**5. Analysis of step-size selection in 16-QAM transmission**

In this section we numerically review the system performances of different step-size selection methods to implement DBP. We apply a logarithmic distribution of step sizes and numerically investigate the influence of varying step size on DBP performance. This algorithm is applied in a single-channel 16-QAM system with bit rate of 112Gbit/s over a 20x80km link of standard single mode fiber without in-line dispersion compensation. The results of calculating the non-linearity at different positions, including symmetric, asymmetric, and the modified (**?**) schemes, are compared. We also demonstrate the performance of using both logarithmic step sizes and constant step sizes, revealing that use of logarithmic step sizes performs better than constant step sizes in case of applying the same number of steps, especially at smaller numbers of steps. Therefore the logarithmic step-size method is still a potential option in terms of improving DBP performance although more calculation efforts are needed compared with the existing multi-span DBP techniques such as (Ip et al., 2010; Li et al., 2011). Similar to the constant step-size method, the logarithmic step-size methods is also applicable to any kind of modulation formats.
