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

## TL;DR

This paper derives a closed-form correction formula for the Gaussian Noise model that accounts for modulation format dependence and inter-channel stimulated Raman scattering, enabling rapid and accurate nonlinear interference estimation in fiber-optic systems.

## Contribution

A novel closed-form modulation format correction formula for the GN model in the presence of ISRS, applicable to various fiber systems and configurations.

## Key findings

- The correction formula accurately predicts NLI across the C+L band.
- Validation shows high agreement with numerical simulations.
- The method simplifies nonlinear interference estimation in complex fiber links.

## Abstract

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 an arbitrary link function, making the result applicable for generic 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, inter-channel stimulated Raman scattering, 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.