Optimal power allocation in nonlinear MDM-WDM systems using Gaussian noise model

Mode-division multiplexing (MDM) using few-mode fibre (FMF) has received increasing attention to address the exponential growth of data traffic in long-haul optical communication systems. Also, combining the MDM with wavelength-division multiplexing (WDM) is a promising approach for dramatically growing the transmission capacity in such systems. However, a major barrier in this regard is the FMF nonlinear effects, which can significantly reduce the link performance. In this paper, in order to alleviate the FMF nonlinear effects, we focus on power allocation in FMF links by optimizing the input power of each optical WDM channel of each spatial mode, which leads to maximizing the total capacity transmission and also the minimum signal to noise ratio (SNR) margin. The FMF nonlinearity has been already modelled as the Gaussian noise (GN) for which no closed-form formulation has been developed so far. Here, we derive a closed-form GN model for this problem and verify it by comparing with the integral-form GN model and split-step Fourier method. In this approach, an optimal power is independently determined for each channel of each mode by optimizing a capacity maximization and a minimum SNR margin maximization problem in convex forms. The performance of different links including the single mode fibre-WDM, MDM-single channel, and MDM-WDM are compared using computer simulations. These systems are comprehensively investigated in equal/non-equal required SNR as well as flat/non-flat amplifier gain scenarios. It is shown that optimized power allocation to each channel of each mode has a significant enhancement in the minimum SNR margin maximization scheme compared to the best equal power allocation. Furthermore, this improvement is much more in non-equal required SNR and the non-flat amplifier gain scenarios, showing the efficiency of the established approach in practical communication links.