Using the inverse scattering method known for solving partial differential equations such as nonlinear Schrödinger equation, we analyse a fibre optic communication system which maps data on both discrete and continuous spectra defined by nonlinear Fourier transform. By signalling over both spectra, the degrees of freedom of the channel can be exploited to potentially increase the achievable data-rate in an attempt to approach the capacity of the optical fiber.
Considering such a system, our results demonstrate the signal-dependency of the noise mapped to the nonlinear frequency domain. The temporal broadening factor is also studied for different pulse shapes and pulse sequence lengths modulated over the continuous spectrum. Finally, the error rate performance of the communication system signalling over both discrete and continuous spectra is presented.