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Second-order theory for nonlinear phase noise in coherent fiber-optic system based on phase shift keying

A second-order perturbation technique is used to develop analytical expressions for the phase variance in a nonlinear fiber optic system based on phase-shift keying. Typically, in short-haul fiber optic communication system, the nonlinear effects are smaller than dispersive effect, and it is found that the difference between the first and second-order solution is negligible. However, when the transmission distance is long and/or lunch power is large, nonlinearity becomes a stronger perturbation, and the first-order theory is not adequate to describe the phase fluctuations. Coupling between fiber non-linearity and amplitude noise leads to a random walk of the signal phase, which degrades the transmission performance of phase-shift keying system. An analytical expression has been obtained based on a second-order perturbation technique for the variance of nonlinear phase noise, which is found to be in good agreement with numerical simulation.