The advent of silica-based low-cost standard single-mode fibers revolutionized the whole communication industry. The deployment of optical fibers in the networks induces a paradigm shift in the communication technologies used for long-haul information transfer. However, the communication using the optical fibers is affected by several linear and nonlinear effects. The most common linear effects are attenuation and chromatic dispersion, whereas the dominant nonlinear effect is the Kerr effect. The Kerr effect induces a power-dependent nonlinear distortion for the signal propagating in the optical fiber. The detrimental effects of the Kerr nonlinearity limit the capacity of long-haul optical communication systems. Fiber Kerr nonlinearity compensation using digital signal processing (DSP) techniques has been well investigated over several years. In this paper, we provide a comprehensive tutorial, including the fundamental mathematical analysis, on the characteristics of the optical fiber channel, the origin of the Kerr nonlinearity effect, the theory of the pulse propagation in the optical fiber, and the numerical and analytical tools for solving the pulse propagation equation. In addition, we provide a concise review of various DSP techniques for fiber nonlinearity compensation, such as digital back-propagation, Volterra series-based nonlinearity equalization, perturbation theory-based nonlinearity compensation, and phase conjugation. We also carry out numerical simulation and the complexity evaluation of the selected nonlinearity compensation techniques.

基于二氧化硅的低成本标准单模光纤的出现彻底改变了整个通信行业。光纤在网络中的部署引发了用于长途信息传输的通信技术的范式转变。然而，使用光纤的通信受到多种线性和非线性效应的影响。最常见的线性效应是衰减和色散，而主要的非线性效应是克尔效应。对于在光纤中传播的信号，克尔效应会引起与功率相关的非线性失真。克尔非线性的不利影响限制了长距离光通信系统的容量。多年来，人们对使用数字信号处理 (DSP) 技术的光纤克尔非线性补偿进行了深入研究。在本文中，我们提供了一个综合教程，包括基础数学分析、光纤通道特性、克尔非线性效应的起源、光纤中脉冲传播理论以及数值和分析工具用于求解脉冲传播方程。此外，我们简要回顾了用于光纤非线性补偿的各种 DSP 技术，例如数字反向传播、基于 Volterra 级数的非线性均衡、基于微扰理论的非线性补偿和相位共轭。我们还对选定的非线性补偿技术进行了数值模拟和复杂性评估。光纤通道的特性，克尔非线性效应的起源，光纤中脉冲传播的理论，以及求解脉冲传播方程的数值和解析工具。此外，我们简要回顾了用于光纤非线性补偿的各种 DSP 技术，例如数字反向传播、基于 Volterra 级数的非线性均衡、基于微扰理论的非线性补偿和相位共轭。我们还对选定的非线性补偿技术进行了数值模拟和复杂性评估。光纤通道的特性，克尔非线性效应的起源，光纤中脉冲传播的理论，以及求解脉冲传播方程的数值和解析工具。此外，我们简要回顾了用于光纤非线性补偿的各种 DSP 技术，例如数字反向传播、基于 Volterra 级数的非线性均衡、基于微扰理论的非线性补偿和相位共轭。我们还对选定的非线性补偿技术进行了数值模拟和复杂性评估。我们简要回顾了用于光纤非线性补偿的各种 DSP 技术，例如数字反向传播、基于 Volterra 级数的非线性均衡、基于微扰理论的非线性补偿和相位共轭。我们还对选定的非线性补偿技术进行了数值模拟和复杂性评估。我们简要回顾了用于光纤非线性补偿的各种 DSP 技术，例如数字反向传播、基于 Volterra 级数的非线性均衡、基于微扰理论的非线性补偿和相位共轭。我们还对选定的非线性补偿技术进行了数值模拟和复杂性评估。