Error probability of DPSK signals with cross-phase modulation induced nonlinear phase noise

The error probability is derived analytically for differential phase-shift keying (DPSK) signals contaminated by both self- and cross-phase modulation (SPM and XPM)-induced nonlinear phase noise. XPM-induced nonlinear phase noise is modeled as Gaussian distributed phase noise. When fiber dispersion is compensated perfectly in each fiber span, XPM-induced nonlinear phase is summed coherently span after span and is the dominant nonlinear phase noise for typical wavelength-division-multiplexed (WDM) DPSK systems. For systems without or with XPM-suppressed dispersion compensation, SPM-induced nonlinear phase noise is usually the dominant nonlinear phase noise. With longer walkoff length, for the same mean nonlinear phase shift, 10-Gb/s systems are more sensitive to XPM-induced nonlinear phase noise than 40-Gb/s systems.