A noise theory for four-wave-mixing (FWM) tone generated by nonlinear interaction of channels of a wavelength-division-multiplexed system is described. Analytical expressions for power spectral density and variance of FWM noise are derived without ignoring group-velocity walk-off between channels. The results show that the variance of FWM noise exhibits sharp minima and maxima as a function of channel separation which is due to the coherent interaction between channels. When the walk-off distance is large or comparable to effective fiber length, FWM penalty can be reduced by introducing a suitable initial delay between interacting channels.
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