Intra-Channel Four-Wave Mixing Impairments in Dispersion-Managed Coherent Fiber-Optic Systems Based on Binary Phase-Shift Keying

In this paper, we mathematically derive the probability density function (PDF) of the received electrical signal for coherent fiber-optic transmission systems. Both amplified spontaneous emission (ASE) noise and fiber nonlinearity are taken into account. The results show that the PDF of a bit “0” or “1” is asymmetric when intra-channel four-wave mixing (IFWM) is dominant. However, the PDF becomes nearly symmetric when the variance of ASE is much larger than that due to IFWM. The standard deviation of the received signal is calculated analytically. It is shown that the variance varies quadratically with launch power. We also investigate the optimum system scheme, including optimum dispersion map and pre-compensation ratio, for the coherent fiber-optic systems based on analytically calculated variance of IFWM.