Systems and method of compensating for transmission impairment are disclosed. One such method comprises receiving a wavelength-division multiplexed optical signal. The received optical signal has been distorted in the physical domain by an optical transmission channel. The method further comprises propagating the distorted optical signal backward in the electronic domain in a corresponding virtual optical transmission channel. The backward propagation fully compensates for fiber dispersion, self-phase modulation, and cross-phase modulation (XPM) and partially compensates for four-wave mixing (FWM).