A Modulation Format Correction Formula for the Gaussian Noise Model in the Presence of Inter-Channel Stimulated Raman Scattering

A closed-form formula is derived, which corrects for the modulation format dependence of the Gaussian noise (GN) model in the presence of inter-channel stimulated Raman scattering (ISRS). The analytical result enables a rapid estimate of the nonlinear interference (NLI) for arbitrary modulation formats and avoids the need for complex integral evaluations and split-step simulations. It is shown that the modulation format dependent NLI can be approximated by two contributions, one originating from a single span and one asymptotic contribution for a large number of spans. The asymptotic contribution is solved in closed-form for arbitrary links consisting of identical spans, making the result applicable for fiber systems using lumped, distributed, or hybrid amplification schemes. The methodology is applied to the ISRS GN model and a modulation format correction formula in closed-form is derived, which accounts for an arbitrary number of spans, ISRS, arbitrary launch power distributions and wavelength dependent dispersion and attenuation. The proposed formula is validated by numerical simulations over the entire C+L band for multiple fiber types.