  Nonlinear phase noise induced by the interaction of 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
taking into account, the joint statistics of quadratic phase noise and additive
Gaussian noise is derived analytically. When the error probability for
differential phase-shift keying (DPSK) signals is evaluated, depending on the
number of fiber spans, the signal-to-noise ratio (SNR) penalty is increased by
up to 0.23 dB due to the dependence between the Gaussian noise and the
quadratic phase noise.
