## 4 Results and Discussion  
Under different turbulence conditions, different modulation methods, different pointing errors, different RF channel fading parameters, and different network structures, the performance of the multi-hop parallel hybrid FSO/RF cooperation system proposed in this paper is estimated, and further compared with the performance of the hybrid FSO/RF direct link and the FSO-only direct link. When the parameter \(n\) is selected as 30, the average BER of the multi-hop parallel hybrid FSO/RF system can be obtained according to Equation (18). The structure parameters \((N=2,M=3)\), \((N=2,M=5)\), \((N=4,M=3)\) have been selected to avoid entanglement. Without losing generality, it is assumed that the distance between each hop and the direct link is 1 km, and the average SNR of each bit in the FSO and RF links is equal--that is, \(\overline{\gamma}_{x,y}^{FSO}=\overline{\gamma}_{x,y}^{RF}\). For different turbulence intensities, FSO sub-link and channel parameters can be obtained from Tables 2 and 3, respectively[22]. Numerical results are validated by Monte Carlo simulations, and the inverse transform method was used to generate the random channel. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Wavelength & \(\lambda^{FSO}\) & 1550 nm \\ Length of the sub-Link & \(L_{x,y}\) & 1000 m \\ Receiver aperture diameter & \(D\) & 0.02 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: FSO sub-link parameters. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Channel Condition** & \(\alpha_{x,y}\) & \(\beta_{x,y}\) & \(\sigma_{x,y}^{2}\) \\ \hline Strong turbulence & 2.064 & 1.342 & 3.67 \\ Moderate turbulence & 2.296 & 1.822 & 1.75 \\ Weak turbulence & 2.902 & 2.51 & 1.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: FSO sub-channel parameters under different turbulence intensity. In the case of pointing errors, parameter \(\rho=6\) and RF channel fading parameter \(m^{RF}=2\), it can be seen from Figure 2 that whether CBPSK or DBPSK subcarrier modulation is used, the ABER of the FSO-only direct link is higher, while the BER of hybrid FSO/RF direct link is significantly smaller. Therefore, hybrid FSO/RF parallel transmission can effectively improve the ABER performance of the system. Whether for FSO direct link or hybrid FSO/RF direct link, the ABER performance of the system using CBPSK modulation is better than DBPSK, and this performance difference gradually decreases with the increase of the average SNR of the receiver. From Figure 2, we can also see that, compared with the FSO-only direct link, the ABER performance of the hybrid FSO/RF link is less sensitive to turbulence intensity--that is, the change of turbulence intensity has little impact on the ABER performance of the hybrid system. This is because the FSO link performance deteriorates rapidly with the increase of turbulence intensity, the hybrid link selects the RF sub-link signal for output. Therefore, the hybrid FSO/RF link can significantly mitigate the impact of turbulence on the BER performance. When CBPSK modulation is adopted and the pointing error parameter \(\rho=6\), Figure 3 describes the relationship between ABER and SNR of the hybrid FSO/RF direct link under different turbulence intensity and the RF fading parameter \(m^{RF}\). Figure 3 shows that as the RF channel fading parameter \(m^{RF}\) increases, the ABER performance of the hybrid FSO/RF direct link is better. In the case of high SNR, the increase of fading parameter \(m^{RF}\) will significantly improve the ABER performance. For example, when the average SNR of the receiver is 10 dB, compared with the case of \(m^{RF}=2\), the ABER performance of the hybrid direct link when \(m^{RF}=6\) is improved by an order of magnitude; When the average SNR of the receiver is 20 dB, compared with the case of \(m^{RF}=2\), the ABER performance of the hybrid direct link when \(m^{RF}=6\) is improved by two orders of magnitude.