Closed-form Expression for the Power Profile in Wideband Systems with Inter-channel Stimulated Raman Scattering

Wideband systems experience significant inter-channel stimulated Raman scattering (ISRS) and channel-dependent losses. Due to the non-uniform attenuation profile, the combined effects of ISRS and fiber loss can only be accurately estimated using numerical methods. In this work, we present an approximate closed-form expression for the channels' power profile accounting for these combined effects. We validate the proposed expression against numerical solutions in the case of CLU transmission, showing high accuracy for both single-span and multi-span fiber-optic links. Additionally, we derive an inverse expression, formulated as a function of the output power, which can be utilized to target a desired optical signal-to-noise ratio (OSNR) profile through pre-emphasis of the launched channel powers.