Signal Statistics in Fiber-Optical Channels With Polarization Multiplexing and Self-Phase Modulation

In this paper, the statistics of received signals in a single-channel dispersion-managed dual-polarization fiber-optical channel are derived in the limit of low dispersion. The joint probability density function (pdf) of the received amplitudes and phases of such a system is derived for both lumped and distributed amplification. The new pdf expressions are used to numerically evaluate the performance of modulation formats over channels with nonlinear phase noise. For example, a sensitivity gain of up to 2 dB is calculated for a specific system using polarization-multiplexed 8-ary phase-shift keying compared with a similar single-polarization system at the same spectral efficiency and a symbol error rate of 5 × 10^-4. Moreover, the accuracy of the derived pdf is evaluated for some single-channel dispersion-managed fiber-optical links with different dispersion maps using the split-step Fourier transform method.