Statistics of the Nonlinear Discrete Spectrum of a Noisy Pulse

Francisco Javier Garcia-Gomez; Vahid Aref

doi:10.1109/jlt.2019.2917996

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arXiv · 1901.11419

Statistics of the Nonlinear Discrete Spectrum of a Noisy Pulse

Francisco Javier Garcia-Gomez·Vahid Aref

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Abstract

In the presence of additive Gaussian noise, the statistics of the nonlinear Fourier transform (NFT) of a pulse are not yet completely known in closed form. In this paper, we propose a novel approach to study this problem. Our contributions are twofold: first, we extend the existing Fourier Collocation (FC) method to compute the whole discrete spectrum (eigenvalues and spectral amplitudes). We show numerically that the accuracy of FC is comparable to the state-of-the-art NFT algorithms. Second, we apply perturbation theory of linear operators to derive analytic expressions for the joint statistics of the eigenvalues and the spectral amplitudes when a pulse is contaminated by additive Gaussian noise. Our analytic expressions closely match the empirical statistics obtained through simulations.

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Francisco Javier Garcia-Gomez, Vahid Aref. 2019-04-18. Statistics of the Nonlinear Discrete Spectrum of a Noisy Pulse. https://doi.org/10.1109/jlt.2019.2917996

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