A Gaussian noise model of spectral amplitudes in soliton communication systems

Using the nonlinear Fourier transform, one can transform a time-domain fibre channel (characterised by the nonlinear Schrödinger equation) into multiple parallel independent channels. Exploiting this property, nonlinear frequency division multiplexing (NFDM) was proposed [1]. Such an NFT-based transmission approach has prompted the study of the channel noise (on the eigenvalues and spectral amplitudes) in the (nonlinear) spectral domain. In this paper, we propose a consistent noise model for the evolution of an eigenvalue. Then, following the approach in [2], we develop a Gaussian noise model for a spectral amplitude (assuming its perturbation is largely due to the perturbation in the eigenvalue).