We derive a Stokes parameter model to calculate the penalties due to the combination of polarization mode dispersion (PMD), polarization dependent loss (PDL), and polarization dependent gain (PDG) in long-haul,dense wavelength divison multiplexed (WDM) systems. In this model, we follow the Stokes parameters for the signal and the noise in each channel instead of following the full time domain behavior of each channel. This approach allows us to determine the statistical distribution of penalties with up to 105 fiber realizations and 40 channels. We validate this model to the extent possible by comparison to full numerical simulations. Using this model, we find that the interaction of PMD and PDL is the major source of penalties and that the effect of PDG is negligible in WDM systems with more than ten channels.
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