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A Novel Optical-Based Methodology for Improving Nonlinear Fourier Transform

Author

Listed:
  • Julian Hoxha

    (College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait)

  • Wael Hosny Fouad Aly

    (College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait)

  • Erdjana Dida

    (Engineering and Technology, American College of the Middle East, Egaila 54200, Kuwait)

  • Iva Kertusha

    (College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait)

  • Mouhammad AlAkkoumi

    (College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait)

Abstract

The increasing demand for bandwidth and long-haul transmission has led to new methods of signal processing and transmission in optical fiber communication systems. The nonlinear Fourier transform is one of the most recent methods proposed, and is able to represent an integrable nonlinear Schrödinger equation (NLSE) channel in terms of its continuous and discrete spectrum, to overcome the limitation of the bandwidth imposed by the Kerr effect on silica fibers. In this paper, we will propose and investigate the Boffetta-Osburne method for the direct nonlinear Fourier implementation, and the Gel’fand-Levitan-Marchenko equation for the inverse nonlinear Fourier, as only the continuous part of the nonlinear spectrum will be used to encode information. A novel methodology is proposed to improve their numerical implementation with respect to the NLSE, and we analyze in detail how the improved algorithm can be used in a real optical system, by investigating three different modulation schemes. We report increased performance transmission and consistency in the numerical results when the proposed methodology is applied. Our results show that b-modulation will increase the Q-factor by 2 dB with respect to the other two modulations. The improvement results with our proposed methodology suggest that b-modulation applied only to a continuous part of the nonlinear spectrum is a very effective method for maximizing both the transmission bandwidth and distance in optical fiber communication systems.

Suggested Citation

  • Julian Hoxha & Wael Hosny Fouad Aly & Erdjana Dida & Iva Kertusha & Mouhammad AlAkkoumi, 2022. "A Novel Optical-Based Methodology for Improving Nonlinear Fourier Transform," Mathematics, MDPI, vol. 10(23), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4513-:d:988132
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    References listed on IDEAS

    as
    1. Andrei D. Polyanin, 2019. "Comparison of the Effectiveness of Different Methods for Constructing Exact Solutions to Nonlinear PDEs. Generalizations and New Solutions," Mathematics, MDPI, vol. 7(5), pages 1-19, April.
    2. Bo Xu & Sheng Zhang, 2022. "Analytical Method for Generalized Nonlinear Schrödinger Equation with Time-Varying Coefficients: Lax Representation, Riemann-Hilbert Problem Solutions," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
    3. Weideman, J.A.C. & Herbst, B.M., 1997. "Finite difference methods for an AKNS eigenproblem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(1), pages 77-88.
    4. Julian Hoxha & Satoshi Shimizu & Gabriella Cincotti, 2020. "On the performance of all-optical OFDM based PM-QPSK and PM-16QAM," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 75(4), pages 355-367, December.
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