Optimizing the noise performance of broad-band WDM systems with distributed Raman amplification

We derive the fundamental limit for the ratio of path-averaged signal power to optical signal-to-noise ratio (OSNR), and show that for a fixed nonlinear weight, the OSNR is maximized if the signal power variation along the fiber is minimal. We also derive the conditions under which the noise performance of Raman amplification can be improved by erbium-doped fiber amplifier post amplification.