Limits on WDM systems due to four-wave mixing: a statistical approach

For wavelength division multiplexing (WDM) systems over nonzero dispersion fiber, we evaluate the statistics of the eye-closure due to four-wave mixing (FWM) in the presence of arbitrary data values and optical phases in all WDM channels. By Monte Carlo (MC) experiments, we determine the distribution function and the standard deviation of the eye-closure for several channel counts. Convolution of the distribution after a single span yields the eye-closure distribution after multiple amplified spans. The results are used to assess the Q-factor penalty in a WDM system. The limits for optical power, chromatic dispersion and channel spacing can then be found. It is shown that the power of the FWM products can be used to estimate the system penalty due to FWM. When comparing standard single-mode fiber with nonzero dispersion-shifted fiber (NZDSF), we find that standard fiber allows for a triple narrower channel spacing than NZDSF, given the same set of system parameters.