Performance of DPSK Signals With Quadratic Phase Noise

Abstract

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 error probability for differential phase-shift keying (DPSK) signals is derived analytically. 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. 1 this paper, the additive phase noise is quadratic function of the electric field. When the electric field is contaminated with additive Gaussian noise, although the quadratic phase noise is uncorrelated with the linear phase noise, both non-Gaussian distributed, the phase noise weakly depends on the additive Gaussian noise.Differential phase-shift keying (DPSK) signals [6][7][8][9][10][11][12][13][14][15][16] have received renewed attention recently for long-haul or spectrally efficiency lightwave transmission systems. When optical amplifiers are used periodically to compensate the fiber loss, the interaction of optical amplifier noise and fiber Kerr effect induced nonlinear phase noise, often called Gordon-Mollenauer effect [17], or more precisely, nonlinear phase noise induced by self-phase modulation. Added directly into the signal phase, Gordon-Mollenauer effect is a quadratic function of the electric field and degrades DPSK signal [11,14,[17][18][19][20][21][22][23].Previous studies found the variance or the corresponding Q-factor of the quadratic phase noise [11,17,[24][25][26][27] or the spectral broadening of the signal [14,18,28]. Recently, quadratic phase noise is found to be non-Gaussian distributed both experimentally [20] and theoretically [29,30]. As non-Gaussian random variable, neither the variance nor Q-factor is sufficient to completely characterize the phase noise. The probability density of quadratic phase noise is found in [30] and used in [23] to evaluate the error probability of DPSK signal by assuming that quadratic phase noise and Gaussian noise are independent of each other. However, as shown in the simulation of [22,23], the dependence between Gaussian noise with quadratic phase noise increases the error probability.Using the distributed assumption of infinite number of fiber spans, the joint statistics of nonlinear phase noise and Gaussian noise is derived analytically by [19,21,31]. The characteristic function of nonlinear phase noise becomes a very simple expression with the distributed assumption [29]. The error probability of DPSK signal has been derived with [22] and without [21,32] the assumption that nonlinear phase noise is independent of the Gaussian noise. Based on the distributed assumption, it is found that the dependence between linear and nonlinear phase noise increases both the error probability and SNR penalty [21,32].The distributed assumption is very accurate when the number of fiber spans is larger than 32 [21,29]. For a typical fiber span...

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