Signal Modulation and Processing in Nonlinear Fibre Channels by Employing the Riemann–Hilbert Problem

Most of the nonlinear Fourier transform (NFT) based optical communication systems studied so far deal with the burst mode operation that substantially reduce achievable spectral efficiency. The burst mode requirement emerges due to the very nature of the commonly used version of the NFT processing method: it can process only rapidly decaying signals, requires zero-padding guard intervals for processing of dispersion-induced channel memory, and does not allow one to control the time-domain occupation well. Some of the limitations and drawbacks imposed by this approach can be rectified by the recently introduced more mathematically demanding periodic NFT processing tools. However, the studies incorporating the signals with cyclic prefix extension into the NFT transmission framework have so far lacked the efficient digital signal processing (DSP) method of synthesizing an optical signal, the shortcoming that diminishes the approach flexibility. In this paper, we introduce the Riemann-Hilbert problem (RHP) based DSP method as a flexible and expandable tool that would allow one to utilize the periodic NFT spectrum for transmission purposes without former restrictions. First, we outline the theoretical framework and clarify the implementation underlying the proposed new DSP method. Then we present the results of numerical modelling quantifying the performance of long-haul RHP-based transmission with the account of optical noise, demonstrating the good performance quality and potential of RHP-based optical communication systems.