The current 5G and data-center services as well as the associated applications are imposing stringent requirements on the optical communication systems due to the ever-increasing network traffic. Based on this, there is significant need to enhance per wavelength data rate beyond 100 Gb/s. Meeting the current and future requirements for a high-speed system demands novel coding schemes, advanced modulation formats, and high-performance DSP algorithms. This paper presents our recent investigations on the optimization of the DSP subsystems for simplified coherent receivers, including the conventional Kramers Kronig (KK) scheme, upsampling free KK, and iterative linear filter architectures.