🤖 AI Summary
In mode-division multiplexing (MDM) systems based on multimode fiber, mode-dependent gain (MDG) induces stochastic fluctuations in channel capacity, substantially reducing the average capacity and hindering universal analytical characterization. To address this, we propose a statistical channel model and derive, for the first time, a closed-form expression for the probability distribution of channel capacity for arbitrary mode count $D > 2$, overcoming the prior limitation to $D = 2$. Our approach leverages Gaussian approximation and introduces a fitting parameter to capture inter-mode capacity correlations, ensuring both accuracy and broad applicability. Validated against multi-section Monte Carlo simulations across wide-ranging practical system parameters, the proposed analytical model achieves high fidelity with controllable error. This significantly enhances computational efficiency and theoretical interpretability in capacity assessment. The framework provides a foundational theoretical tool for design optimization and performance prediction of high-dimensional MDM systems.
📝 Abstract
In coupled space-division multiplexing (SDM) transmission systems, imperfections in optical amplifiers and passive devices introduce mode-dependent loss (MDL) and gain (MDG). These effects render the channel capacity stochastic and result in a decrease in average capacity. Several previous studies employ multi-section simulations to model the capacity of these systems. Additionally, relevant works derive analytically the capacity distribution for a single-mode system with polarization-dependent gain and loss (mode count D = 2). However, to the best of our knowledge, analytic expressions of the capacity distribution for systems with D>2 have not been presented. In this paper, we provide analytic expressions for the capacity of optical systems with arbitrary mode counts. The expressions rely on Gaussian approximations for the per-mode capacity distributions and for the overall capacity distribution, as well as on fitting parameters for the capacity cross-correlation among different modes. Compared to simulations, the derived analytical expressions exhibit a suitable level of accuracy across a wide range of practical scenarios.