Overview and Comparison of Nonlinear Interference Modelling Approaches in Ultra-Wideband Optical Transmission Systems
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paper_title: The GN-Model of Fiber Non-Linear Propagation and its Applications

paper_content:

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.
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paper_title: Channel Power Optimization of WDM Systems Following Gaussian Noise Nonlinearity Model in Presence of Stimulated Raman Scattering

paper_content:

The impact of interchannel stimulated Raman scattering (SRS) on optimization of channel powers to maximize the minimum channel margin is examined using a discrete Gaussian noise model for the Kerr nonlinearity. The simultaneous consideration of these two nonlinear effects is found to be incompatible with the goal of a convex SNR expression that can be optimized globally. A sequence of convex optimizations is employed to obtain a locally optimal solution, along with a bound on the degree of suboptimality. Optimization results obtained are most accurate for Gaussian-distributed signals, such as probabilistically shaped high-order-modulated signals. In a dispersion-uncompensated 4000-km fiber system utilizing the full C -band with perfect per-span SRS gain compensation, power optimization yields benefits of 0.25 to 2 dB over optimal spectrally flat power allocations. In systems including both C- and L -band, an optimization method that accounts for both SRS and Kerr nonlinearity effects provides a 0.23 to 0.60 dB margin benefit over a method compensating for SRS gain alone. In a system spanning only the C -band, per-span SRS gain compensation is not critical, as the maximum benefit is a 0.14 dB gain in minimum margin for optimized power allocations. By contrast, in a system spanning both C- and L -band, per-span SRS gain compensation provides a gain of up to 1.23 dB with optimized power allocations and larger gains with suboptimal power allocations.
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paper_title: Experiments on Stimulated Raman Scattering in S- and L-bands 16-QAM Signals for Ultra-Wideband Coherent WDM Systems

paper_content:

We experimentally evaluated stimulated Raman scattering (SRS) effect between S- and L-bands over 210-km SSMF 16-QAM transmission. SRS mainly induced power transition from S- to L-band, and was not the cause of nonlinear crosstalk penalty.
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paper_title: The ISRS GN Model, an Efficient Tool in Modeling Ultra-Wideband Transmission in Point-to-Point and Network Scenarios

paper_content:

An analytical model to estimate nonlinear performance in ultra-wideband optical transmission networks is presented. The model accurately accounts for inter-channel stimulated Raman scattering, variably loaded fibre spans and is validated through C+L band simulations for uniform and probabilistically shaped 64-QAM.
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paper_title: Achievable rate degradation of ultra-wideband coherent fiber communication systems due to stimulated Raman scattering

paper_content:

As the bandwidths of optical communication systems are increased to maximize channel capacity, the impact of stimulated Raman scattering (SRS) on the achievable information rates (AIR) in ultra-wideband coherent WDM systems becomes significant, and is investigated in this work, for the first time. By modifying the GN-model to account for SRS, it is possible to derive a closed-form expression that predicts the optical signal-to-noise ratio of all channels at the receiver for bandwidths of up to 15 THz, which is in excellent agreement with numerical calculations. It is shown that, with fixed modulation and coding rate, SRS leads to a drop of approximately 40% in achievable information rates for bandwidths higher than 15 THz. However, if adaptive modulation and coding rates are applied across the entire spectrum, this AIR reduction can be limited to only 10%.
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paper_title: Inter-channel Stimulated Raman Scattering and its Impact in Wideband Transmission Systems

paper_content:

The impact of inter-channel stimulated Raman scattering (ISRS) in wideband optical transmission systems is studied. ISRS cross-talk due to channel modulation was found to be negligible and a good agreement was found with theoretical results.
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paper_title: Evolution of stimulated Raman crosstalk in wavelength division multiplexed systems

paper_content:

An exact analytical solution for the evolution of stimulated Raman crosstalk in a singlemode WDM fiber system is presented utilizing the triangular approximation to the Raman gain spectrum. This approach provides a rigorous expression for crosstalk impairment. In the limit of small interchannel power exchange, our result reduces to Chraplyvy's previous estimate. Our formulation can be employed to predict the Raman penalty in future multiwavelength fiber communication systems.
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paper_title: Achievable rate degradation of ultra-wideband coherent fiber communication systems due to stimulated Raman scattering

paper_content:

As the bandwidths of optical communication systems are increased to maximize channel capacity, the impact of stimulated Raman scattering (SRS) on the achievable information rates (AIR) in ultra-wideband coherent WDM systems becomes significant, and is investigated in this work, for the first time. By modifying the GN-model to account for SRS, it is possible to derive a closed-form expression that predicts the optical signal-to-noise ratio of all channels at the receiver for bandwidths of up to 15 THz, which is in excellent agreement with numerical calculations. It is shown that, with fixed modulation and coding rate, SRS leads to a drop of approximately 40% in achievable information rates for bandwidths higher than 15 THz. However, if adaptive modulation and coding rates are applied across the entire spectrum, this AIR reduction can be limited to only 10%.
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paper_title: The ISRS GN Model, an Efficient Tool in Modeling Ultra-Wideband Transmission in Point-to-Point and Network Scenarios

paper_content:

