The few-mode fiber nonlinearity has been well modeled by an additive Gaussian Noise (GN) source. The available GN models in Mode Division Multiplexing–Wavelength Division Multiplexing (MDM–WDM) systems are incoherent and neglect the dispersion slope. The incoherent GN model assumes that the Nonlinear Interference (NLI) noise created at each span is summed up in power incoherently at the receiver and leads to underestimating the NLI noise power. In the first part of this paper, a coherent GN model is derived by taking into account the dispersion slope and verified through Split-Step Fourier Method (SSFM) simulations. In the second part of this paper, the total capacity maximization, as well as the minimum Signal to Noise Ratio (SNR) margin maximization problems are presented and solved based on the obtained GN model. MDM–WDM multi-node nonlinear network under different scenarios including Equal/Non-Equal Required SNR (ERS/NERS), and Flat/Non-Flat Amplifier Gain (FG/NFG) are considered in the numerical simulations. Considering 200 different sets of randomized traffic demands (random channel-mode distributions) the cumulative distribution function of minimum SNR margin improvement in optimized power allocation compared with the best flat power allocation is in 99% more than 1 dB, 1.2 dB, 2.4 dB, and 2.8 dB, for ERS-FG, ERS-NFG, NERS-FG, and NERS-NFG scenarios, respectively.

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