Nonlinear Fourier Spectrum Characterization of Time-Limited Signals


Addressing the optical communication systems employing the nonlinear Fourier transform (NFT) for the data modulation/demodulation, we provide an explicit proof for the properties of the signals emerging in the so-called $b$ -modulation method, the nonlinear signal modulation technique that provides explicit control over the signal extent. We present details of the procedure and related rigorous mathematical proofs addressing the case where the time-domain profile corresponding to the $b$ -modulated data has a limited duration, and when the bound states corresponding to specifically chosen discrete solitonic eigenvalues and norming constants, are also present. We also prove that the number of solitary modes that we can embed without violating the exact localisation of the time-domain profile, is actually infinite. Our theoretical findings are illustrated with numerical examples, where simple example waveforms are used for the $b$ -coefficient, demonstrating the validity of the developed approach. We also demonstrate the influence of the bound states on the noise tolerance of the b-modulated system.

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Divisions: College of Engineering & Physical Sciences > School of Informatics and Digital Engineering > Electrical and Electronic Engineering
College of Engineering & Physical Sciences > Aston Institute of Photonics Technology (AIPT)
Additional Information: © 2020 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.
Uncontrolled Keywords: b-modulation,coherent communications,inverse scattering,nonlinear Fourier transform,Optical fibre communication,optical solitons,Electrical and Electronic Engineering
Publication ISSN: 1558-0857
Full Text Link: https://arxiv.o ... /abs/1907.01331
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2020-05-31
Published Online Date: 2020-02-11
Accepted Date: 2020-02-01
Authors: Shepelsky, Dmitry
Vasylchenkova, Anastasiia (ORCID Profile 0000-0002-6997-9427)
Prilepsky, Jaroslaw E. (ORCID Profile 0000-0002-3035-4112)
Karpenko, Iryna



Version: Accepted Version

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