In a coherent optical receiver receiving a polarization multiplexed optical signal through an optical communications network, a method of compensating noise due to polarization dependent loss (PDL). A Least Mean Squares (LMS) compensation block processes sample streams of the received optical signal to generate symbol estimates of symbols modulated onto each transmitted polarization of the optical signal. A decorrelation block de-correlates noise in the respective symbol estimates of each transmitted polarization and generating a set of decorrelated coordinate signals. A maximum likelihood estimator soft decodes the de-correlated coordinate signals generated by the decorrelation block.