Some results on discrete eigenvalues for the Stochastic Nonlinear Schrödinger Equation in fiber optics

Abstract

We study a stochastic Nonlinear Schrödinger Equation (NLSE), with additive white Gaussian noise, by means of the Nonlinear Fourier Transform (NFT). In particular, we focus on the propagation of discrete eigenvalues along a focusing fiber. Since the stochastic NLSE is not exactly integrable by means of the NFT, then we use a perturbation approach, where we assume that the signal-to-noise ratio is high. The zeroth-order perturbation leads to the deterministic NLSE while the first-order perturbation allows to describe the statistics of the discrete eigenvalues. This is important to understand the properties of the channel for recently devised optical transmission techniques, where the information is encoded in the nonlinear Fourier spectrum.

Mitigating the Impact of Noise on Nonlinear Frequency Division Multiplexing

“…A fundamental difference of NFDM with respect to OFDM is that the NFT, unlike the ordinary Fourier transform, is not a unitary transformation, so that the statistics of the amplified spontaneous emission (ASE) noise, modeled as additive white Gaussian noise (AWGN) in time domain, are not preserved in the nonlinear frequency domain [3,8,[19][20][21]. These modified statistics result in an unfavorable dependence of performance on the signal duration, which practically limits the achievable spectral efficiency [9].…”