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A comprehensive treatment of digital backward propagation (DBP) accounting for the vectorial nature of optical transmission is presented. Experimental results show that self-phase and cross-phase modulation are the major sources of nonlinear impairments, even for small channel spacings and for transmission in low dispersion fibers. It is verified that compensating only the incoherent nonlinear impairments not only has the advantage of requiring lower computational load but also removes the necessity of using phase-locked carriers for the signal or phase-locked local oscillators. Simulation results show that polarization-mode dispersion has to be taken into account for practical wavelength division multiplexing systems for DBP to work properly. It is found that to compensate interchannel nonlinear impairments, the changes in the polarization states of channels have to be followed at every span.