A Closed-Form Approximation of the Gaussian Noise Model in the Presence of Inter-Channel Stimulated Raman Scattering

Abstract

An accurate, closed-form expression evaluating the nonlinear interference (NLI) power in coherent optical transmission systems in the presence of inter-channel stimulated Raman scattering (ISRS) is derived. The analytical result enables a rapid estimate of the signal-to-noise ratio (SNR) and avoids the need for integral evaluations and split-step simulations. The formula also provides new insight into the underlying parameter dependence of ISRS on the NLI. The proposed result is applicable for dispersion unmanaged, ultra-wideband transmission systems that use optical bandwidths of up to 15 THz.The accuracy of the closed-form expression is compared to numerical integration of the ISRS Gaussian Noise model and split-step simulations in a point-to-point transmission, as well as in a mesh optical network scenario.

A Modulation Format Correction Formula for the Gaussian Noise Model in the Presence of Inter-Channel Stimulated Raman Scattering

“…This integral has been solved in our previous work [38]. Hence, the modulation format correction for the ISRS GN model can be obtained using the results in this paper and the GN contribution derived in closed-form in [38].…”

“…However, this integral resembles the mathematical structure of the GN model contribution η GN,n (f i ) (cf. [38,Eq. (14)]) In other words, if there exists a closed-form approximation for the GN model contribution after one span for an arbitrary transmission system, a modulation format correction formula in closed-form for any number of spans immediately follows with the results in this paper using (8)(9)(12).…”

“…In our previous work [38,Eq. (18)], an approximation of (13) has been derived under the XPM assumption and a firstorder description of ISRS.…”

“…Extensions of the conventional GN model to account for ISRS, named ISRS GN model, have been recently proposed in integral form [31]- [36]. An approximation in closed-form has been first proposed in [31] which recently has been significantly generalized to include arbitrary launch power distributions, wavelength dependent dispersion and a more accurate description of ISRS [37], [38]. A comparible formula, based on the same approach and with a similar result, has been reported in [39].…”

Overview and Comparison of Nonlinear Interference Modelling Approaches in Ultra-Wideband Optical Transmission Systems

“…Although, the integral approaches above estimate the NLI with very good accuracy, they are not directly suitable for real-time applications and network optimisation where vast numbers of light paths must be evaluated. For such scenarios, approximations in closed-form, that yield results within picoseconds, have been proposed for the effective attenuation approach, as well as for the ISRS GN model [3], [9]- [12].…”