Exact Noise Statistics in Equalized Polarization Multiplexing Systems in the Presence of Polarization Dependent Loss

In polarization multiplexing systems, signal and noise have different correlation matrices in the presence of polarization dependent loss (PDL). Therefore, the noise will be correlated after the signal equalization process, and the statistical characteristics of the noise correlation matrix is vital for the system capacity evaluation. In this paper, a stochastic differential equation (SDE) for the evolution of the noise correlation matrix after equalization is derived and the statistics of the correlation matrix elements are obtained by the related ordinary differential equations (ODEs). A threshold of the link gain, which equals half of the local PDL vector variance, exists. If the gain is above the threshold, one may ensure the average accumulated noise power not to grow exponentially. Monte Carlo simulations are conducted to verify the proposed theory and an excellent agreement is observed.