## 4 Results and Discussion  
The performance of the mixed RF-FSO system with hybrid PPM-BPSK-SIM is shown in figures below, including outage probability performance, average BER, and average channel capacity. Note that, the RF link is assumed to obey Rayleigh distribution and we use Gamma-Gamma fading to describe the turbulence of the FSO link from weak to strong, the receiver employs IM/DD. The parameters for turbulence intensity are shown in Table 1[35; 36], the wavelength is 1550 nm, and the distance between the transmitter and the receiver is set to be 5 km. The outage probability of the hybrid RF-FSO system against average SNR per hop is shown in Figure 2, effects of atmospheric turbulence and pointing errors are taken into account. \(\gamma_{th}\) is set to be 10 dB, the average SNRs of the two different links are equal to each other (i.e., \(\overline{\gamma_{1}}=\overline{\gamma_{2}}=\overline{\gamma}\)). As seen, the decrease of atmospheric turbulence leads to the improvement of the outage performance. Moreover, taking into consideration the pointing error, the greater the parameter, \(\xi\), the better the outage performance. For instance, when the outage probability is \(P_{out}=10^{-3}\), the system has a 6 dB decrease on average SNR from strong turbulence to weak turbulence while \(\xi=1\), but the difference value is less than 0.5 dB while \(\xi=5\). Therefore, a conclusion is reached that pointing error aggravates the influence of atmospheric turbulence on outage probability. Comparison diagram of average BER of BPSK in the FSO system and the hybrid RF-FSO system is shown in Figure 3. The simulation of BPSK refers to reference [37]. It can be observed that by adopting the RF link, the hybrid RF-FSO system has an improvement in BER performance compared to the FSO system. The BER of BPSK in the FSO system is lower than that in hybrid RF-FSO system, and higher average SNR of the RF channel leads to greater improvement. In order to study the performance of the hybrid RF-FSO system, we set \(\overline{\gamma_{1}}=\overline{\gamma_{2}}=\overline{\gamma}\) in the following. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Turbulence** & \(\alpha\) & \(\beta\) \\ \hline Weak & 11.6 & 10.1 \\ Moderate & 4.0 & 1.9 \\ Strong & 4.2 & 1.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters for different turbulence intensities. Figure 4 depicts the average BER of LPPM and BPSK in the mixed RF-FSO system against the average SNR per hop, the parameter of pointing error is 1 and \(C=1\). It can be seen from the figure that LPPM has a better BER performance as L increases. When the value of L is greater than four, the performance of LPPM in this system is better than that of BPSK. In Figure 5, comparison between various PPM-BPSK-SIM and BPSK has been shown, the same conclusion can be drawn that the BER of the hybrid system decreases when L increases, but the marginal values are different. For instance, when the value of L is greater than eight instead of four, the hybrid system adopting various PPM-BPSK-SIM achieves better performance than the system with BPSK. Simulation results in Figure 6 show that under moderate turbulence, a decrease in the value of C causes the improvement of the average BER, but it is irrelevant to the marginal value, the PPM-BPSK-SIM outperforms BPSK when the symbol length is greater than eight, that is, this is not a special case. An increase in the symbol length will reduce  
Figure 3: Average bit error rate (BER) of binary phase shift keying (BPSK) against average SNR under moderate turbulence and the pointing error parameter is \(\xi=1\). Turbulence parameters are \(\alpha=4.0\) and \(\beta=1.9\), the constant is assumed to be \(C=1\). Figure 2: Outage probability against average signal-to-noise ratio (SNR) per hop for various turbulence intensities and different pointing error parameters. The constant is assumed to be \(C=1\), and the threshold of the hybrid system is \(\gamma_{hl}=10\) dB.