# Energy-Efficient Power Allocation in Non-Linear Energy Harvesting Multiple Relay Systems
## 4 Simulations  
In this section, the simulation results will be analyzed, and the effectiveness of the proposed algorithm will be proven. The simulation scenario is shown in Figure 1, where the distance between \(S\) and \(D\) is \(d=10\)\(m\) and the relay is randomly distributed in the circle with the midpoint of \(S\) and \(D\) as the center and radius, expressed as \(r=2\)\(m\). Like [12], all the channels are Rayleigh fading channels, where the path loss exponent \(\alpha\) is \(\alpha=3\) and the small-scale fading is Rayleigh fading with a mean value of 0 and variance of 1. In accordance with [12,20,21], we set the simulation parameters as follows: \(P_{S}=30\) dBm, \(P_{C}=10\) mW, \(P_{Q}=0.1\) mW, \(\sigma^{2}=-70\) dBm and \(R_{\min}=3\) bps/Hz. The parameters of the EH model in Figure 2 are shown in Table 1.  
Figure 3: The workflow of the power allocation algorithm. Figure 4 shows the variation of the EE in different EH models under the same relay total transmit power threshold. It can be seen that the EE increased as the number of relays increased. This is because, compared with a single relay, multiple relays can improve the information transmission rate. Since the relay uses the harvested energy for DF without consuming fixed energy, the increase in the number of relays can also improve the EE of the system. In addition, it can also be observed that the performance of the piecewise linear EH model was better than that of the linear EH model in [7]. This is because the piecewise linear EH model improves the accuracy of the traditional linear EH one. The more segments, the better the performance, but its growth rate will decrease with the increase in the segment number. Therefore, the piecewise linear EH model with \(L=5\) was selected for simulation analysis in this paper. Figure 5 shows that the EE changed with the total transmit power threshold of relays \(P_{\max}\), and the number of relays was \(N=4\). It can be seen that the EE increased with the increase of \(P_{\max}\), and the increase gradually decreased until it no longer increased. This was because the energy harvested by the EH model was limited. When \(P_{\max}\) exceeds the total power that can be used after EH, the EE will not increase with the increase of \(P_{\max}\). In this simulation scenario, when \(P_{\max}>40\) mW, the EE would not change significantly with the increase in \(P_{\max}\). \begin{table}
\begin{tabular}{c c} \hline Linear EH model & \(P_{th}=[0,60]\) mW, a = \([0.3957,0]\), b = \([0,23\).742] mW \\ \hline Piecewise linear EH model (\(L=4\)) & \(P_{th}=[0,5,15,60]\) mW, a = \([0.4,0.88,0.2877,0]\), b = \([0,-2.4,6.4845,23.7465]\) mW \\ \hline Piecewise linear EH model (\(L=5\)) & \(P_{th}=[0,5,15,25,60]\) mW, a = \([0.4,0.88,0.896,0.1139,0]\), b = \([0,-2.4,-2.64,16.9125,23.7465]\) mW \\ \hline Piecewise linear EH model (\(L=6\)) & \(P_{th}=[0,5,15,25,40,60]\) mW, a = \([0.4,0.88,0.896,0.2406,0.018625,0]\), b = \([0,-2.4,-2.64,13.745,22.629,23.7465]\) mW \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of the EH model. Figure 4: Energy efficiency versus number of relays under different EH models. Figure 6 shows that the EE varied with the different transmit powers of source \(P_{S}\). It can be seen that the EE first increased with the increase of \(P_{S}\) and then decreased with the increase of \(P_{S}\). This is because when \(P_{S}\) is very small, the energy harvested by the relay may not be enough to complete the information transmission, which makes the EE relatively low. With the increase of \(P_{S}\), the relay can harvest more sufficient energy to complete the information transmission, so the EE correspondingly increases. However, when \(P_{S}\) exceeds a certain value, the energy consumption is too high, and the EE will decrease with the increase of \(P_{S}\). In this simulation scenario, when \(P_{S}\)= 18 dBm, the EE is the highest. In addition, compared with the single-relay in [13], multi-relay cooperation can effectively improve performance.