Closed-form FWM expressions accounting for the impact of modulation format

Four Wave Mixing (FWM) is one of the main transmission impairments in coherent optical systems and a broad gamut of analytical expressions calculating its power already exists in the literature. Most of these expressions, such as the GN-model, assume that due to the large values of accumulated dispersion, each transmitted signal behaves as stationary circular Gaussian noise, ignoring the dependence of FWM on the employed modulation format. This assumption leads to significant error especially in the case of quadrature-phase-shift keying (QPSK), in systems with small number of spans and in the dispersion managed case. In addition, the GN-model is inaccurate when applied to metro networks, due to the low accumulated dispersion. In this paper, we derive closed-form expressions which incorporate the impact of modulation format on FWM generation, extending and improving the accuracy compared to existing closed-form FWM expressions. Moreover, the proposed method includes terms that make it applicable to systems with small span lengths (