Coherent detection employing high modulation formats has become one of the most attractive technologies for long-haul transmission systems due to the high power and spectral efficiencies. Appropriate digital signal processing (DSP) is used to equalize and compensate for distortion caused by laser and fiber characteristics and impairments, such as polarization mode dispersion (PMD), polarization rotation, laser phase noise and nonlinear effects. Research on the various DSP algorithms in the coherent optical communication systems is the most promising investigation. In this research, two new modulation formats; polarization QAM modulation (POL-QAM) and set-partitioning QAM (SP-QAM) are investigated due to their high spectral efficiency and novelty. For PMD and polarization rotation equalization, a new modified constant modulus algorithm (CMA) is proposed for POL-QAM. We investigate the bit error rate (BER) performance of the two modulation formats over fiber channel considering PMD and polarization rotation effects. Furthermore, we investigate the BER performance of the two modulation formats over long-haul fiber optic transmission systems. Carrier phase estimation (CPE) algorithms are also investigated, which are used to mitigate phase noise caused by the transmitter.