Performance Limit of Fiber-Longitudinal Power Profile Estimation Methods

This paper presents analytical results on longitudinal power profile estimation (PPE) methods, which visualize signal power evolution in optical fibers at a coherent receiver. The PPE can be formulated as an inverse problem of the nonlinear Schr\"odinger equation, where the nonlinear coefficient (and thus signal power) is reconstructed from boundary conditions, i.e., transmitted and received signals. Two types of PPE methods are reviewed and analyzed, including correlation-based methods (CMs) and minimum-mean-square-error-based methods (MMSEs). The analytical expressions for their output power profiles and spatial resolution are provided, and thus the theoretical performance limits of the two PPE methods and their differences are clarified. The derived equations indicate that the estimated power profiles of CMs can be understood as the convolution of a true power profile and a smoothing function. Consequently, the spatial resolution and measurement accuracy of CMs are limited, even under noiseless and distortionless conditions. Closed-form formulas for the spatial resolution of CMs are shown to be inversely proportional to the product of a chromatic dispersion coefficient and the square of signal bandwidth. With MMSEs, such a convolution effect is canceled out and the estimated power profiles approach a true power profile under a fine spatial step size.