Analytical expressions for the phase variance in a nonlinear fiber optic system based on phase-shift keying are developed. The Gauss-Hermite functions are used as the orthogonal basis to represent the noise field. Number of degrees of freedom (DOF) to accurately model the phase variance is estimated. The amplifier noise excites higher order Gauss-Hermite noise modes and the nonlinear mixing of a signal pulse and higher order Gauss-Hermite noise mode leads to new noise fields which enhance the nonlinear phase noise. The higher order noise modes propagate linearly and enhance the linear phase noise if the matched filter is not used at the receiver. Analytical expression for the optimum launch power is developed taking into account the linear and nonlinear phase noise.
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