# Wireless Energy Harvesting Two-Way Relay Networks with Hardware Impairments
## 5 Numerical Results
### Effects of Various Parameters on OPS design  
The purpose of this set of simulations is to validate the validness of the OPS design and investigate the effect of parameters setting on OPS design for that uses the DF protocol or AF protocol. Since in a practical scenario, the energy conversion efficiency can be known in advance, we mainly focus on the effect of tranmitted power \(P_{t}\), impairments distortion level \(\kappa_{\text{ave}}\) and relay deployment \(d_{1}\) on OPS design in this section. Parameters chosen are: \(\kappa_{1}=\kappa_{2}=\kappa_{\text{ave}}\), \(\sigma^{2}=10^{-6}\), \(\eta=0.8\), \(d_{1}+d_{2}=10\) m, \(\lambda_{1}=\lambda_{2}=1\), \(m=2.7\) and \(P_{1}=P_{2}=P_{t}\). To better understand the importance and the effect of OPS design, we use \(\rho\) as x-axis to see the ergodic capacities (EC) and average achievable sum rate (ASR) changes with the increase of \(\rho\). In Figure 6, we present the effect of PS ratio on EC and on average ASR for DF protocol, where the EC is obtained by using the derived closed-form expressions in Section 3.1 and the average ASR is obtained by doing Monte Carlo simulation using (14). It can be notice that, there exists a maximum value for both ergodic capacity and average ASR with the increase of \(\rho\), and the value of \(\rho\) that maximize EC and average ASR varies with different transmit power \(P_{t}\) sets and different distortion level \(\kappa_{\text{ave}}\) sets. The curves of EC and average ASR are not exactly the same, and with the increase of \(P_{t}\) and \(\kappa_{\text{ave}}\), the gaps becomes smaller. Though simulation inspect, we find that this is because due to different calculating of EC and average ASR, the correlative influence introduced by multiple-access restraint differs. In addition, with the increase of \(P_{t}\) and \(\kappa_{\text{ave}}\), the correlative influence comparatively decreases. In Figure 7, the EC and average ASR with the increase of \(\rho\) for AF protocol are presented. The EC is obtained by using the derived closed-form expressions in Section 3.2 and the average ASR is obtained by doing Monte Carlo simulation using (18). It can be noted that the curves of EC coincide with the curves of average ASR. This is because without the multiple-access constraint influence in AF protocol, the calculation of EC is equal to the calculation of average ASR. In addition, we also find that the transmit power \(P_{t}\) sets and the distortion level \(\kappa_{\text{ave}}\) effect the OPS value. Figure 6: Comparison between ergodic capacity and average achievable sum rate versus \(\rho\) for DF protocol. In the following configuration, we analyze the effect of parameters setting on OPS design, and the OPS ratio is obtained aiming at maximizing the instantaneous achievable sum rate which is derived in Section 4. Figure 8 shows the average achievable sum rate as a function of the transmit power \(P_{t}\) for DF and AF protocols. The setting of distortion level \(\kappa_{\text{ave}}=\{0.08,0.175\}\) is adopted. Both the numerical search (NS) and the OPS closed-form derived in Section 4 are used to find the OPS ratio and calculate the corresponding achievable sum rate. The achievable sum rate with EPS is presented as benchmark performance. It can be noted that the curves obtained by numerical search coincide with that obtained by using closed-form OPS. It also shows that the OPS design outperforms EPS in each \(\kappa_{\text{ave}}\) setting, and the gap grows with the increase of \(\kappa_{\text{ave}}\). The effect of OPS design with DF protocol is more obvious than that with AF protocol. Figure 9 presents the value of OPS ratio versus the transmit power \(P_{t}\) for DF and AF protocols. The setting of distortion level \(\kappa_{\text{ave}}=\{0.08,0.175\}\) is adopted. Seen from this figure, we find that the OPS ratio obtained by closed-form coincides with that obtained by doing NS for DF protocol, and the OPS ratio obtained by closed-form is quite similar with that obtained by doing NS for AF protocol.