## 4 Numerical Results and Discussions  
In this paper, the chaotic system chooses the logistic map and sets the spreading factor to 240. In simulations, \(P_{s}\) is set to 1 Watt (W) [15; 19], and the path loss factor \(m\) is set to 2.7 for propagation in urban cellular networks [19; 23]. It is also assumed that \(N_{0,p}=N_{0}\) and \(N_{0,c}=0.5N_{0,p}\). For a multipath Rayleigh fading channel, three paths (\(L=3\)) are considered, which have equal average power gain as \(E[\alpha_{1}{}^{2}]=E[\alpha_{2}{}^{2}]=E[\alpha_{3}{}^{2}]=1/3\), with different time delays \(\tau_{1}=0,\tau_{2}=2T_{c}\) and \(\tau_{3}=5T_{c}\). In the following figures, 'com','sim', and 'MP' represent the analytical BER, the simulation BER, and BER under Rayleigh fading channel, respectively. To achieve better BER and harvest enough energy, the value of \(\mu\) and \(\beta_{1}\) should be optimized. To achieve the impacts of \(\mu\) and \(\beta_{1}\) on BER, either of them is fixed to obtain the effect of the other one on BER. Figure 2 shows the BER performance of GCI-DCSK SWIPT scheme changes along with \(\mu\) over AWGN channel with \(P_{s}/N_{0}=18\) dB and fixed \(\beta_{1}\). It shows that the performance of BER degrades as \(\mu\) increases. Because as \(\mu\) increases, the energy of the inactive carrier increases which is adverse to BER. However, as mentioned in Section 3.3, \(\mu\) should be larger than the optimal value to harvest enough energy. Figure 3 shows the BER performance of GCI-DCSK SWIPT scheme changes along with \(\beta_{1}\) setting \(P_{s}/N_{0}=18\) dB and \(\mu\) fixed. With \(\beta_{1}\) increasing, the BER increases after initially decreasing, and the minimum value of BER is obtained at \(\beta_{1}=180\). Hence, \(\beta_{1}\) is set to 180 during the simulation for better BER. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Modulation** & **CI-DCSK1 SWIPT** & **CI-DCSK2 SWIPT** & **GCI-DCSK** & **GCI-DCSK SWIPT** \\ \hline SE & \(\dfrac{p_{1}+1}{n+1}\) & \(\dfrac{p_{1}+n-1}{n+1}\) & \(\dfrac{p_{1}+p_{2}}{n+1}\) & \(\dfrac{p_{1}+p_{2}}{n+1}\) \\ EE & \(\dfrac{p_{1}+1}{2+\mu(n-1)E_{c}^{p}}\) & \(\dfrac{p_{1}+p_{2}}{(n+\mu)E_{c}^{p}}\) & \(\dfrac{p_{1}+p_{2}}{P_{s}[p_{2}+1+\mu^{2}(n-p_{2})]E_{c}^{p}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The formulas of EE and SE for the four systems. Based on the above analysis, putting \(\beta_{1}=180\) into Formula (32), the optimal value of \(\mu\) is achieved. As shown in Figure 4, with \(P_{s}/N_{0}\) being 40 dB, \(\beta_{1}\) being 180, and \(\mu\) being the optimal value, the scheme is self-sufficient. Moreover, if \(d_{tr}\) increases, the optimal value of \(\mu\) increases to overcome the impact of more path loss. Figure 3: BER performance of GCI-DCSK SWIPT changes along with \(\beta_{1}\) over AWGN channel with \(P_{s}/N_{0}=18\) dB. Figure 2: BER performance of GCI-DCSK SWIPT changes along with \(\mu\) over AWGN channel with \(P_{s}/N_{0}=18\) dB. Figure 5 shows the BER of GCI-DCSK SWIPT changes along with \(d_{tr}\) over a multipath Rayleigh fading channel. It shows that the BER gets worse with the increase of \(d_{tr}\) for different cases because when the distance between the transmitter and receiver increases, the probability of correct reception decreases due to the influence of increasing path loss. The analytical and simulation results for GCI-DCSK SWIPT over AWGN and Rayleigh fading channels are shown in Figure 6 and Figure 7, respectively. The results show that the analytical results match well with the simulation results in different cases, which demonstrates the accuracy of the analytical BER expressions. To analyze the impact of conversion noise on BER performance, the curves without conversion noise are plotted  
Figure 4: The ratio of the harvested energy to the transmitted energy changes along with \(\mu\) for GCI-DCSK SWIPT at \(d_{tr}=1\) and \(d_{tr}=1.2\), where \(\beta_{1}=180\) and \(P_{s}/N_{0}=40\) dB.