# Wireless Energy Harvesting Two-Way Relay Networks with Hardware Impairments
## 5 Numerical Results
### Effects of Various Parameters on OPS design
It is easy to noted that the OPS ratio is a monotonic decreasing function with the increase of \(P_{t}\) for both protocols. The reason for this phenomenon is because when the source provide high transmit power, the recruit of harvested energy is more prone to satisfy the relay to destination transmission, and the enhancement of system performance is relies on the source to relay trans  
Figure 8: Average achievable sum rate comparison versus \(P_{t}\) for DF and AF protocols. Figure 7: Comparison between ergodic capacity and average achievable sum rate versus \(\rho\) for AF protocol. more information needed to be split to information decoder circuit, i.e., \((1-\rho)\) enhances. We also find that the OPS ratio with \(\kappa_{\text{ave}}=0.175\) setting is higher than that with \(\kappa_{\text{ave}}=0.08\) setting for both protocols. The reason for this phenomenon will be discussed below Figure 11.  
Figure 10 plots the achievable sum rate versus hardware impairments distortion level \(\kappa_{\text{ave}}\) for both DF and AF protocols with different transmit power \(P_{t}=\{15,30\}\) dBm. The curves with black solid line were generated by utilizing the OPS through numerical search (NS), and the curves with mark were generated by utilizing the OPS derived in Section 4. EPS design is adopted as benchmark performance. As shown in this figure, the achievable sum rate is decreasing and will tend to flatten out as \(\kappa_{\text{ave}}\) increases, and the lower the transmit power, the faster the rate approaching to flat. This figure also verifies that OPS design outperforms EPS scheme, and the gaps of DF protocol between OPS and EPS design is bigger than that of AF protocol. The effect of \(\kappa_{\text{ave}}\) on OPS design for DF and AF protocols are presented in Figure 11. This figure presents that the OPS ratio obtained by closed-form is identical with that obtained by doing NS for DF protocol, and for AF protocol, the OPS ratio obtained by closed-form is very close to that obtained by doing NS. It is observed that the OPS ratio is a decreasing function of \(\kappa_{\text{ave}}\), and the decreasing  
Figure 10: Average achievable sum rate comparison versus \(\kappa_{\text{ave}}\) for DF and AF protocols. Figure 9: The effect of \(P_{t}\) on OPS design for DF and AF protocols. slope increases with the increase of \(P_{t}\). This is because the higher \(\kappa_{\rm ave}\) makes worse decoding ability. To enhance system performance, more energy need to be diverted to the ID circuit to satisfy the decoding process, thus, OPS value decreases. We also find when \(\kappa_{\rm ave}\) is the same, the OPS value with the higher \(P_{t}\) is lower than that with the lower \(P_{t}\). This is because in higher \(P_{t}\) region, the harvested energy is more prone to satisfy the BC transmission with small \(\rho\). With fixed \(\kappa_{\rm ave}=0.1\), we analyze the effect of relay deployment on average ASR with the set of \(P_{t}=\{15,30\}\) dBm for DF and AF protocols (\(d_{1}\) is chosen as the x-axis) in Figure 12. This figure verifies that the average ASR with OPS obtained in Section 4 and that obtained by using NS are the same, and the OPS scheme outperform the EPS scheme. For DF protocol, the average ASR is a convex function with the increase of \(d_{1}\) for \(P_{t}=\{15,30\}\) dBm. While for AF protocol, the average ASR is convex function when \(P_{t}=15\) dBm, while when \(P_{t}=30\) dBm, the average ASR is a concave function. This phenomenon echoes the conclusion in Figure 3 (right) that when \(P_{t}\) increase to high enough, the relay is better to deploy close to any one of the source nodes. Figure 13 plots the value of OPS ratio versus \(d_{1}\) for DF and AF protocols. It shows that the OPS ratio obtained by closed-form is identical with that obtained by doing NS for DF protocol, and for AF  
Figure 11: The effect of \(\kappa_{\rm ave}\) on OPS design for DF and AF protocols. Figure 12: Average achievable sum rate comparison versus \(d_{1}\) for DF and AF protocols.