### 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 |
---|---|

Country | Germany |

City | Munich |

Period | 23/06/19 → 27/06/19 |

Internet address |

### Fingerprint

### Bibliographical note

2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.### 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

}

*2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2019.*, 8872660, IEEE, CLEO/Europe-EQEC Conference, Munich, Germany, 23/06/19. https://doi.org/10.1109/CLEOE-EQEC.2019.8872660

**Signal-dependent noise for b-modulation NFT-based transmission.** / Vasylchenkova, Anastasiia; Pankratova, Maryna; Prilepsky, Jaroslaw E.; Chichkov, Nikolay B.; Turitsyn, Sergei K.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Signal-dependent noise for b-modulation NFT-based transmission

AU - Vasylchenkova, Anastasiia

AU - Pankratova, Maryna

AU - Prilepsky, Jaroslaw E.

AU - Chichkov, Nikolay B.

AU - Turitsyn, Sergei K.

N1 - 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

PY - 2019/10/17

Y1 - 2019/10/17

N2 - 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).

AB - 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).

UR - http://www.cleoeurope.org/

UR - https://ieeexplore.ieee.org/document/8872660

UR - http://www.scopus.com/inward/record.url?scp=85074661278&partnerID=8YFLogxK

U2 - 10.1109/CLEOE-EQEC.2019.8872660

DO - 10.1109/CLEOE-EQEC.2019.8872660

M3 - Conference contribution

SN - 978-1-7281-0470-6

BT - 2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2019

PB - IEEE

ER -