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