An analytical model to estimate nonlinear performance in ultra-wideband optical transmission networks is presented. The model accurately accounts for inter-channel stimulated Raman scattering, variably loaded fibre spans and is validated through C+L band simulations for uniform and probabilistically shaped 64-QAM.
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paper_title: The Gaussian Noise Model in the Presence of Inter-channel Stimulated Raman Scattering

paper_content:

A Gaussian noise (GN) model is presented that properly accounts for an arbitrary frequency dependent signal power profile along the link. This enables the evaluation of the impact of inter-channel stimulated Raman scattering (ISRS) on the optical Kerr nonlinearity. Additionally, the frequency dependent fiber attenuation can be taken into account and transmission systems that use hybrid amplification schemes can be modeled, where distributed Raman amplification is partly applied over the optical spectrum. To include the latter two cases, a set of coupled ordinary differential equations must be numerically solved in order to obtain the signal power profile yielding a semi-analytical model. However for lumped amplification and negligible variation in fiber attenuation, a less complex and fully analytical model is presented which is referred to as the ISRS GN model. The derived model is exact to first-order for Gaussian modulated signals and extensively validated by numerical split-step simulations. A maximum deviation of $0.1$~dB in nonlinear interference power between simulations and the ISRS GN model is found. The model is applied to a transmission system that occupies an optical bandwidth of $10$~THz, representing the entire C+L band. At optimum launch power, changes of up to $2$~dB in nonlinear interference power due to ISRS are reported. Furthermore, comparable models published in the literature are benchmarked against the ISRS GN model.
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paper_title: Evolution of stimulated Raman crosstalk in wavelength division multiplexed systems

paper_content:

An exact analytical solution for the evolution of stimulated Raman crosstalk in a singlemode WDM fiber system is presented utilizing the triangular approximation to the Raman gain spectrum. This approach provides a rigorous expression for crosstalk impairment. In the limit of small interchannel power exchange, our result reduces to Chraplyvy's previous estimate. Our formulation can be employed to predict the Raman penalty in future multiwavelength fiber communication systems.
---
paper_title: Evolution of stimulated Raman crosstalk in wavelength division multiplexed systems

paper_content:

An exact analytical solution for the evolution of stimulated Raman crosstalk in a singlemode WDM fiber system is presented utilizing the triangular approximation to the Raman gain spectrum. This approach provides a rigorous expression for crosstalk impairment. In the limit of small interchannel power exchange, our result reduces to Chraplyvy's previous estimate. Our formulation can be employed to predict the Raman penalty in future multiwavelength fiber communication systems.
---
paper_title: Achievable rate degradation of ultra-wideband coherent fiber communication systems due to stimulated Raman scattering

paper_content:

As the bandwidths of optical communication systems are increased to maximize channel capacity, the impact of stimulated Raman scattering (SRS) on the achievable information rates (AIR) in ultra-wideband coherent WDM systems becomes significant, and is investigated in this work, for the first time. By modifying the GN-model to account for SRS, it is possible to derive a closed-form expression that predicts the optical signal-to-noise ratio of all channels at the receiver for bandwidths of up to 15 THz, which is in excellent agreement with numerical calculations. It is shown that, with fixed modulation and coding rate, SRS leads to a drop of approximately 40% in achievable information rates for bandwidths higher than 15 THz. However, if adaptive modulation and coding rates are applied across the entire spectrum, this AIR reduction can be limited to only 10%.
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Title: Overview and Comparison of Nonlinear Interference Modelling Approaches in Ultra-Wideband Optical Transmission Systems

Section 1: Modelling Approaches in Integral Form
Description 1: This section discusses the GN model and its extensions to account for inter-channel stimulated Raman scattering (ISRS) in integral form.

Section 2: The Effective Attenuation Approach
Description 2: This section details the first approach to extend the conventional GN model by introducing exponential decays with channel-dependent attenuation coefficients.

Section 3: The ISRS GN Model in Integral-Form
Description 3: This section elaborates on the rederived GN model to account for arbitrary ISRS power transfers and distributed amplification with higher accuracy.

Section 4: Comparison with Split-Step Simulations
Description 4: This section compares the accuracy of the modelling approaches against split-step simulations in specific ultrawideband transmission scenarios.

Section 5: Modelling Approaches in Closed-Form
Description 5: This section introduces closed-form approximations of the GN model for real-time application and network optimization, balancing accuracy and computational complexity.

Section 6: The ISRS GN Model in Closed-Form
Description 6: This section presents the analytical closed-form approximation of the ISRS GN model, which is suitable for real-time nonlinear interference (NLI) estimation.

Section 7: Conclusions
Description 7: This section provides a summative comparison of the different modelling approaches and recommendations based on estimation accuracy and computational efficiency.