Analytical Modeling of Nonlinear Fiber Propagation for Four Dimensional Symmetric Constellations

Abstract

Coherent optical transmission systems naturally lead to a four dimensional (4D) signal space, i.e., two polarizations each with two quadratures. In this paper we derive an analytical model to quantify the impact of Kerr nonlinearity on such 4D spaces, taking the interpolarization dependency into account. This is in contrast to previous models such as the GN and EGN models, which are valid for polarization multiplexed (PM) formats, where the two polarizations are seen as independent channels on which data is multiplexed. The proposed model agrees with the EGN model in the special case of independent two-dimensional modulation in each polarization. The model accounts for the predominant nonlinear terms in a WDM system, namely self-phase modulation and and cross-phase modulation. Numerical results show that the EGN model may inaccurately estimate the nonlinear interference of 4D formats. This nonlinear interference discrepancy between the results of the proposed model and the EGN model could be up to 2.8 dB for a system with 80 WDM channels. The derived model is validated by splitstep Fourier simulations, and it is shown to follow simulations very closely.

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

“…An analytical model for asymmetric 4D modulation formats was presented in [17], comprising only the SCI. In [18], a 4D nonlinear model able to quantify the impact of SCI (the pink lozenge-shaped island in [9,Fig. 7]) and XPM (the blue lozenge-shaped islands in [9, Fig.…”

“…7], named as X1) was derived. The model in [18] is only able to estimate the impact of NLI in high dispersion systems because it discards XCI (except for XPM) and MCI terms. No one has as yet ascertained how to estimate the XCI (the islands marked as X2, X3, and X4 in [9,Fig.…”

“…This paper is an extension of [18] providing a far more thorough and complete approach to deriving the NLI terms, such as SCI, XCI and MCI, by taking the interpolarization dependency into consideration. Unlike the model presented in [18] that applies only to high dispersion fiber systems, this work accurately models the nonlinear interference in various scenarios, including narrow bandwidth channels often encountered in elastic optical networks and transmission over low dispersion fiber. To the best of our knowledge, it is the first paper that presents a comprehensive solution to modeling the NLI that is applicable to any system using a 4D modulation format.…”

“…( 1)] through a distance-dependent scaling function, compensating for gain/loss, as in [14, Sec. II], [18,Eq. 2].…”

Universal Virtual Lab: A Fast and Accurate Simulation Tool for Wideband Nonlinear DWDM Systems

“…The time varying ISI model, on the other hand, accounts for temporal correlation properties of the NLIN and therefore it is suitable for addressing scenarios including fast adaptive nonlinear equalization [27][28]. Furthermore, it is also compliant with four-dimensional modulation formats exhibiting inter-polarization dependency [29].…”