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non-optimized
γ DBP (Fig. 12(c)), and with optimized
γ DBP (Fig. 12(d)). The optimized value
is 1.28(km 1 W 1 ). With optimization of
γ DBP , the constellation diagram can be rotated back
completely.
Fig. 11. (a) Required number of steps per span at various launch powers for different SSFM
algorithms, and (b) Step-size distribution and average power in each step.
Fig. 12. Constellation diagrams of received 16-QAM signals. (a) constant step size with
non-optimized
γ DBP , (b) constant step size with with optimized
γ DBP , (c) logarithmic step
sizes with non-optimized
γ DBP and (d) logarithmic step sizes with optimized
γ DBP .
5.3 Conclusion
We studied logarithmic step sizes for DBP implementation and compared the performance
with uniform step sizes in a single-channel 16-QAM transmission system over a length of
20x80km at a bit rate of 112Gbit/s. Symmetric, asymmetric and modified SSFM schemes have
been applied for both logarithmic and constant step-size methods. Using logarithmic step
sizes saves up to 50% in number of steps with respect to using constant step sizes. Besides, by
using logarithmic step sizes, the asymmetric scheme already performs nicely and optimizing
non-linear calculating position becomes less important in enhancing the DBP performance,
which further reduces the computational efforts for DBP algorithms
6. Acknowledgement
The authors gratefully acknowledge funding of the Erlangen Graduate School in Advanced
Optical Technologies (SAOT) by the German National Science Foundation (DFG) in the
framework of the excellence initiative.
 
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