Probability Density Function of Kerr Effect Phase Noise

The probability density function of Kerr effect phase noise, often called the Gordon-Mollenauer effect, is derived analytically. The Kerr effect 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 Kerr effect 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 phase noise can be approximated by Gaussian distribution better than the Kerr effect phase noise without correction.