  In this letter, we propose the extension of a previously presented analytical
model for the estimation of the signal-to-noise ratio (SNR) at the output of an
adaptive equalizer in coherent optical transmission systems when transmission
is modeled as a generic 2x2 matrix transfer functions, to be applied to
polarization multiplexed communications based on advanced modulation formats
(PM-QAM). We present the model and then we extensively test its accuracy on an
possible application environment. Our findings show a remarkable agreement,
with maximum SNR discrepancies of about 0.5 $dB$ between time-domain
simulations and analytical results.
