An Enhanced Analytical Model of Nonlinear Fiber Effects for Four-Dimensional Symmetric Modulation Formats

Abstract

Optical transmission systems intrinsically enjoy a four-dimensional (4D) constellation space, corresponding to two quadratures in two polarization states. In this paper, we introduce a general nonlinear model that is valid for 4D symmetric modulation formats. We take the inter-polarization dependency into account to derive this model. The model accounts for all perturbative nonlinear interference (NLI) terms, including selfchannel, cross-channel and multi-channel interferences. Split step Fourier simulations show that the proposed model has the ability to predict the NLI with high levels of accuracy for both low and high fiber dispersion regimes. The simulation results further show that previous models, including the EGN model, inaccurately predict the NLI in certain scenarios.

Analysis of Nonlinear Fiber Kerr Effects for Arbitrary Modulation Formats

“…The main reason for this deviation is the impact of MCI nonlinear terms ignored in this paper. Note that for PM modulation formats that do not violate the assumptions made in [20], [21], our model yields the same results as the EGN model.…”

“…In [20], we derived a nonlinear model which quantifies the impact of Kerr nonlinearity on 4D symmetric constellations, accounting for the SCI and XPM nonlinear terms. We extended the model in [20] to a general nonlinear model [21] that accounts for all the NLI terms, including the SCI, XCI, and MCI terms. Although the model given in [21] has the power to take all the NLI terms into account, it still lacks the ability to predict the NLI of constellations that lack symmetry.…”

“…We extended the model in [20] to a general nonlinear model [21] that accounts for all the NLI terms, including the SCI, XCI, and MCI terms. Although the model given in [21] has the power to take all the NLI terms into account, it still lacks the ability to predict the NLI of constellations that lack symmetry. The contribution of the SCI variance for arbitrary modulation formats was derived in [22], but it does not address the NLI terms that disturb multi-channel WDM systems.…”

“…The significance of our model is its ability to capture the NLI on any 4D signal space. Not only does this paper give expressions to evaluate the NLI of asymmetric constellations, which has not been done before for multichannel systems, it also tackles the shortcoming in [20], [21] brought about by the assumptions made therein. There exist 4D symmetric constellations whose NLI cannot be predicted by [20], [21] such as BPSK, SP-QAM4_32 [26], SP-QAM4_512 [26], etc.…”

“…Not only does this paper give expressions to evaluate the NLI of asymmetric constellations, which has not been done before for multichannel systems, it also tackles the shortcoming in [20], [21] brought about by the assumptions made therein. There exist 4D symmetric constellations whose NLI cannot be predicted by [20], [21] such as BPSK, SP-QAM4_32 [26], SP-QAM4_512 [26], etc. However, we are able to compute the NLI of such constellation through the model proposed in this paper.…”