This paper is devoted to an in-depth discussion of the Gaussian Noise (GN) model which describes non-linear propagation in uncompensated coherent transmission systems. Similar models and validation efforts are reviewed. Then, the main equations of the GN model are introduced. An intuitive physical interpretation of the equations and their features is proposed. The main characteristics of the non-linear interference (NLI) noise spectra that the GN model produces are discussed. To ease model exploitation, a new formulation in hyperbolic coordinates is proposed, which makes numerical integration faster. New approximate closed-form solutions are also provided. An extension of the GN model to distributed-amplification scenarios is introduced. NLI noise accumulation vs. distance and bandwidth are studied in depth. Finally, the GN model implications as to system and networks design and optimization are discussed.

Several approximate non-linear fiber propagation models have been proposed over the years. Recent reconsideration and extension of earlier modeling efforts has led to the formalization of the so-called Gaussian-Noise (GN) model.The evidence collected so far hints at the GN-model as being a relatively simple and, at the same time, sufficiently reliable tool for performance prediction of uncompensated coherent systems, characterized by a favorable accuracy vs. complexity trade-off.This paper tries to pull together the recent results regarding the GN-model definition, understanding, relations vs. other models, validation, limitations, closed form solutions, approximations and, in general, its applications and implications in link analysis and optimization, also within a network environment.

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The GN-model has been proposed as an approximate but sufficiently accurate tool for predicting uncompensated optical coherent transmission system performance, in realistic scenarios. For this specific use, the GN-model has enjoyed substantial validation, both simulative and experimental. Recently, however, it has been pointed out that its predictions, when used to obtain a detailed picture of non-linear interference (NLI) noise accumulation along a link, may be affected by a substantial NLI overestimation error, especially in the first spans of the link. In this paper we analyze in detail the GN-model errors. We discuss recently proposed formulas for correcting such errors and show that they neglect several contributions to NLI, so that they may substantially underestimate NLI in specific situations, especially over low-dispersion fibers. We derive a complete set of formulas accounting for all single, cross, and multi-channel effects, This set constitutes what we have called the enhanced GN-model (EGN-model). We extensively validate the EGN model by comparison with accurate simulations in several different system scenarios. The overall EGN model accuracy is found to be very good when assessing detailed span-by-span NLI accumulation and excellent when estimating realistic system maximum reach. The computational complexity vs. accuracy trade-offs of the various versions of the GN and EGN models are extensively discussed.

We present analytical results on the impact of nonlinear propagation in uncompensated links. We test the accuracy of our model in the context of ultradense wavelength-division-multiplexing polarization-multiplexed quadrature phase-shift keying (PM-QPSK) systems, at the Nyquist spectral efficiency limit. We show that the predicted system performance matches simulation results very accurately over a broad range of system scenarios. A simple closed-form analytical formula provides an effective tool for the quick and accurate prediction of system performance. IndexTerms-Dense wavelength-division multiplexing (DWDM), Nyquist wavelength-division multiplexing (WDM), optical transmission, polarization-multiplexed quadrature amplitude modulation (PM-QAM), polarization-multiplexed quadrature phase-shift keying (PM-QPSK), uncompensated systems.