A thorough analysis of equalization-enhanced phase noise (EEPN) and its impact on the coherent optical system is presented. We show with a time-domain analysis that EEPN is caused due to the interference of multiple delayed versions of the dispersed signal, generated by intermixing of the received dispersed signal, and the noise side bands of the local oscillator (LO) in the photodetectors. We derive statistical properties such as the mean, variance, and error vector magnitude of the received signal influenced with EEPN. We show that in coherent optical systems utilizing electronic dispersion compensation, this noise corresponds to multipath fading in wireless communication systems. Closed-form expressions of necessary LO linewidth and/or mitigation bandwidth for a general system configuration and specified OSNR penalty are given. The expressions for system design parameters, validated with system simulations, show that higher order modulation formats, such as 16-quadrature amplitude modulation and beyond, put stringent demands on the LO linewidth unless a mitigation technique is used.