Statistics of the Nonlinear Discrete Spectrum of a Noisy Pulse
| Autor: | Garcia-Gomez, Francisco Javier, Aref, Vahid |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Journal of Lightwave Technology, 2019 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1109/JLT.2019.2917996 |
| Popis: | 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. Comment: Updated numerical results |
| Databáze: | arXiv |
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