Probability density of nonlinear phase noise

The probability density of nonlinear phase noise, often called the Gordon–Mollenauer effect, is derived analytically. The nonlinear phase noise can be accurately modeled as the summation of a Gaussian random variable and a noncentral chi-square random variable with two degrees of freedom. Using the received intensity to correct for the phase noise, the residual nonlinear phase noise can be modeled as the summation of a Gaussian random variable and the difference of two noncentral chi-square random variables with two degrees of freedom. The residual nonlinear phase noise can be approximated by Gaussian distribution better than the nonlinear phase noise without correction.