We systematically investigate the combined effect on the system performance in an optical fiber communication system of a signal that is depolarized due to polarization-mode dispersion (PMD) and noise that is partially polarized due to polarization-dependent loss. We derive a formula for the variance of the electric current of the signal due to the signal-noise beating between a depolarized signal and partially polarized noise. We validate this theoretical formula by comparing the Q -factor calculated using the theory to results obtained from Monte Carlo simulations and experiments. We show that the system performance strongly depends on the power-splitting ratio, the degree of polarization of the noise, and the angle between the states of polarization of the signal and the polarized part of the noise. Although the theoretical formula is derived assuming that the optical fiber only has first-order PMD, we show that for arbitrary fiber, this formula still produces a reliable estimate of the Q-factor provided that the second-order PMD is on the order of 300 ps2 or less.