###### Abstract  
Nowadays, the distributed fiber Raman amplifier (FRA) has become more and more popular in long-haul fiber systems, owing to its lower noise figures and weaker nonlinear effects in the link. The critical issue in distributed FRAs is the presence of various kinds of noises and their interactions with the signal. However, the existing Raman channel models and their numerical solving methods can only partially describe how the randomly distributed noises interact with the signal. This causes the difficulties in analyzing the distributed FRA precisely and the inconveniences for the applications and the maintenance of FRA systems. In this paper, we propose a modified Raman channel model to describe more comprehensively the interactions between the distributed noises and the signal under the influence of loss, distributed gain, dispersion, and nonlinear effects in the distributed FRA systems. With the comparisons of the error-vector magnitude (EVM) curves, our model can get lower errors in the experimental results regarding bidirectional pumped FRA single-span fiber systems and multi-span systems with backward-pumped FRAs. distributed fiber Raman amplifier; channel modeling; nonlinear Schrodinger equation (NLSE) 2020 103330/app100101330/app10010  
the noise distributions and the nonlinear interactions make it difficult to model the Raman channel precisely, which limits the applications and the commercial use of distributed FRA systems. A Raman channel model with an economical computation cost is significant for expanding the applications of distributed FRAs. There are three main types of Raman channel model. The most accurate channel model is used to solve the coupled nonlinear Schrodinger equation (NLSE) of the pump and signal lights [14; 15; 16]. Unfortunately, there is no general solution for the coupled NLSEs governing different pump architectures. The numerical methods to solve the coupled NLSEs have an extremely high computation cost. When we neglect the pump depletion, the coupled NLSE can be simplified to a simplified NLSE of the signal light. With the equation, we can analyze phenomena such as self-phase modulation (SPM), RIN transfer, and cross-phase modulation (XPM) from the pump lights to the signal lights [17]. However, pump depletion cannot always be neglected, and it will induce dominant errors in the system with high pump power and high Raman gain. The third type of Raman channel model, which refers to the coupled intensity equations of Raman scattering, is a convenient and widely used tool to analyze the change of signal and pump power along the fiber [14; 15; 18]. However, the coupled intensity equations cannot describe the change of signal optical fields, which is disabled to analyze the performance of high-order modulation format communication systems with distributed FRAs. In this paper, referring to the simplified NLSE neglecting pump depletion and the coupled intensity equations of Raman scattering, we propose a novel modified Raman channel model, which describes the propagation of optical signals in fibers governed by a multitude of simultaneous linear and nonlinear phenomena. In our model, we took almost physical processes of distributed FRA into account and employed fewer approximations, which led to a higher accuracy than that of the simplified NLSE neglecting pump depletion and the coupled intensity equations of Raman scattering. When compared with the coupled NLSEs, our model could be solved with an acceptable computation cost. Then, with the experiments, we verified that our model could effectively describe the fiber communication systems employing distributed FRAs. This indicated that our method was more capable of modeling the distributed noise, especially when the latter interacted severely with the signal due to the nonlinear effects.