Abstract
Nonlinearity mitigation based on the enhanced split-step Fourier method (ESSFM) for the implementation of low-complexity digital backpropagation (DBP) is investigated and experimentally demonstrated. After reviewing the main computational aspects of DBP and of the conventional split-step Fourier method (SSFM), the ESSFM for dual-polarization signals is introduced. Computational complexity, latency, and power consumption of DBP based on the SSFM and ESSFM algorithms are estimated and compared. Effective low-complexity nonlinearity mitigation in a 112 Gb/s polarization-multiplexed QPSK system is experimentally demonstrated by using a single-step DBP based on the ESSFM. The proposed DBP implementation requires only a single step of the ESSFM algorithm to achieve a transmission distance of 3200 km over a dispersion-unmanaged link. In comparison, a conventional DBP implementation requires 20 steps of the SSFM algorithm to achieve the same performance. An analysis of the computational complexity and structure of the two algorithms reveals that the overall complexity and power consumption of DBP are reduced by a factor of 16 with respect to a conventional implementation, while the computation time is reduced by a factor of 20. Similar complexity reductions can be obtained at longer distances if higher error probabilities are acceptable. The results indicate that the proposed algorithm enables a practical and effective implementation of DBP in real-time optical receivers, with only a moderate increase in the computational complexity, power consumption, and latency with respect to a simple feed-forward equalizer for bulk dispersion compensation.
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Notes
We consider the classical Cooley–Tukey radix-2 FFT algorithm [5] and assume that each complex multiplication requires four real multiplications and two real additions. Though slightly more efficient implementations are possible, this provides a reasonable indication of the required operations. Moreover, we assume that all fixed quantities (e.g., \(\gamma \Delta zc_{i}\) or \(\exp (-j2\pi ^{2}\beta _{2}f_{k}^{2}\Delta z)\)) are precalculated, and that the complex exponential in (5) is evaluated by using a lookup table.
This approach can be employed even in a real system, as the optimization can be done off-line when designing the link. A more practical (and possibly accurate) approach is that of minimizing the MSE between the output samples (after DBP, equalization, and phase noise/frequency offset compensation) and the transmitted symbols, as suggested in [28]. This, however, needs some care to handle possible interactions with the convergence of the butterfly equalizer and is left to a future investigation.
When the total number of spans is not an exact multiple of the number of spans per step, a final shorter step is considered to account for the remaining spans.
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This work was supported in part by the Italian MIUR under the FIRB project COTONE and by the EU FP-7 GÉANT project COFFEE.
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Secondini, M., Rommel, S., Meloni, G. et al. Single-step digital backpropagation for nonlinearity mitigation. Photon Netw Commun 31, 493–502 (2016). https://doi.org/10.1007/s11107-015-0586-z
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DOI: https://doi.org/10.1007/s11107-015-0586-z