Digital backpropagation in the nonlinear Fourier domain

Sander Wahls, Son Thai Le, Yaroslav E. Prylepskiy, H. Vincent Poor, Sergei K. Turitsyn

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Nonlinear and dispersive transmission impairments in coherent fiber-optic communication systems are often compensated by reverting the nonlinear Schrödinger equation, which describes the evolution of the signal in the link, numerically. This technique is known as digital backpropagation. Typical digital backpropagation algorithms are based on split-step Fourier methods in which the signal has to be discretized in time and space. The need to discretize in both time and space however makes the real-time implementation of digital backpropagation a challenging problem. In this paper, a new fast algorithm for digital backpropagation based on nonlinear Fourier transforms is presented. Aiming at a proof of concept, the main emphasis will be put on fibers with normal dispersion in order to avoid the issue of solitonic components in the signal. However, it is demonstrated that the algorithm also works for anomalous dispersion if the signal power is low enough. Since the spatial evolution of a signal governed by the nonlinear Schrödinger equation can be reverted analytically in the nonlinear Fourier domain through simple phase-shifts, there is no need to discretize the spatial domain. The proposed algorithm requires only OpDlog2 Dq floating point operations to backpropagate a signal given by D samples, independently of the fiber's length, and is therefore highly promising for real-time implementations. The merits of this new approach are illustrated through numerical simulations.

Original languageEnglish
Title of host publication16th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC
PublisherIEEE
Pages445-449
Number of pages5
ISBN (Electronic)978-1-4799-1931-4
ISBN (Print)9781479919307
DOIs
Publication statusPublished - 27 Aug 2015
Event16th IEEE International Workshop on Signal Processing Advances in Wireless Communications - Stockholm, Sweden
Duration: 28 Jun 20151 Jul 2015

Conference

Conference16th IEEE International Workshop on Signal Processing Advances in Wireless Communications
Abbreviated titleSPAWC 2015
CountrySweden
CityStockholm
Period28/06/151/07/15

Fingerprint

Backpropagation
Nonlinear equations
Fibers
Backpropagation algorithms
Phase shift
Fiber optics
Fourier transforms
Communication systems
Computer simulation

Bibliographical note

© 2015 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.

Keywords

  • digital backpropagation
  • nonlinear Fourier transform
  • nonlinear Schrödinger equation
  • optical fiber

Cite this

Wahls, S., Le, S. T., Prylepskiy, Y. E., Poor, H. V., & Turitsyn, S. K. (2015). Digital backpropagation in the nonlinear Fourier domain. In 16th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC (pp. 445-449). IEEE. https://doi.org/10.1109/SPAWC.2015.7227077
Wahls, Sander ; Le, Son Thai ; Prylepskiy, Yaroslav E. ; Poor, H. Vincent ; Turitsyn, Sergei K. / Digital backpropagation in the nonlinear Fourier domain. 16th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC. IEEE, 2015. pp. 445-449
@inproceedings{b5e9df31d40847b49e04a0ec03aeb0be,
title = "Digital backpropagation in the nonlinear Fourier domain",
abstract = "Nonlinear and dispersive transmission impairments in coherent fiber-optic communication systems are often compensated by reverting the nonlinear Schr{\"o}dinger equation, which describes the evolution of the signal in the link, numerically. This technique is known as digital backpropagation. Typical digital backpropagation algorithms are based on split-step Fourier methods in which the signal has to be discretized in time and space. The need to discretize in both time and space however makes the real-time implementation of digital backpropagation a challenging problem. In this paper, a new fast algorithm for digital backpropagation based on nonlinear Fourier transforms is presented. Aiming at a proof of concept, the main emphasis will be put on fibers with normal dispersion in order to avoid the issue of solitonic components in the signal. However, it is demonstrated that the algorithm also works for anomalous dispersion if the signal power is low enough. Since the spatial evolution of a signal governed by the nonlinear Schr{\"o}dinger equation can be reverted analytically in the nonlinear Fourier domain through simple phase-shifts, there is no need to discretize the spatial domain. The proposed algorithm requires only OpDlog2 Dq floating point operations to backpropagate a signal given by D samples, independently of the fiber's length, and is therefore highly promising for real-time implementations. The merits of this new approach are illustrated through numerical simulations.",
keywords = "digital backpropagation, nonlinear Fourier transform, nonlinear Schr{\"o}dinger equation, optical fiber",
author = "Sander Wahls and Le, {Son Thai} and Prylepskiy, {Yaroslav E.} and Poor, {H. Vincent} and Turitsyn, {Sergei K.}",
note = "{\circledC} 2015 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.",
year = "2015",
month = "8",
day = "27",
doi = "10.1109/SPAWC.2015.7227077",
language = "English",
isbn = "9781479919307",
pages = "445--449",
booktitle = "16th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC",
publisher = "IEEE",
address = "United States",

