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Achieving reliable communication over different channels and modes is one ofthe main goals of Mode Division Multiplexing-Wavelength Division Multiplexing(MDM-WDM) communication networks. The reliability can be described by minimumSignal to Noise Ratio (SNR) margin which dependents on launched power,Multimode-Erbium Doped Fiber Amplification (MM-EDFA) gain, and MMFnonlinearity. In this paper, an analytical model for MMF nonlinearity isderived based on Enhanced Gaussian Noise (EGN) model formulation by consideringcarrier phase estimation and the first four dispersion terms. The proposed EGNmodel is verified through the split step Fourier method simulation. Consideringa multi-node linear network, the joint optimized power and gain allocationbased on minimum SNR margin maximization is formulated. The practicalconstraints including MM-EDFA saturation power and maximum gain are consideredand the problem is solved by using convex optimization. Three scenarios areassumed including best equal power, optimized power, and joint optimized powerand gain. In the first scenario, equal powers are considered for differentchannels and modes with equal MM-EDFA gain in all spans. It is worth mentioningthat the MM-EDFA gain is equal to span loss. In the second scenario, differentpowers are allocated to different channels and modes with equal MM-EDFA gain inall spans. In the third case, allocated powers to each channel and mode areoptimized. Moreover, the MM-EDFA gain for each span is optimized separately.

Joint Power and Gain Allocation in MDM-WDM Optical Communication Networks Based on Enhanced Gaussian Noise Model