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 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 $\mathcal{O}(D{\log }^{2}D)$ 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.

Invited paper presented in the special session on "Signal Processing, Coding, and Information Theory for Optical Communications" at IEEE SPAWC 2015. Minor changes

References in corpus (4)

• Information Transmission using the Nonlinear Fourier Transform, Part II: Numerical Methods
• Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers
• Fast Numerical Nonlinear Fourier Transforms
• Soliton-based discriminator of non-coherent optical pulses

Cited by in corpus (5)

• 125 Gbps Pre-Compensated Nonlinear Frequency-Division Multiplexed Transmission
• Nonlinear Inverse Synthesis for Optical Links with Distributed Raman Amplification
• Signaling on the Continuous Spectrum of Nonlinear Optical fiber
• Direct nonlinear Fourier transform algorithms for the computation of solitonic spectra in focusing nonlinear Schrödinger equation
• Fast Inverse Nonlinear Fourier Transforms for Continuous Spectra of Zakharov-Shabat Type