# Energy Harvesting over Rician Fading Channel:
## 4 Numerical Results and Discussion
### Effects of Various Parameters on the System Performance  
Figures 3 and 4 show the effect of \(P/N_{0}\) on the outage probability and throughput of the proposed system, respectively. For this simulation, the utilized parameter settings are: \(\kappa=\kappa_{r}=0.1\) or \(0.2,\alpha=0.5\) and \(\eta=0.7\). We choose \(\alpha=0.5\) to consider the case that the duration of energy harvesting and the duration of transmission are balanced. The case \(\kappa=0\) (no hardware impairment) is also introduced for comparison. The first observation is that the outage probability and throughput obtained from mathematical analysis match with the corresponding Monte Carlo simulations. Regarding the effect of \(\kappa\), the outage probability decreases and the throughput increases as \(\kappa\) varies from 0 to 0.2. When \(P/N_{0}\) increases, the outage probability and throughput approach the corresponding asymptotic values obtained from analysis. Furthermore, the lower the value of \(\kappa\), the faster the outage probability and throughput converge to their asymptotic values. The effect of hardware impairment level on the outage probability and the achievable throughput at each node is presented more thoroughly in Figures 5 and 6. Here, \(P/N_{0}\) is set at 20 dB and the transmission rate is fixed at 1.5 bps. Three values of \(\alpha\) are chosen: 0.2, 0.5, and 0.8, corresponding to three cases: the energy harvesting duration is dominant, there is a balance between energy harvesting and information transmission, and the information transmission duration is dominant. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Symbol** & **Parameter Names** & **Values** \\ \hline \(\eta\) & Energy harvesting efficiency & 0.7 \\ \(\lambda_{1}\) & Mean of \(|g_{1}|^{2}\) & 0.5 \\ \(\lambda_{2}\) & Mean of \(|g_{2}|^{2}\) & 0.5 \\ \(K\) & Rician K-factor & 3 \\ \(P/N_{0}\) & Source-power-to-noise ratio & 0–50 dB \\ \(\kappa=\kappa_{r}\) & Hardware impairment levels & 0, 0.15, 0.25 \\ \(R\) & Source transmission rate & 1.5 bps/Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 3: Outage probability versus \(P/N_{0}\). Again, it is observed that the exact-form expressions of outage probability and throughput obtained by the analysis coincide with the ones that are obtained by Monte Carlo simulations. From the numerical results, it is evident that the achievable throughput decreases and the outage probability increases significantly at each destination node when the impairment level \(\kappa\) increases. In addition, the outage probability tends to reduce at higher time-switching factor. This can be explained because the larger value of \(\alpha\) means more power is used for data transmission. However, this doesn't mean that the throughput is better for larger \(\alpha\). In Figure 6, the throughput performance is improved when \(\alpha\) increases from 0.2 to 0.5, but then degraded when \(\alpha\) increases from 0.5 to 0.8. Figure 4: Achievable throughput versus \(P/N_{0}\). Figure 5: Outage probability versus \(\kappa\). Figures 7 and 8 illustrate more clearly the effect of time-switching factor on the outage and throughput performance. In this simulation, the parameters are chosen as \(\eta=0.7\) and \(P/N_{0}=20\) dB (this value is chosen because it is in the middle range of \(P/N_{0}\)). The transmission rate varies among three values: 0.5 bps/Hz, 1 bps/Hz and 1.5 bps/Hz, while the time-switching factor varies in the range \((0,1)\). The results confirm what we mentioned just above. There should be a unique value of \(\alpha\) that maximizes the throughput. This is because, when we increase \(\alpha\) initially, there is more power used for transmission, so the outage probability is reduced and the throughput increases correspondingly. However, when \(\alpha\) keeps increasing, the duration of transmission is also reduced, hence, less data is transmitted during a given time interval. As a result, the throughput performance becomes worse. Figure 6: Achievable throughput versus \(\kappa\).