Solving phase-noise Fokker-Planck equations using the motion-group Fourier transform

A quantity of importance in coherent optical communications is the probability density of a filtered signal in the presence of phase noise (PN). The Fokker-Planck(FP) approach has been recognized as a rigorous way to describe these statistical properties. However, computational difficulties in solving these FP equation shave prevented their widespread application. In this paper, we present a new and simple computational solution method based on techniques from noncommutative harmonic analysis on motion groups. This proposed method can easily solve all the PN FP equations with any kind of intermediate frequency filter. We also present a new derivation of PN FP equations from the viewpoint of stochastic processes.