Second order statistics of the scattering vector defining the d-t nonlinear Fourier transform

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Abstract

The impact of time-domain noise on the nonlinear Fourier transform is currently not well understood. Most, if not all, available results are based on perturbation theory and become exact only in the low-noise regime. In this paper, it is pointed out that the mean and the (conventional and complementary) covariance of the scattering vector [a(z) b(z)](exp T) that is used to define the discrete-time nonlinear Fourier transform can be computed exactly if a known deterministic signal is contaminated with circular symmetric white noise. Since the scattering vector is a polynomial in z(exp -1), also the second-order statistics of its coefficient vector are derived. This result is finally used to determine the second-order statistics of an arbitrary multipoint scattering vector, in which the values of the scattering vector for several arguments are stacked. The results are illustrated in a numerical example, and potential extensions are discussed.
Original languageEnglish
Title of host publicationProceedings of the 11th International ITG Conference on Systems, Communications and Coding (SCC 2017)
EditorsG. Bauch, A. Klein
Place of PublicationBerlin-Offenbach, Germany
PublisherVDE Verlag
Number of pages6
ISBN (Print)978-3-8007-4362-9
Publication statusPublished - 2017
EventSCC 2017 11th International ITG Conference on Systems, Communications and Coding - Hamburg, Germany
Duration: 6 Feb 20179 Feb 2017

Conference

ConferenceSCC 2017 11th International ITG Conference on Systems, Communications and Coding
Abbreviated titleSCC 2017
CountryGermany
CityHamburg
Period6/02/179/02/17

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  • Cite this

    Wahls, S. (2017). Second order statistics of the scattering vector defining the d-t nonlinear Fourier transform. In G. Bauch, & A. Klein (Eds.), Proceedings of the 11th International ITG Conference on Systems, Communications and Coding (SCC 2017) VDE Verlag.