Improved signal fidelity at higher SNR using probabilistic constellation shaping with enhanced Gaussian noise model

摘要

Abstract The paper discusses the implementation of enhanced Gaussian noise (EGN) model-based probabilistic shaping (PS) in long-haul optical transmission systems to mitigate the effects of non-linearities that can occur when using different input distributions for constellation shaping. This approach aims to increase the achievable information rate (AIR) while maintaining a reasonable signal-to-noise ratio (SNR) at optimal launch power. The authors propose that this approach can improve the efficiency and reliability of long-haul optical transmission systems by reducing the impact of fiber non-linearities. The proposed method aims to maximize mutual information in a coherent optical system without relying on digital signal processors. This is achieved by optimizing PS using sequential quadratic programming in a back-to-back configuration with 16-Quadrature Amplitude Modulation. The objective function is set to minimize the second and fourth order moments of input, resulting in reduced higher order noise coefficients and minimal non-linear interference noise at higher values of SNR. The EGN model is used to optimize the PS, resulting in an SNR value of 14.52 dBm and a minimal SNR penalty of 0.15 dBm towards the uniform probability distribution. The optimized EGN model returns μ^4documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${widehat{mu }}_{4}$$end{document} and μ^6documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${widehat{mu }}_{6}$$end{document} values of 1.41 and 2.24 respectively, which further contribute to reducing the impact of higher order noise coefficients on the system.