A Closed-form Expression for the Gaussian Noise Model in the Presence of Raman Amplification

A closed-form model for the nonlinear interference (NLI) in Raman amplified links is presented, the formula accounts for both forward (FW) and backward (BW) pumping schemes and inter-channel stimulated Raman scattering (ISRS) effect. The formula also accounts for an arbitrary number of pumps, discrete or distributed Raman amplification setup, wavelength-dependent fibre parameters, and launch power profiles. The formula is suitable for ultra-wideband (UWB) optical transmission systems and is applied in a system with 13 THz optical bandwidth corresponding to transmission over the S-, C-, and L- band. The accuracy of the closed-form formula is validated through comparison with numerical integration of the Gaussian noise (GN) model and split-step Fourier method (SSFM) simulations in a point-to-point transmission link.