Performance of DPSK signals with quadratic phase noise

Nonlinear phase noise induced by the interaction of the fiber Kerr effect and amplifier noises is a quadratic function of the electric field. When the dependence between the additive Gaussian noise and the quadratic phase noise is taken into account, the error probability for differential phase-shift keying signals is derived analytically. Depending on the number of fiber spans, the signal-to-noise ratio penalty is increased by up to 0.23 dB, due to the dependence between the Gaussian noise and the quadratic phase noise.