Achieving reliable communication over different wavelength channels and modes is one of the main goals of Mode Division Multiplexing-Wavelength Division Multiplexing (MDM-WDM) transmission. The reliability can be described by the minimum Signal to Noise Ratio (SNR) margin which depends on launch power, the gain of Few-Mode Erbium-Doped Fiber Amplifiers (FM-EDFA), and the nonlinear impairments of Few-Mode Fiber (FMF). In this paper, we develop the Enhanced Gaussian Noise (EGN) nonlinear model for FMF, which can be used in both weak and strong coupling regimes. We validate the model by comparing simulation results with those obtained through the Split-Step Fourier Method. Based on our proposed EGN model, we address the problem of joint optimized power and gain allocation based on minimum SNR margin maximization when accounting for practical FM-EDFA constraints such as saturation power and maximum gain. The problem is solved using a convex optimization approach and considering different scenarios such as the best equal power, optimized power, and joint optimized power and gain. Results demonstrate that the minimum SNR margin improvement for the joint optimized power and gain allocation compared to the best equal power allocation is 1.4 dB and 1.7 dB for MDM-single channel and single-mode fiber-WDM systems, respectively.

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