A Closed-form Expression of the Gaussian Noise Model Supporting O-Band Transmission

Abstract: We present a novel closed-form model for nonlinear interference (NLI) estimation in low-dispersion O-band transmission systems. The formulation incorporates the four-wave mixing (FWM) efficiency term as well as the coherent contributions of self- and cross-phase modulation (SPM/XPM) across multiple identical spans. This extension enables accurate evaluation of the NLI in scenarios where conventional closed-form Gaussian Noise (GN) models are limited. The proposed model is validated against split-step Fourier method (SSFM) simulations and numerical integration across 41-161 channels, with a 96 GBaud symbol rate, bandwidths of up to 16.1 THz, and transmission distances from 80 to 800 km. Results show a mean absolute error of the NLI signal-to-noise ratio (SNR) below 0.22 dB. The proposed closed-form model offers an efficient and accurate tool for system optimisation in O-band coherent transmission.