We numerically investigate the impact of channel baud-rate on the performance of logarithmic step-size based spilt-step Fourier method (SSFM). This algorithm is used to implement digital backward propagation (DBP) to efficiently compensate fiber chromatic dispersion (CD) and non-linearities (NL). The DBP method is implemented in N-channel dual-polarization quadrature phase shift keying (DP-QPSK) transmission over 2000km standard single mode fiber (SMF) with no in-line optical dispersion compensation. We investigate the same-capacity and same-bandwidth transmission systems with 56Gbit/s/ch (14GBaud), 112Gbit/s/ch (28GBaud) and 224Gbit/s/ch (56GBaud). Each system has the bandwidth occupancy of 500GHz with a total transmission capacity of 1.12Tbit/s. Moreover, we have also compared the multiple channel transmission performance with single channel transmission to quantify the impact of inter-channel (cross-phase modulation ‘XPM’ and four-wave mixing ‘FWM’) and intra-channel (self-phase modulation ‘SPM’) non-linearities. The logarithmic step-size based DBP algorithm (L-DBP) depicts efficient mitigation of CD and NL impairments. The benefit of the logarithmic step-size is the reduced complexity and computational time for higher baud-rate transmission systems.