Polynomial Modeling of Noise Figure in Erbium-Doped Fiber Amplifiers

Erbium-Doped Fiber Amplifiers (EDFAs) are fundamental to optical communication networks, providing signal amplification while introducing noise that affects system performance. Accurate noise figure estimation is critical for optimizing link budgets, monitoring optical Signal-to-Noise Ratio (OSNR), and enabling real-time network optimization. Traditional analytical models, while computationally efficient, often fail to capture device-specific variations, whereas machine-learning-based approaches require large training datasets and introduce high computational overhead. This paper proposes a polynomial regression model for real-time EDFA noise figure estimation, striking a balance between accuracy and computational efficiency. The model leverages Generalized Least Squares (GLS) regression to fit a multivariate polynomial function to measured EDFA noise figure data, ensuring robustness against measurement noise and dataset variations. The proposed method is benchmarked against experimental measurements from multiple EDFAs, achieving prediction errors that are within the measurement uncertainty of Optical Spectrum Analyzers (OSAs). Furthermore, the model demonstrates strong generalization across different EDFA architectures, outperforming analytical models while requiring significantly less data than deep-learning approaches. Computational efficiency is also analyzed, showing that inference time is below 0.2 ms per evaluation, making the model suitable for real-time digital-twin applications in optical networks. Future work will explore hybrid modeling approaches, integrating physics-based regression with Machine Learning (ML) to enhance performance in high-variance spectral regions. These results highlight the potential of lightweight polynomial regression models as an alternative to complex ML-based solutions, enabling scalable and efficient EDFA performance prediction for next-generation optical networks.