Overview and Comparison of Nonlinear Interference Modelling Approaches in Ultra-Wideband Optical Transmission Systems <s> MODELLING APPROACHES IN INTEGRAL FORM <s> 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. <s> BIB001 </s> Overview and Comparison of Nonlinear Interference Modelling Approaches in Ultra-Wideband Optical Transmission Systems <s> MODELLING APPROACHES IN INTEGRAL FORM <s> 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. <s> BIB002 </s> Overview and Comparison of Nonlinear Interference Modelling Approaches in Ultra-Wideband Optical Transmission Systems <s> MODELLING APPROACHES IN INTEGRAL FORM <s> 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%. <s> BIB003 </s> Overview and Comparison of Nonlinear Interference Modelling Approaches in Ultra-Wideband Optical Transmission Systems <s> MODELLING APPROACHES IN INTEGRAL FORM <s> 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. <s> BIB004 </s> Overview and Comparison of Nonlinear Interference Modelling Approaches in Ultra-Wideband Optical Transmission Systems <s> MODELLING APPROACHES IN INTEGRAL FORM <s> 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. <s> BIB005 </s> Overview and Comparison of Nonlinear Interference Modelling Approaches in Ultra-Wideband Optical Transmission Systems <s> MODELLING APPROACHES IN INTEGRAL FORM <s> 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. <s> BIB006 </s> Overview and Comparison of Nonlinear Interference Modelling Approaches in Ultra-Wideband Optical Transmission Systems <s> MODELLING APPROACHES IN INTEGRAL FORM <s> 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. <s> BIB007
The GN model is a first-order solution with respect to the nonlinearity coefficient of the nonlinear Schrödinger equation assuming Gaussian modulation BIB002 . The nonlinear interference (NLI) power is given as P NLI = ηP 3 i , with NLI coefficient η and channel launch power P i . To extend the conventional GN model to account for ISRS, it is assumed that the temporal gain dynamics of ISRS are negligible. This is motivated by the averaging of many independently modulated channels involved in the scattering process, smoothing the occurring ISRS gain in time. As a resulting simplification, ISRS can be modelled as a frequency-and distance-dependent signal power profile ρ (z, f ), which is obtained by solving the continuous-wave Raman equations BIB001 . The validity of this approach has recently been experimentally demonstrated in BIB005 , BIB006 . In general, approaches to include ISRS in the conventional GN model can be categorised into two groups. The first approach, termed the effective attenuation approach, is to approximate ρ (z, f ) with exponential decays, that have modified attenuation coefficients or effective lengths BIB003 ,  . The second approach, termed the ISRS GN model, is to fully rederive the conventional GN model based on the exact signal power profile for higher accuracy but with increased complexity BIB004 - BIB007 .