Contents I. Introduction
Nonlinear frequency division multiplexing (NFDM) technology used the mathematical tool of nonlinear Fourier transform (NFT) to modulate the signal to the nonlinear frequency domain, which effectively offsets the influence of dispersion and nonlinear effects, showing strong competitiveness and broad application prospects. Therefore, its related research in various directions received extensive attention [1]. When the NFDM system no longer considered the effects of dispersion and nonlinear effects, fiber loss and noise became the main factors affecting the performance of the NFDM system. In order to solve the loss problem, the lossless path-averaged (LPA) proposed in Ref. [2] approximated the channel model affected by fiber loss to the lossless nonlinear Schrodinger equation (NLSE) or Manakov equation, which basically satisfied the integrability of the channel model. As for the noise, the NFDM system mainly consisted of three types of noise such as optical amplified spontaneous emission (ASE) noise, processing noise caused by the decrease of the accuracy of the NFT/INFT algorithm, and phase noise due to the laser linewidth. In the linear domain, ASE noise was usually modeled as Gaussian white noise, but it did not apply to the nonlinear frequency domain. For processing noise, there was no specific model on processing noise. As for phase noise, it caused the overall rotation of the nonlinear spectrum in NFDM systems, which seriously affected the system performance. The above factors brought more challenges to the study of noise in NFDM systems and made it a major hotspot.
