Noise and Performance Analysis of Fiber-Longitudinal Power Profile Estimation

Previous investigations have preliminarily revealed that the two main methods of fiber-longitudinal power profile estimation (PPE), the correlation-based (CM) and minimum-mean-square-error-based (MMSE) methods, show different performance and noise robustness. To thoroughly comprehend the PPE behavior in the presence of stochastic noise, this study introduces the first comprehensive noise analysis of CM-PPE and MMSE-PPE. By introducing a novel metric, the profile-to-noise ratio (PNR), we derive equations verifying that the CM-PPE offers enhanced noise tolerance at the expense of reduced power profile fidelity, whereas MMSE-PPE exhibits the converse characteristics. Moreover, a further noise analysis is also performed with the real-time assumption that the number of processed samples per block is limited and the profiles output by different processing blocks are averaged. Based on the theoretical expressions and the aid of numerical simulation, we confirm that the conventional averaging operation is suitable for CM-PPE, while MMSE-PPE needs to modify the averaging implementation structure for a more stable estimation. Our theoretical insights facilitate a deeper comprehension of PPE, paving the way for its real-time application.