The transmission of optical signals under the effects of cross-phase modulation (XPM) and self-phase modulation (SPM) together in pump-probe wave structure is investigated in intensity modulation-direct detection wavelength division multiplexing (IM-DD WDM) systems. A simple expression for frequency domain IM of probe channel is derived. The analytical method to determine the temporal shape of probe wave when arbitrary wave is inputted in pump channel is confirmed. The impact of channel separation and transmission rate to XPM is assessed. We find that the SPM in pump channel increase temporal intensity modulation index reflected XPM to a certain extent. The analytical result agrees well with numerical simulation.