Modeling of nonlinear interference (NLI) generated by the fiber Kerr effect is a hot topic in coherent optical transmission systems. Four years ago, the Gaussian-noise (GN) model was proposed as an approximate tool for predicting the system maximum reach performance, in realistic optical coherent transmission scenarios, over lumped-amplification dispersion uncompensated links. For this specific use, the GN model has enjoyed substantial validation, both simulative and experimental. The original GN model reference formula (GNRF) only described the simple second-order fiber dispersion. In this thesis, we first extend that formula to take the general dispersive propagation constant into account. We then make a comparison with the results of the GNRF over various types of fibers with quite different dispersions. It turns out that third-order dispersion has a very substantial effect on nonlinearity, especially near a fiber dispersion-zero. It should be mentioned that the GN model may lose accuracy for fundamental reasons when approaching a dispersion zero. These can be overcome by the enhanced-GN (EGN) model, introduced below. On the other hand, the EGN model has two contributions, one of which is the GN model, so the extension of the GN model that was the first part of this thesis provides useful results for the EGN model too. The GN model predictions, when used to obtain a detailed picture of NLI accumulation along a link rather than an estimate of the system maximum reach, may be affected by a substantial overestimation error, especially in the first few spans of the link. The error is larger for low-cardinality formats and systems with very short spans, or that use nearly-ideal distributed amplification. In this thesis, 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 of formulas constitutes what we have called the 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, and the presence and relevance of phase noise within NLI are discussed. However, although the EGN model is theoretically rigorous, the complexity is substantially larger than that of the GN model, which makes its use difficult for real-time applications. Fortunately, we are able to derive a simple closed-form GN model correction formula based on the EGN model. The GN model, together with the correction formula, provides a low-complexity approximation to the EGN model. Such approximation has limitations, but already in its present form it effectively and rather accurately corrects for the GN model tendency to overestimate NLI, which is carefully validated over a wide range of system scenarios. The correction formula also allows to clearly identify the correction dependence on key system parameter, such as span length and loss. As a reliable model, the EGN model is then employed to evaluate NLI generation in some study-cases: 1. Dispersion pre-compensation over mixed-fiber links: The dispersion pre-compensation impact both on homogeneous links (single fiber type) and inhomogeneous links (links using a mixture of high and low dispersion fibers) is analyzed. All results demonstrate that the EGN model is capable of dealing with the dispersion pre-compensation in mixed-fiber links. 2. Determining the optimum system symbol rate: The system symbol rate impact on NLI generation is studied in detail. The EGN model is found to be quite accurate in identifying the optimum symbol rate, as well as in predicting the related performance improvement. We also derived a simple closed-form formula that very reliably predicts the optimum symbol rate for quasi-Nyquist systems with lumped amplification. 3. NLI modeling for dynamically reconfigurable networks: the variability of NLI accumulation in dynamically reconfigurable networks with re-routing, different formats and accumulated dispersion is investigated. The EGN model can take the propagation history of all channels into account, and correctly assess NLI generation with different link features. Finally, an experiment is carried out to validate the EGN model for the first time. Using a PM-QPSK Nyquist WDM transmission, we confirm the enhanced accuracy of the EGN model comparing maximum reach predictions with those of the GN model.

The EGN model of nonlinear propagation in coherent optical transmission systems and its applications / Jiang, Yanchao. - (2014). [10.6092/polito/porto/2592161]

The EGN model of nonlinear propagation in coherent optical transmission systems and its applications

JIANG, YANCHAO
2014

Abstract

Modeling of nonlinear interference (NLI) generated by the fiber Kerr effect is a hot topic in coherent optical transmission systems. Four years ago, the Gaussian-noise (GN) model was proposed as an approximate tool for predicting the system maximum reach performance, in realistic optical coherent transmission scenarios, over lumped-amplification dispersion uncompensated links. For this specific use, the GN model has enjoyed substantial validation, both simulative and experimental. The original GN model reference formula (GNRF) only described the simple second-order fiber dispersion. In this thesis, we first extend that formula to take the general dispersive propagation constant into account. We then make a comparison with the results of the GNRF over various types of fibers with quite different dispersions. It turns out that third-order dispersion has a very substantial effect on nonlinearity, especially near a fiber dispersion-zero. It should be mentioned that the GN model may lose accuracy for fundamental reasons when approaching a dispersion zero. These can be overcome by the enhanced-GN (EGN) model, introduced below. On the other hand, the EGN model has two contributions, one of which is the GN model, so the extension of the GN model that was the first part of this thesis provides useful results for the EGN model too. The GN model predictions, when used to obtain a detailed picture of NLI accumulation along a link rather than an estimate of the system maximum reach, may be affected by a substantial overestimation error, especially in the first few spans of the link. The error is larger for low-cardinality formats and systems with very short spans, or that use nearly-ideal distributed amplification. In this thesis, 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 of formulas constitutes what we have called the 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, and the presence and relevance of phase noise within NLI are discussed. However, although the EGN model is theoretically rigorous, the complexity is substantially larger than that of the GN model, which makes its use difficult for real-time applications. Fortunately, we are able to derive a simple closed-form GN model correction formula based on the EGN model. The GN model, together with the correction formula, provides a low-complexity approximation to the EGN model. Such approximation has limitations, but already in its present form it effectively and rather accurately corrects for the GN model tendency to overestimate NLI, which is carefully validated over a wide range of system scenarios. The correction formula also allows to clearly identify the correction dependence on key system parameter, such as span length and loss. As a reliable model, the EGN model is then employed to evaluate NLI generation in some study-cases: 1. Dispersion pre-compensation over mixed-fiber links: The dispersion pre-compensation impact both on homogeneous links (single fiber type) and inhomogeneous links (links using a mixture of high and low dispersion fibers) is analyzed. All results demonstrate that the EGN model is capable of dealing with the dispersion pre-compensation in mixed-fiber links. 2. Determining the optimum system symbol rate: The system symbol rate impact on NLI generation is studied in detail. The EGN model is found to be quite accurate in identifying the optimum symbol rate, as well as in predicting the related performance improvement. We also derived a simple closed-form formula that very reliably predicts the optimum symbol rate for quasi-Nyquist systems with lumped amplification. 3. NLI modeling for dynamically reconfigurable networks: the variability of NLI accumulation in dynamically reconfigurable networks with re-routing, different formats and accumulated dispersion is investigated. The EGN model can take the propagation history of all channels into account, and correctly assess NLI generation with different link features. Finally, an experiment is carried out to validate the EGN model for the first time. Using a PM-QPSK Nyquist WDM transmission, we confirm the enhanced accuracy of the EGN model comparing maximum reach predictions with those of the GN model.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2592161
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