# Polynomial Modeling of Noise Figure in Erbium-Doped Fiber Amplifiers
## 5 Conclusions  
This paper presented the development and evaluation of a polynomial model for estimating the noise figure of Erbium-Doped Fiber Amplifiers (EDFAs). The model leverages machine-learning techniques to determine polynomial coefficients, achieving high accuracy and computational efficiency. The polynomial model demonstrated high accuracy in estimating the noise figure, with errors comparable to the inherent uncertainty in the measurement datasets. The 90%-threshold for absolute errors ranged from 0.05 to 0.28 dB, and the 99%-threshold ranged from 0.09 to 0.46 dB. These results indicate that the model provides reliable noise figure estimations, comparable to the accuracy of the measurement instruments. The analysis revealed that incorporating data from multiple devices is essential to account for manufacturing variations. Accuracy improved consistently up to three datasets, after which it stabilized with only minor gains as the number increased. This finding suggests that using measurements from multiple devices, even with smaller datasets, is a more effective strategy for achieving good model performance. The model's computational efficiency was evaluated by measuring the execution time of the noise figure evaluation functions. The estimate_NF_array method was found to be approximately 80 times faster than the estimate_NF method when evaluating per-element computation time with a large array length. This efficiency makes the model suitable for integration into larger, more comprehensive EDFA models without becoming a performance bottleneck. The memory usage of the model was also found to be minimal, with the total size of the Python scripts and model files being approximately 46 kB and the RAM usage of the EDFA class instance being 25.72 kB. The integration of the polynomial model into a deep-learning framework for EDFA performance prediction demonstrated its practical applicability. The results showed that the estimation model significantly reduced the maximum and mean absolute errors in noise figure predictions compared to the fixed-value method. This improvement highlights the model's ability to enhance prediction accuracy and overall performance in real-world applications. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Case** & **EDFA 1** & **EDFA 2** & **EDFA 3** & **EDFA 4** & **EDFA 5** & **EDFA 6** & **EDFA 7** \\ \hline Fixed NF & 0.1269 & 0.0849 & 0.0583 & 0.0590 & 0.0566 & 0.0587 & 0.0771 \\ \hline Model NF & 0.1093 & 0.0816 & 0.0543 & 0.0596 & 0.0555 & 0.0625 & 0.0772 \\ \hline  & \(-13.87\%\) & \(-3.89\%\) & \(-6.86\%\) & \(+1.02\%\) & \(-1.94\%\) & \(+6.47\%\) & \(+0.13\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance of deep-learning EDFA model, mean absolute error [dB]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Case** & **EDFA 1** & **EDFA 2** & **EDFA 3** & **EDFA 4** & **EDFA 5** & **EDFA 6** & **EDFA 7** \\ \hline Fixed NF & 92.2129 & 95.3613 & 95.9068 & 97.7005 & 91.6659 & 94.8887 & 93.1631 \\ \hline Model NF & 89.3877 & 95.2287 & 96.0442 & 97.5909 & 91.9185 & 94.2216 & 93.5089 \\ \hline  & \(-2.82\%\) & \(+0.09\%\) & \(+0.14\%\) & \(-0.11\%\) & \(+0.25\%\) & \(-0.67\%\) & \(+0.35\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance of deep-learning EDFA model, adjusted \(R^{2}\) score [%]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Case** & **EDFA 1** & **EDFA 2** & **EDFA 3** & **EDFA 4** & **EDFA 5** & **EDFA 6** & **EDFA 7** \\ \hline Fixed NF & 0.1908 & 0.1413 & 0.0810 & 0.0813 & 0.0782 & 0.0828 & 0.1093 \\ \hline Model NF & 0.1715 & 0.1390 & 0.0773 & 0.0828 & 0.0758 & 0.0885 & 0.1081 \\ \hline  & \(-10.11\%\) & \(-1.63\%\) & \(-4.57\%\) & \(+1.84\%\) & \(-3.07\%\) & \(+6.88\%\) & \(-1.10\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Performance of deep-learning EDFA model, RMSE [dB]. While the polynomial model has shown promising results, there are some limitations to consider.