Abstract
In long-haul optical communication systems, compensating nonlinear effects through digital signal processing (DSP) is difficult due to intractable interactions between Kerr nonlinearity, chromatic dispersion (CD) and amplified spontaneous emission (ASE) noise from inline amplifiers. Optimizing the standard digital back propagation (DBP) as a deep neural network (DNN) with interleaving linear and nonlinear operations for fiber nonlinearity compensation was shown to improve transmission performance in idealized simulation environments. Here, we extend such concepts to practical single-channel and polarization division multiplexed wavelength division multiplexed experiments. We show improved performance compared to state-of-the-art DSP algorithms and additionally, the optimized DNN-based DBP parameters exhibit a mathematical structure which guides us to further analyze the noise statistics of fiber nonlinearity compensation. This machine learning-inspired analysis reveals that ASE noise and incomplete CD compensation of the Kerr nonlinear term produce extra distortions that accumulates along the DBP stages. Therefore, the best DSP should balance between suppressing these distortions and inverting the fiber propagation effects, and such trade-off shifts across different DBP stages in a quantifiable manner. Instead of the common ‘black-box’ approach to intractable problems, our work shows how machine learning can be a complementary tool to human analytical thinking and help advance theoretical understandings in disciplines such as optics.
Highlights
In long-haul optical communication systems, compensating nonlinear effects through digital signal processing (DSP) is difficult due to intractable interactions between Kerr nonlinearity, chromatic dispersion (CD) and amplified spontaneous emission (ASE) noise from inline amplifiers
As different wavelength channels might have traveled through different links in a mesh network before arriving at the same receiver, interchannel nonlinear effects cannot be fully extracted from the received signals that significantly reduce the effectiveness of any joint-channel digital back propagation (DBP) that includes all the signals from neighboring channels, and attempts to compensate both self-phase modulation (SPM) and XPM effects
We show that a low-complexity implementation of such deep neural network (DNN)-based DBP demonstrates a 0.9-dB Q-factor gain compared with optimal DBP performance with arbitrary complexity for single-channel 28-GBaud 16-QAM systems
Summary
Based DBP is optimized by using 200 epochs with step size 0.01, and the converged linear filter spectra Sk(f) and phase derotation coefficients ξk are shown in Fig. 6b–d at 2.2-dBm signal-launched power. Note that as supposed to ξk that refers to the kth-step DNN-based DBP, ξL−Δz here relates to the phase derotation to estimate the transmitted signal at z = L − Δz, which is given by. It is a trade-off between compensating CD of the signal and mitigating the third-order nonlinear distortion term jEzj2Ez and its accumulation along the DBP stages. The optimal nonlinear-phase derotation attempts to strike a balance between reversing the nonlinear phase during propagation and minimizing additional phase noise accumulation along the DBP stages due to corrupted signal power levels.
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