# Wireless Energy Harvesting with Cooperative Relaying under the Best Relay Selection Scheme
## 5 Numerical Results
For example, at 20 dB SNR with \(N=2\), SE for the conventional and WEH-AF relays are 1.7 and 1.3 bits/s/Hz, respectively, while for \(N=5\), SE for the conventional and WEH-AF relays are 2 and 1.5 bits/s/Hz, respectively. The loss occurs because of information processing from harvested energy. Previous works in this field focused on the degradation of SE due to WEH. For example, in [48], researchers proposed SWIPT for orthogonal frequency division multiplexing (OFDM), and degradation in SE reached approximately 40%. Figure 7: SE of conventional and wireless energy harvesting (WEH) relaying for the best relay selection (BRS) scheme. Figure 8 represents the effect of the power-splitting ratio on the EE for PS protocol, The EE decreases as \(\rho\) increases from 0.1 to 0.9, for example, when \(\rho=0.1\) means that 0.9 of the transmitted power from the relay will reach to the destination, which improve the EE, while in case of \(\rho=0.9\) means that 0.1 of the transmitted power from the relay will reach to the destination, so the EE decreases. The steady-state convergence occurred after the initial ten iterations. Figure 9 shows the EE of conventional and WEH relaying systems for different \(N\) relays. It is evident that EE performs better by increasing the relays. For example, at 10 dB SNR for WEH relaying, the EE is approximately 0.07 bits/J and 0.1 bits/J for \(N=2\) and \(N=5\), respectively. On the other hand, EE for WEH relaying outperformed conventional relaying; for example at 10 dB SNR and \(N=2\), the EE is approximately 0.01 bits/J and 0.07 bits/J for conventional and WEH relaying, respectively. Notably, EE for conventional relaying starts at approximately \(10^{-3}\) bits/J at low SNR, whereas EE for WEH relaying is approximately \(10^{-2}\) bits/J. According to [49], EE performs better in WEH relaying than in conventional relaying. For the low-SNR region, the EE of EH relaying increases faster than conventional relaying. This result leads to the conclusion that WEH relaying is the optimum solution for energy-constrained systems. Figure 8: EE at 20 dB versus different power splitting ratio. Figure 9: EE of conventional relaying and WEH relaying versus SNR for different \(N\). The relationship shown in Figure 10 illustrates the SE-EE trade-off metric. It is clear that there is an initial simultaneous increase of SE and EE, indicating the absence of a trade-off in this interval. The SE and EE trade-off starts at the point of inflection, followed by a decrement in EE along with SE. The square markers indicate that only EE is considered in the design of the wireless networks, while diamond markers indicate that only SE is considered. The region between square markers and diamond markers illustrates the trade-off between SE and EE. As shown, the maximum SE for WEH and non-WEH occurred at 1.4 bits/s/Hz and 2 bits/s/Hz, respectively, while the maximum EE for WEH and non-WEH occurred at 0.6 bits/s/Hz and 1.1 bits/s/Hz, respectively. According to [50], the SE-EE trade-off metric leads to a reduction in the energy consumed and transceiver architecture, thereby improving the complexity involved in the process and reducing the cost of operation. The SE-EE trade-off metric in [50] is shown for the non-WEH relay, while in this work, the WEH relay is shown and compared with the non-WEH relay. As expected, EE is better for the WEH relay than the non-WEH relay.