On nonlinear Fourier transform-based fibre-optic communication systems for periodic signals

  • Morteza Kamalian Kopae

Student thesis: Doctoral ThesisDoctor of Philosophy


As the demand for information rate grows on a daily basis, new ways of improving the efficiency of fibre-optic communication systems, the backbone of the global data network,are highly anticipated. Nonlinear Fourier transform (NFT) is one of the newly emerged techniques showing promising results in recent studies both in simulation and experiment. Along this path, this method has shown its potential to overcome some difficulties of the fibre-optic communication regarding nonlinear distortions, especially the crosstalk between the user’s bands in wavelength division multiplexing (WDM) systems.

NFT-based systems, however, in the conventional, widely considered case of vanishing boundary signals, have exhibited some drawbacks related to the computational complexity and spectral efficiency. Both problems are the direct consequences of large signal duration ensued from the vanishing boundary condition. Considering periodic solutions to the nonlinear Schrödinger equation is among attempts to solve this problem. It helps to decrease the processing window at the receiver and gives full control over the communication-related parameters of the signal. Periodic NFT (PNFT) can also be implemented through fast numerical methods which makes it yet more appealing.

In this thesis, a general framework to implement PNFT in fibre-optic communication systems is proposed. As the most challenging part of such a system, the inverse transformation stage is particularly taken attention to, and a few ways to perform it are put forward. From the simplest signals with analytically known nonlinear spectrum to a complete periodic solution with arbitrary, finite number of degrees of freedom, several system configurations are conferred and evaluated in terms of their performance. Common measures such as bit error rate, quality factor and mutual information are considered in scrutinising the systems.Based on simulation results, we conclude that the PNFT can, in fact, improve the mutual information by overcoming some shortcomings of the vanishing boundary NFT.
Date of Award4 Dec 2018
Original languageEnglish
SupervisorSergei Turitsyn (Supervisor) & Yaroslav Prylepskiy (Supervisor)


  • optical communications
  • nonlinear Fourier transform
  • Reimann-Hilbert problem
  • periodic nonlinear Fourier transform

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