SDM Optical Systems with MMSE Equalizers: Information Rates and Performance Monitoring

The information rate of coupled space-division multiplexing (SDM) transmission systems is impaired by the stochastic effects of mode-dependent gain (MDG) and mode-dependent loss (MDL), turning it into a random variable and reducing its average value. In systems operating with minimum mean squared error (MMSE) equalizers and no channel-state information (CSI), co-channel interference further reduces the instantaneous and average information rates. Analytical solutions for the average information rate in MDG- and MDL-impaired systems under strong coupling have been presented in early studies assuming ideal maximum-likelihood (ML) equalization. However, to the best of our knowledge, a solution encompassing co-channel interference under MMSE equalization has not been presented yet. In this work, we derive statistical models for the MMSE equalizer coefficients and develop analytical solutions for the post-filtering information rate. We also use these statistical models and analytical solutions to carry out MDG and signal-to-noise ratio (SNR) monitoring in coupled SDM systems. The derived analytical solutions and monitoring techniques are validated by Monte-Carlo simulations, exhibiting a suitable accuracy within practical operational values.