### Abstract

The nonlinear Fourier transform (NFT) is a potentially promising way to mitigate nonlinear signal distortions in fiber-optic communication systems [1-4]. Recently, the new approach named the b-modulation was introduced [1] that allows to control the temporal duration of NFT-generated signals. In the 'traditional' NFT-based communication, the nonlinear spectrum, r (ξ) is used to modulate data. Then the signal duration depends on the signal energy and is not predetermined and controlled. The utilisation of the NFT scattering coefficient b (ξ) gives a possibility to control the pulse duration in time domain under condition that the Fourier spectrum of b (ξ) is localized. In particular, the OFDM format satisfies that condition. It was already shown that the properties of the effective noise in the NFT domain differ from a circular Gaussian noise. More specifically, such a noise is signal-dependent and non-circular [2, 3]. It was shown in [4] that the covariance B
_{1} and pseudo-covariance B
_{2} characteristics related to b-coefficient of NFT spectrum depend on the propagation distance. Here, we extend our previous work and examine noise characteristics for a novel b-modulation transmission introduced in [1]. We demonstrate that the variances behaviour is generic and do not depend on a specifics of NFT modulation. The presence of amplifier spontaneous emission in the optical link translates into the effective noise in the nonlinear spectral domain as an effective additive term N (ξ, b (ξ, 0)): e{-4 i \xi{2L}b}(\xi, L) = b(\xi, 0) + N(\xi, b(\xi, 0), L), where \xi is the 'nonlinear frequency' (NFT spectral parameter): \langle N (\xi)N (\xi ')\rangle = 2DL\pi \delta (\xi -\xi')B{1}(\xi, L), \langle N (\xi)N(\xi')\rangle = 2DL\pi \delta (\xi - \xi ')B {2}(\xi, L).

Original language | English |
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Title of host publication | 2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2019 |

Publisher | IEEE |

ISBN (Electronic) | 978-1-7281-0469-0 |

ISBN (Print) | 978-1-7281-0470-6 |

DOIs | |

Publication status | Published - 17 Oct 2019 |

Event | CLEO/Europe-EQEC Conference - International Congress Centre, Munich, Germany Duration: 23 Jun 2019 → 27 Jun 2019 http://www.cleoeurope.org/ |

### Conference

Conference | CLEO/Europe-EQEC Conference |
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Country | Germany |

City | Munich |

Period | 23/06/19 → 27/06/19 |

Internet address |

### Bibliographical note

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## Cite this

*2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2019*[8872660] IEEE. https://doi.org/10.1109/CLEOE-EQEC.2019.8872660