Noise performance analysis of bi-directionally pumped distributed fiber Raman amplifiers with consideration of fiber nonlinearity and its impact on EDFA output OSNR

Under small-signal assumption, equivalent noise figure normalized by fiber nonlinearities (NENF) of bi-directionally pumped distributed fiber Raman amplifiers (BiDFRA) is derived. Amplified spontaneous Raman scattering noise and double Rayleigh scattering noise are both included. The relation between NENF and Raman gain, forward Raman gain percentage is investigated under different polarization factor and Rayleigh scattering coefficient. It agrees well with numerical simulation results. Based on the analytical expression, the optical signal-to-nose ratio (OSNR) improvement of hybrid pre-BiDFRA/erbium-doped fiber amplifier (EDFA) compared with sole EDFA is studied. It is shown that there is an optimum Raman gain and forward Raman gain percentage to maximize the OSNR improvement. Finally, some guidelines on BiDFRA design are proposed.