Nonlinear frequency division multiplexing (NFDM) techniques encode information in the so-called nonlinear spectrum which is obtained from the nonlinear Fourier transform (NFT) of a signal. NFDM techniques so far have been applied to the nonlinear Schrödinger equation (NLSE) that models signal propagation in a lossless fiber. Conventionally, the true lossy NLSE is approximated by a lossless NLSE using the path-average approach which makes the propagation model suitable for NFDM. The error of the path-average approximation depends strongly on signal power, bandwidth and the span length. It can degrade the performance of NFDM systems and imposes challenges on designing high data rate NFDM systems. Previously, we proposed the idea of using dispersion decreasing fiber (DDF) for NFDM systems. These DDFs can be modeled by a NLSE with varying-parameters that can be solved with a specialized NFT without approximation errors. We have shown in simulations that complete nonlinearity mitigation can be achieved in lossy fibers by designing an NFDM system with DDF if a properly adapted NFT is used. We reported performance gains by avoiding the aforementioned path-average error in an NFDM system by modulating the discrete part of the nonlinear spectrum. In this paper, we extend the proposed idea to the modulation of continuous spectrum. We compare the performance of NFDM systems designed with dispersion decreasing fiber to that of systems designed with a standard fiber with the path-average model. Next to the conventional path-average model, we furthermore compare the proposed system with an optimized path-average model in which amplifier locations can be adapted. We quantify the improvement in the performance of NFDM systems that use DDF through numerical simulations.
Francesco Da Ros, Stenio M. Ranzini, Henning Buelow and Darko Zibar, Reservoir-computing based equalization with optical pre-processing for short-reach optical transmission IEEE Journal of Selected Topics in Quantum Electronics
Chromatic dispersion is one of the key limitations to increasing the transmission distance-rate product for short-reach communication systems relying on intensity modulation and direct detection. The available optical dispersion-compensation techniques have lost favor due to their high impact on the link loss budget. Alternative digital techniques are commonly power-hungry and introduce latency. In this work, we compare different digital, optical and joint hybrid approaches to provide equalization and dispersion compensation for short-reach optical transmission links. Reservoir computing, as a promising technique to provide equalization with memory in an easily trainable fashion, is reviewed and the properties of the reservoir network are directly linked to system performance. Furthermore, we propose a new hybrid method relying on reservoir computing combined with a simple signal pre-conditioning stage directly in the optical domain. The optical pre-processing uses an arrayed waveguide grating to split the received signal into smaller sub-bands. The performance of the proposed scheme is thoroughly characterized both in terms of reservoir properties and appropriate pre-processing. The benefits are numerically demonstrated for 32-GBd on-off keying signal transmission, and show an increase in reach from 10 km to 40 km, corresponding to 400 %, compared with more complex digital-only techniques.
V. Bajaj, S. Chimmalgi, V. Aref and S. Wahls, Exact nonlinear frequency division multiplexing in lossy fibers Proc. 45th European Conference on Optical Communication (ECOC), Dublin, Ireland, Sep. 2019.
The path-average approximation penalizes NFDM transmission over lumped amplified fiber links.We investigate suitably tapered lossy fibers to overcome the approximation error induced by the path average, making the NFDM transmission exact. Error vector magnitude gains up to 4.8 dB are observed.
Magalhaes Ranzini, S., Da Ros, F., & Zibar, D. (Accepted/In press). Joint low-complexity opto-electronic chromatic dispersion compensation for short-reach transmission.. In Proceedings of 2019 IEEE Photonics Conference IEEE. (San Antonio, United States, 29/09/2019)
A low complexity solution to mitigate chromatic dispersion is proposed for short-reach communications. The technique relies on sharing complexity between optical and electronic domain and shows gains in terms of required receiver SNR for up to 20-km fiber transmission.
Magalhaes Ranzini, S, Da Ros, F, Bülow, H & Zibar, D 2020, ‘Tunable Optoelectronic Chromatic Dispersion Compensation Based on Machine Learning for Short-Reach Transmission.‘, Applied Sciences, vol. 9, no. 20. https://doi.org/10.3390/app9204332
In this paper, a machine learning-based tunable optical-digital signal processor is demonstrated for a short-reach optical communication system. The effect of fiber chromatic dispersion after square-law detection is mitigated using a hybrid structure, which shares the complexity between the optical and the digital domain. The optical part mitigates the chromatic dispersion by slicing the signal into small sub-bands and delaying them accordingly, before regrouping the signal again. The optimal delay is calculated in each scenario to minimize the bit error rate. The digital part is a nonlinear equalizer based on a neural network. The results are analyzed in terms of signal-to-noise penalty at the KP4 forward error correction threshold. The penalty is calculated with respect to a back-to-back transmission without equalization. Considering 32 GBd transmission and 0 dB penalty, the proposed hybrid solution shows chromatic dispersion mitigation up to 200 ps/nm (12 km of equivalent standard single-mode fiber length) for stage 1 of the hybrid module and roughly double for the second stage. A simplified version of the optical module is demonstrated with an approximated 1.5 dB penalty compared to the complete two-stage hybrid module. Chromatic dispersion tolerance for a fixed optical structure and a simpler configuration of the nonlinear equalizer is also investigated.