Second Order Statistics of the Scattering Vector Defining the D-T Nonlinear Fourier Transform

Conference: SCC 2017 - 11th International ITG Conference on Systems, Communications and Coding
02/06/2017 - 02/09/2017 at Hamburg, Germany

Proceedings: ITG-Fb. 268: SCC 2017

Pages: 6Language: englishTyp: PDF

Personal VDE Members are entitled to a 10% discount on this title

Authors:
Wahls, Sander (Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628 CD, Delft, The Netherlands)

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.