We study the properties of nonlinear interference noise (NLIN) in fiber-optic communications systems with large accumulated dispersion. Our focus is on settling the discrepancy between the results of the Gaussian noise (GN) model (according to which NLIN is additive Gaussian) and a recently published time-domain analysis, which attributes drastically different properties to the NLIN. Upon reviewing the two approaches we identify several unjustified assumptions that are key in the derivation of the GN model, and that are responsible for the discrepancy. We derive the true NLIN power and verify that the NLIN is not additive Gaussian, but rather it depends strongly on the data transmitted in the channel of interest. In addition we validate the time-domain model numerically and demonstrate the strong dependence of the NLIN on the interfering channels' modulation format.

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Through a series of extensive system simulations we show that all of the previously not understood discrepancies between the Gaussian noise (GN) model and simulations can be attributed to the omission of an important, recently reported, fourth-order noise (FON) term, that accounts for the statistical dependencies within the spectrum of the interfering channel. We examine the importance of the FON term as well as the dependence of NLIN on modulation format with respect to link-length and number of spans. A computationally efficient method for evaluating the FON contribution, as well as the overall NLIN power is provided.

We present a detailed statistical model of nonlinear interference noise (NLIN) in optical communication systems. We demonstrate an efficient method of calculating 2nd order statistics of the NLIN coefficients, particularly their temporal autocorrelation and cross-correlation. The model is highly accurate in predicting system performance metrics such as bit-errorrate and signal-to-noise ratio, and is shown to provide better accuracy with respect to models that use the NLIN variance alone, particularly when accounting for the adaptive filtering of realistic receivers.

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We revisit the problem of estimating the nonlinear channel capacity of fiber-optic systems. By taking advantage of the fact that a large fraction of the nonlinear interference between different wavelength-division-multiplexed channels manifests itself as phase noise, and by accounting for the long temporal correlations of this noise, we show that the capacity is notably higher than what is currently assumed. This advantage translates into nearly doubling of the link distance for a fixed transmission rate.

We propose a practical shaping algorithm for mitigating the effect of nonlinear phase-noise in fiber-optic transmission. The proposed scheme is most beneficial in single-span fiber communications systems of the kind considered for inter-datacenter communications. In such systems the correlation time of the nonlinear phase-noise is too short to allow the mitigation of nonlinear phase-noise by means of adaptive phase-recovery or equalization, but long enough for a shaping approach to be effective. We rely on the implementation of the shell mapping method, optimized so as to provide the largest sum of linear and nonlinear shaping gains.Index Terms-Optical communications, shell mapping, optimal shaping, fiber nonlinearity, nonlinear interference noise (NLIN). 0733-8724 (c)