# Performance Monitoring of Hybrid All-Optical Fiber/FSO Communication Systems
## 3 Results and Discussions
### Performance Comparison with Other ML Models  
The present section compares the performance of the GPR model with that of two other commonly used ML models, namely SVM and random forest (RF) models. Figure 4 illustrates the performance comparison using R-squared and RMSE metrics. For the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Predicted Parameter** & **Channel Impairments** & **R-Squared** & **RMSE** \\ \hline \multirow{4}{*}{OSNR} & ASE & 1.00 & 0.09 dB \\  & ASE+CD & 1.00 & 0.13 dB \\  & ASE+Turbulence & 1.00 & 0.16 dB \\  & ASE+CD+ Turbulence & 0.96 & 0.54 dB \\ \hline \multirow{4}{*}{CD} & CD & 1.00 & 0.00 ps/nm \\  & CD+Turbulence & 0.98 & 0.20 ps/nm \\  & CD+ASE & 0.96 & 0.27 ps/nm \\  & CD+ASE+ Turbulence & 0.93 & 0.37 ps/nm \\ \hline \multirow{4}{*}{\(C_{n}^{2}\)} & Turbulence & 1.00 & 0.10 m\({}^{-2/3}\) \\  & Turbulence +CD & 1.00 & 0.03 m\({}^{-2/3}\) \\ \cline{1-1}  & Turbulence +ASE & 0.84 & 0.57 m\({}^{-2/3}\) \\ \cline{1-1}  & Turbulence +CD+ASE & 0.84 & 0.56 m\({}^{-2/3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of the proposed model performance. turbulence parameter monitoring, it was observed that the GPR model outperformed the other models in terms of both RMSE and R-squared metrics. Specifically, the achieved R-squared was 1 under turbulence conditions alone and also under turbulence and 500 ps/nm CD impairment, as indicated in Figure 4a. Similarly, for these two-channel conditions, the RMSE value was less than 1. However, when the signal was corrupted with turbulence and ASE noise (12 dB OSNR), the R-squared value dropped to 0.84 for the GPR model, which was still slightly better than that of the RF and SVM models. Similarly, the RMSE degraded to 0.55, but still remained better than that of the RF and SVM models as depicted in Figure 4d. The performance of predicting the turbulence parameter under all harsh conditions, i.e., 12 dB OSNR and 500 ps/nm, remained relatively unchanging, as shown in Figure 4a,d. In the following analysis, we compare the performance of the three models in predicting the OSNR parameter under different channel conditions, as shown in Figure 4b,e. The results indicate an R-squared value of 1 using the GPR model under ASE noise alone, as well as when the channel included 500 ps/nm CD and \(10^{-13}\) m\({}^{-2/3}\) turbulence. In comparison, the two other models exhibited slightly lower R-squared values. Furthermore, the GPR model demonstrated significantly better performance in terms of RMSE compared to the two other models. However, when the channel was subjected to both 500 ps/nm CD and \(10^{-13}\) m\({}^{-2/3}\) turbulence, the R-squared value declined to 0.96, while the RMSE degraded to 0.55, which was similar to the obtained performance of the two other models. Finally, we compare the performance of the GPR model with the two other models in predicting the CD parameter, as illustrated in Figure 4c,f. The results exhibit similar performance in terms of R-squared and RMSE for all three models. Specifically, the achieved R-squared was 1 and the RMSE was 0. However, when a severe turbulence condition, defined by \(10^{-13}\) m\({}^{-2/3}\) turbulence value, was added to the channel, the R-squared metric value degraded to 0.98 for all models, and the RMSE increased to 0.2, which was slightly better than that of the SVM model but worse than that of the RF model. When ASE noise was introduced to the channel, defined by 12 dB OSNR, the GPR model's performance slightly degraded in terms of R-squared and RMSE. It exhibited the same performance as the SVM model and was better than that of the RF model. Finally, when both CD and OSNR  
Figure 4: Performance comparison of GPR, RF, and SVM models in terms of R-squared and RMSE metrics for predicting **(a,d)**\(C_{n}^{2}\) parameter, **(b,e)** OSNR parameter, and **(c,f)** CD parameter. Severe channel conditions are considered as follows: 12 dB OSNR, 500 ps/nm CD, and \(10^{-13}\) m\({}^{-2/3}\)\(C_{n}^{2}\) turbulence.