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.

翻译：在耦合空分复用传输系统中，光学放大器与无源器件的缺陷会引入模式相关损耗与模式相关增益。这些效应使得信道容量具有随机性，并导致平均容量下降。先前多项研究采用多段仿真来建模此类系统的容量。此外，已有相关研究通过解析方法推导了单模系统在偏振相关增益与损耗条件下的容量分布。然而，据我们所知，针对模式数D > 2系统的容量分布解析表达式尚未被提出。本文给出了任意模式数光学系统容量的解析表达式。这些表达式基于各模式容量分布与整体容量分布的高斯近似，以及不同模式间容量互相关性的拟合参数。与仿真结果相比，所得解析表达式在广泛的实际场景中均展现出适宜的精度水平。