The reliability and feasibility of optical coherent communication system are strongly conditioned by laser phase noise and fluctuations of the state of polarization (SOP) of the optical field at the output of conventional single mode fiber. The double frequency parameter shift keying (DFPSK) system has been proposed in the literature as an efficient scheme that allows compensation of both effects by sending a reference channel that is suitably frequency shifted by using polarization modulation. This paper presents a comprehensive theoretical analysis for the performance of this system in the presence of dichroism which is introduced when the transmission channel has polarization dependent losses or amplifications. The results indicate that the performance of DFPSK system is affected by dichroism even in the low noise frequency regime.