An optical back propagation (OBP) technique using Raman pumped dispersion compensation fibers (DCF) is investigated to compensate for nonlinear impairments in WDM systems in real time. The proposed inline OBP module consists of an optical phase conjugator, amplifiers and a Raman pumped DCF. In order to suppress the nonlinear effects of the transmission fibers exactly, the power in the backpropagation fiber should increase exponentially with distance. This can be approximately achieved by using forward/backward Raman pumping of the dispersion compensating fiber (DCF). We introduce two configurations to realize the OBP. In this paper, we show that the OBP with forward/backward pumping provides 2.45 dB Q-factor gain compared to single-channel digital back propagation (DBP) when transmission distance is 1500 km for a WDM system with QAM-64. To minimize the variation of effective gain coefficient of the Raman pumped DCF as a function of distance, bidirectional pumping scheme which can provide the signal power profile closest to that required by the ideal OBP condition is proposed. The bidirectional pumping scheme provides a superior performance over forward/backward pumping and wideband DBP (i.e., DBP is applied on the entire WDM signal). Our numerical simulation results show that the bidirectional pumping scheme provides 7.6 dB and 5 dB advantage in Q-factor as compared to single-channel DBP and wideband DBP, respectively at a transmission distance of 5000 km. The maximum achievable reach of a long haul WDM system can be enhanced by 225% using bidirectional pumping scheme as compared to wideband DBP.