On the Statistics of Intrachannel Four-Wave Mixing in Phase-Modulated Optical Communication Systems

We have analytically derived the correlation functions of intrachannel four-wave mixing (IFWM)-induced phase and amplitude noises in phase-modulated optical communication systems. The phase and amplitude noises are correlated with each other for binary phase-shift keying (PSK) systems but uncorrelated for $M$-ary PSK systems with $M>2$. We have also derived analytical approximations to the probability distribution of IFWM-induced phase noise for PSK and differential PSK systems. Furthermore, we have studied the performance of an optimal linear phase-noise predictor derived from the IFWM-induced phase-noise autocorrelation function. This yields a performance improvement of 1.8 dB when IFWM-induced phase noise is the dominant impairment, and an improvement of 0.8 to 1.2 dB in the presence of amplified spontaneous emission noise and nonlinear phase noise in typical terrestrial links.