptotic results is small, which verifies the correction of our derivations.