In this paper, 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 polarization multiplexed (PM)-QAM coherent optical systems when transmission is modeled as a generic 2x2 frequency dependent transfer function matrix. We present the model and then we statistically test its accuracy in two possible application environments. Our findings show a remarkable agreement between time-domain simulations and analytical results, with average SNR discrepancies of the order of 0.1 dB. We believe our model can find important applications in next generation physical layer aware network planning tools that need to take into account polarization dependent loss/gain and strong filtering, for instance in ultra high baud rate coherent systems.
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