Yanchao Jiang

The GN-Model of Fiber Non-Linear Propagation and its Applications

Several approximate non-linear fiber propagation models have been proposed over the years. Recent re-consideration 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 versus complexity trade-off. This paper tries to gather the recent results regarding the GN-model definition, understanding, relations versus 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.

EGN model of non-linear fiber propagation

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.

A Simple and Effective Closed-Form GN Model Correction Formula Accounting for Signal Non-Gaussian Distribution

The GN model of nonlinear fiber propagation has been shown to overestimate the variance of nonlinearity due to the signal Gaussianity approximation, leading to maximum reach predictions for realistic optical systems, which may be pessimistic by about 5% to 15%, depending on fiber type and system setup. Analytical corrections have been proposed, which, however, substantially increase the model complexity. In this paper, we provide a simple closed-form GN model correction formula, derived from the EGN model, which we show to be quite effective in correcting for the GN model tendency to overestimate nonlinearity. The formula also permits to clearly identify the correction dependence on key system parameters, such as span length and loss.

Analytical and Experimental Results on System Maximum Reach Increase Through Symbol Rate Optimization

We investigated the reach increase obtained through nonlinearity mitigation by means of transmission symbol rate optimization (SRO). First, we did this theoretically and simulatively. We showed that the nonlinearity model that properly accounts for the phenomenon is the EGN model, in its version that specifically includes four-wave mixing. We then found that for PM-QPSK systems at full C-band, the reach increase may be substantial, on the order of 10-25%, with optimum symbol rates on the order of 2-6 GBd. We show that for C-band PM-QPSK systems over SMF, the potential mitigation due to SRO is greater than that ideally granted by digital backpropagation (the latter applied over a bandwidth of a 32-GBd channel). We then set up an experiment to obtain confirmation of the theoretical and simulative predictions. It consisted of 19 PM-QPSK channels, operating at 128 Gb/s per channel, over PSCF, with span length 108 km and EDFA-only amplification. We demonstrated a reach increase of about 13.5%, when going from single-carrier per channel transmission, at 32 GBd, to eight subcarrier per channel, at 4 GBd, in line with the EGN model predictions. We also extended the theoretical investigation of SRO to PM-16QAM, where we found a qualitatively similar effect to PM-QPSK, although the potential reach increase appears to be typically only about 50% to 60% that of PM-QPSK. Further investigation is, however, in order, specifically to explore the effect on PM-16QAM SRO of the removal of long-correlated phase and polarization noise.

Impact of low-OSNR operation on the performance of advanced coherent optical transmission systems

We find evidence that low-OSNR operation causes substantial penalty on the system maximum reach due to non-linearity generated by ASE noise and due to signal-power conversion into non-linear noise. Neglecting these effects may lead to quite substantial performance prediction error.

Experimental Investigation of Nonlinear Interference Accumulation in Uncompensated Links

Noise due to nonlinear effects in uncompensated links has recently been shown to be Gaussian and additive. We experimentally investigate the law governing its accumulation. Our results suggest a mild super-linear accumulation versus number of spans, compatible with coherent accumulation models.

Experimental demonstration of fiber nonlinearity mitigation in a WDM multi-subcarrier coherent optical system

Thanks to the use of a digital multi-subcarrier architecture, we experimentally demonstrate a maximum reach increase of 11% for a 19×128Gbit/s PM-QPSK WDM comb with respect to an equivalent single-subcarrier system, achieving 14,100-km transmission over PSCF fiber with EDFA-only amplification.

On the impact of non-linear phase-noise on the assessment of long-haul uncompensated coherent systems performance

We accurately characterize nonlinear phase noise in uncompensated coherent optical systems. We find that, though present, its impact on system performance is typically negligible in a wide range of practical system scenarios.

On the ultimate potential of symbol-rate optimization for increasing system maximum reach

We investigate the reach-increase obtained by optimizing the transmission symbol rate. We show that for PM-QPSK systems at full-C-band the increase may be larger than obtained through ideal single-channel backward-propagation, and similar for PM-16QAM.

What is the right physical layer model for a highly dynamic reconfgurable optical network

We investigated the variability of non-linearity generation in dynamically-reconfigurable network scenarios with re-routing, non-homogenous formats and variable accumulated dispersion among channels. Based on the results, we discuss practical modeling options fore real-time physical-layer awareness in dynamically reconfigurable networks.