Statistics of the Nonlinear Discrete Spectrum of a Noisy Pulse
Garcia-Gomez, Francisco Javier ; Aref, Vahid
arXiv, Tome 2019 (2019) no. 0, / Harvested from
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.
Publié le : 2019-01-31
Classification:  Computer Science - Information Theory 
@article{1901.11419,
     author = {Garcia-Gomez, Francisco Javier and Aref, Vahid},
     title = {Statistics of the Nonlinear Discrete Spectrum of a Noisy Pulse},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1901.11419}
}

Garcia-Gomez, Francisco Javier; Aref, Vahid. Statistics of the Nonlinear Discrete Spectrum of a Noisy Pulse. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1901.11419/