# Performance Analysis of Dual-Hop AF Relaying with Non-Linear/Linear Energy Harvesting
## 6 Results and Discussion
Figure 3: Relative approximation error versus parameter Y of the WP DH AF relaying system for \(P_{T}=40\) dB, and \(P_{th}=35\) dB. Figure 6 shows the BER performance versus \(d_{h}\), where it is assumed that \(d_{sd}=2\). It is seen from Figure 6 that the results provided for \(P_{T}=30\) dB and \(P_{T}=40\) dB are similar for both linear and non-linear EH models, since the threshold power in the non-linear EH model is assumed as \(P_{th}=35\) dB, and the amount of harvested energy in both models is equal. However, for higher values of \(P_{T}\), the linear EH model outperforms the non-linear EH where the amount of harvested power is saturated at \(P_{th}=35\) dB, which weakens the system performance compared to the linear EH model. Please note that for \(P_{T}=50\) dB and \(P_{T}=60\) dB, the results provided for the non-linear EH model are approximately the same, since for higher input power of PB, \(P_{s}\) and \(P_{r}\) are limited by \(P_{th}=35\) dB. The throughput of the considered system versus \(P_{T}\) for \(d_{sd}=1\) is illustrated in Figure 7. It is shown that for a target rate value of \(R=1\) bit/sec/Hz, the linear and non-linear EH models provide approximately the same performance, while for both \(R=2\) and \(R=3\), the linear EH model has higher throughput compared to the non-linear EH model. This is based on the fact that the linear EH model causes a misrepresentation of the system performance compared to the considered EH model since the amount of the harvested  
Figure 5: BER performance of the WP DH AF relaying system versus \(P_{T}\) dB where \(P_{th}=35\) dB. energy at both S and R nodes is miscalculated. Hence, this provides a misunderstanding of the design of the EH systems. Figure 8 depicts the throughput with respect to \(P_{T}\) for different values of \(d_{sd}\). The target rate is fixed at \(R=1\). The results reveal that, for the distances \(d_{sd}=1,2,3\), the linear EH model provides performance approximately equivalent to that of the non-linear EH since the amount of harvested powers are approximately equal for both EH models. Moreover, in all cases, the throughput reaches its maximum value at \(P_{T}=42\) dB. The throughput performance versus \(P_{T}\) for different values of \(P_{th}\) is shown in Figure 9. It is seen from Figure 9 that, by increasing \(P_{th}\) from 10 dB to 35 dB, the throughput increases and reaches its maximum value for \(P_{th}=35\) dB, which is approximately equivalent to the linear EH model throughput performance. In other words, a high level of threshold power in the non-linear EH model provides the same results as in the linear EH model since the amount of harvested power for both EH models is equal. Figure 8: Throughput performance of the WP DH AF relaying system versus \(P_{T}\) (\(R=1\) bits/s/Hz, \(P_{th}=35\) dB). Figure 7: Throughput performance of the WP DH AF relaying system versus \(P_{T}\) (\(d_{sd}=1\), \(P_{th}=35\) dB). Figure 10 plots the source and relay harvested powers versus \(P_{T}\). Please note that, from Appendix D, for an equal distance of S and R from PB, and for equal fading channel parameters, the harvested powers \(P_{s}\) and \(P_{r}\) are equal. The curves in Figure 10 are obtained using (A34) and (A35) for linear and non-linear EH models, respectively. As seen from Figure 10a,b, the distance (\(d_{sd}\)) and energy efficiency (\(\eta\)) have a significant effect on the amount of powers harvested at S and R. It is observed that, for high values of \(P_{T}\), the average harvested power in the linear EH model is higher compared to the considered non-linear EH model, which is saturated to a predefined threshold value \(P_{th}\). This high value is contrary to the amount of harvested energy in practical NL EH models, where it results in an overestimation of system performance. Figure 11 shows the BER performance versus channel estimation error power \(\sigma_{err}^{2}\) for different SNR values. Both linear and non-linear EH results are obtained considering \(P_{th}=35\) dB and \(d_{sd}=1\).