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Signal propagation in an optical fiber can be described by the nonlinear Schro&#x0308;dinger equation (NLSE). The NLSE has no known closed-form solution when both dispersion and nonlinearities are considered simultaneously. In this paper, we present a novel integral-form approximate model for the nonlinear optical channel, with applications to passive optical networks. The proposed model is derived using logarithmic perturbation in the frequency domain on the group-velocity dispersion (GVD) parameter of the NLSE. The model can be seen as an improvement of the recently proposed regular perturbation (RP) on the GVD parameter. RP and logarithmic perturbation (LP) on the nonlinear coefficient have already been studied in the literature, and are hereby compared with RP on the GVD parameter and the proposed LP model. As an application of the model, we focus on passive optical networks. For a 20 km PON at 10 Gbaud, the proposed model improves the normalized square deviation by 1.5 dB with respect to LP on the nonlinear coefficient. For the same system, histogram-based detectors are developed using the received symbols from the models. The detector obtained from the proposed LP model reduces the uncoded bit-error-rate by up to 5.4 times at the same input power or reduces the input power by 0.4 dB at the same information rate compared to the detector obtained from LP on the nonlinear coefficient.

Frequency Logarithmic Perturbation on the Group-Velocity Dispersion Parameter With Applications to Passive Optical Networks