Fiber optic communication systems (FOCSs) have attained a lot of attention by revolutionizing the telecommunication industry and offering new possibilities with the technical advancements in state-of-the-art high speed digital electronics. Advanced modulation formats make use of the phase, amplitude, and polarization of the optical signals at the same time to provide high spectral efficiency as compared with 1 bit/s/Hz for the intensity modulation direct detection system (IMDD), but are highly prone to transmission impairments. Thus, the effects that add up to the optical fiber impairments such as optical fiber chromatic dispersion (OFCD), polarization model dispersion (PMD), and phase offset and noise (POaN) need to be addressed at the receiver side. The development of components and algorithms to minimize these effects in next generation FOCSs with 100 Gbps data rate and beyond with long-haul transmission is still a challenging issue. In this paper, digital signal processing- (DSP-) assisted dispersion and nonlinear compensation techniques are presented to compensate for physical layer impairments including OFCD, PMD, and POaN. The simulations are performed considering Dual Polarization- (DP-) QPSK modulation format to achieve two-fold data rate to achieve spectral efficiency of 3.28 bits/s/Hz by making use of the polarization diversity and system performance is investigated in terms of bit error rate (BER), constellation diagrams, and quality factor (Q-factor) for different values of optical signal-to-noise ratio (OSNR), launch power (PL), and fiber length.