Improved Soliton Amplitude Estimation via the Continuous Spectrum

In soliton communication systems, the continuous nonlinear spectrum, ideally zero, is conventionally ignored at the receiver. In this paper, we exploit correlation between the received continuous spectrum and perturbations of the discrete soliton eigenvalue. We propose four estimation schemes, classified into two categories, one based on the nonlinear Fourier transform (NFT) and the other based on minimum Euclidean distance. Both categories comprise two schemes, one that exploits the received continuous spectral function to achieve improved estimation and one that does not. Numerical simulations demonstrate that significant reduction in estimation error can be achieved when the continuous spectrum is exploited, translating into improved information transmission rates of up to ${\text{46}}\%$ compared to the reference NFT-based scheme.