}

Wahls, S, Le, ST, Prylepskiy, YE, Poor, HV & Turitsyn, SK 2015, Digital backpropagation in the nonlinear Fourier domain. in 16th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC. IEEE, pp. 445-449, 16th IEEE International Workshop on Signal Processing Advances in Wireless Communications, Stockholm, Sweden, 28/06/15. https://doi.org/10.1109/SPAWC.2015.7227077

Digital backpropagation in the nonlinear Fourier domain. / Wahls, Sander; Le, Son Thai; Prylepskiy, Yaroslav E.; Poor, H. Vincent; Turitsyn, Sergei K.

16th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC. IEEE, 2015. p. 445-449.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Digital backpropagation in the nonlinear Fourier domain

AU - Wahls, Sander

AU - Le, Son Thai

AU - Prylepskiy, Yaroslav E.

AU - Poor, H. Vincent

AU - Turitsyn, Sergei K.

N1 - © 2015 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 - 2015/8/27

Y1 - 2015/8/27

N2 - Nonlinear and dispersive transmission impairments in coherent fiber-optic communication systems are often compensated by reverting the nonlinear Schrödinger equation, which describes the evolution of the signal in the link, numerically. This technique is known as digital backpropagation. Typical digital backpropagation algorithms are based on split-step Fourier methods in which the signal has to be discretized in time and space. The need to discretize in both time and space however makes the real-time implementation of digital backpropagation a challenging problem. In this paper, a new fast algorithm for digital backpropagation based on nonlinear Fourier transforms is presented. Aiming at a proof of concept, the main emphasis will be put on fibers with normal dispersion in order to avoid the issue of solitonic components in the signal. However, it is demonstrated that the algorithm also works for anomalous dispersion if the signal power is low enough. Since the spatial evolution of a signal governed by the nonlinear Schrödinger equation can be reverted analytically in the nonlinear Fourier domain through simple phase-shifts, there is no need to discretize the spatial domain. The proposed algorithm requires only OpDlog2 Dq floating point operations to backpropagate a signal given by D samples, independently of the fiber's length, and is therefore highly promising for real-time implementations. The merits of this new approach are illustrated through numerical simulations.

AB - Nonlinear and dispersive transmission impairments in coherent fiber-optic communication systems are often compensated by reverting the nonlinear Schrödinger equation, which describes the evolution of the signal in the link, numerically. This technique is known as digital backpropagation. Typical digital backpropagation algorithms are based on split-step Fourier methods in which the signal has to be discretized in time and space. The need to discretize in both time and space however makes the real-time implementation of digital backpropagation a challenging problem. In this paper, a new fast algorithm for digital backpropagation based on nonlinear Fourier transforms is presented. Aiming at a proof of concept, the main emphasis will be put on fibers with normal dispersion in order to avoid the issue of solitonic components in the signal. However, it is demonstrated that the algorithm also works for anomalous dispersion if the signal power is low enough. Since the spatial evolution of a signal governed by the nonlinear Schrödinger equation can be reverted analytically in the nonlinear Fourier domain through simple phase-shifts, there is no need to discretize the spatial domain. The proposed algorithm requires only OpDlog2 Dq floating point operations to backpropagate a signal given by D samples, independently of the fiber's length, and is therefore highly promising for real-time implementations. The merits of this new approach are illustrated through numerical simulations.

KW - digital backpropagation

KW - nonlinear Fourier transform

KW - nonlinear Schrödinger equation

KW - optical fiber

UR - http://ieeexplore.ieee.org/document/7227077/

UR - http://www.scopus.com/inward/record.url?scp=84953389428&partnerID=8YFLogxK

U2 - 10.1109/SPAWC.2015.7227077

DO - 10.1109/SPAWC.2015.7227077

M3 - Conference contribution

AN - SCOPUS:84953389428

SN - 9781479919307

SP - 445

EP - 449

BT - 16th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC

PB - IEEE

ER -

Wahls S, Le ST, Prylepskiy YE, Poor HV, Turitsyn SK. Digital backpropagation in the nonlinear Fourier domain. In 16th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC. IEEE. 2015. p. 445-449 https://doi.org/10.1109/SPAWC.2015.7227077