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.

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We demonstrate for the first time transmission of 54 Gbit/s and 48 Gbit/s over 44 km and 150 km, respectively, utilizing an optical bandwidth of only 3 GHz. We used polarization division multiplexed 512QAM and 256QAM modulation formats in combination with Nyquist pulse shaping having virtually zero roll-off. The resulting spectral efficiencies range up to 18 bit/s/Hz and 16 bit/s/Hz, respectively. Taking into account the overhead required for forward error correction, the occupied signal bandwidth corresponds to net spectral efficiencies of 14.4 bit/s/Hz and 15 bit/s/Hz, which could be achieved in a wavelength division multiplexed network without spectral guard bands.

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Based on a recently introduced model of non-linear propagation, we propose analytical formulas for the capacity limit of polarization-multiplexed ultra-dense WDM uncompensated coherent optical systems at the Nyquist limit, assuming both lumped and ideally distributed amplification. According to these formulas, capacity fundamentally depends on the transmitted power spectral density and on the total optical WDM bandwidth, whereas it does not depend on symbol-rate. Also, capacity approximately decreases by 2 [bit/s/Hz] for every doubling of link length. We show examples of capacity calculations for specific ultra-long-haul links with different polarization-multiplexed (PM) constellations, i.e. ideal PM-Gaussian, PM-QPSK (quadrature-phase shift keying) and PM-QAM (quadrature amplitude modulation). We show that the launch power maximizing capacity is independent of link length and modulation format. We also discuss the usable range of PM-QAM systems and validate analysis with simulations.