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A closed-form model for the nonlinear interference (NLI) in Raman amplifiedlinks 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,wavelength-dependent fibre parameters, launch-power profiles, and is testedover a distributed Raman-amplified system setup. The formula is suitable forultra-wideband (UWB) optical transmission systems and is applied in a signalwith 13~THz optical bandwidth corresponding to transmission over the S-, C-,and L- band. The accuracy of the closed-form formula is validated throughcomparison with numerical integration of the Gaussian noise (GN) model andsplit-step Fourier method (SSFM) simulations in a point-to-point transmissionlink.

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