  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,
wavelength-dependent fibre parameters, launch-power profiles, and is tested
over a distributed Raman-amplified system setup. The formula is suitable for
ultra-wideband (UWB) optical transmission systems and is applied in a signal
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.
