Performance Enhancement of the High-order QAM Transmission-based Kerr Non-linearity Coefficient Estimation Scheme for Hollow-core Fibers

Accurate estimation of the non-linearity coefficient in optical fibers is crucial for assessing system transmission capabilities and designing margin. However, the majority of existing non-linearity estimation schemes are only applicable to scenarios with high non-linearity intensity, making it challenging to accurately estimate the coefficients for hollow-core fibers (HCFs) or short pieces of fiber in specific applications. To address this issue, one existing scheme is based on high-order quadrature amplitude modulation (QAM) transmission, that is, the value of the nonlinear coefficient is calculated by analyzing the linear relationship between the square of the amplitude of each constellation point and the corresponding nonlinear phase shift in the high-order QAM signal after transmission in HCF. In this paper, the potential technical challenges associated with this approach are analyzed, including the underestimation of the non-linearity coefficient caused by the overcompensation of the conventional block-wise phase recovery algorithm for the nonlinear phase shift; the erroneous reference constellation point selection used for phase shift calculation due to traditional maximum likelihood decision criteria; and the outlier problem existed in the curve fitting process caused by the weak noise resilience of low-amplitude constellation points. Addressing these issues, an performance-enhanced non-linearity coefficient estimation scheme is proposed, incorporating loop-back blind phase search (BPS) phase recovery, K-means clustering-based optimized decision, and outlier discarding techniques, aiming to enable more accurate and precise estimation of the nonlinear parameter at experimentally achievable signal-to-noise ratios (SNRs). Simulation results demonstrate that the proposed scheme consistently outperforms the traditional scheme under different non-linearity intensities and SNRs, exhibiting a significant reduction in the average relative error and variance of the estimation results.