Nonlinear Interference Mitigation via Deep Neural Networks

Abstract

A neural-network-based approach is presented to efficiently implement digital backpropagation (DBP). For a 32 ×100 km fiber-optic link, the resulting "learned" DBP significantly reduces the complexity compared to conventional DBP implementations.

Wideband Time-Domain Digital Backpropagation via Subband Processing and Deep Learning

“…Real-time digital backpropagation (DBP) based on the split-step Fourier method (SSFM) is widely considered to be impractical due to the complexity of the chromatic dispersion (CD) steps. To address this problem, finite impulse response (FIR) filters may be used instead of fast Fourier transforms (FFTs) to perform time-domain CD filtering [1][2][3][4][5][6][7] . Indeed, the FIR filters can be as short as 3 taps per SSFM step, provided that the step size is sufficiently small (i.e., many steps are used) and the filters in all steps are jointly optimized 6 .…”

“…The complexity of time-domain DBP (TD-DBP) is dominated by the total number of CD filter taps in all steps. Recent work has focused on relatively narrowband signals (e.g., 10 Gbaud in 6 and 20 Gbaud in [3][4][5] ) for which the overall CD memory is low. Since the memory increases quadratically with bandwidth, it is not clear if TD-DBP can be scaled gracefully also to more wideband signals.…”

Model-Based Machine Learning for Joint Digital Backpropagation and PMD Compensation

“…Similar to the NLSE, the Manakov-PMD equation has no general closed-form solutions but can be solved numerically using the SSM. The SSM alternates linear and nonlinear steps, where the nonlinear steps are described by σ (x) = xe jγ 8 9 δ x 2 for x ∈ C 2 and step size δ . The linear steps can be approximated by 2 × 2 MIMO-FIR filters in discrete time, which leads to the model shown in Fig.…”

“…For fiberoptic systems, this can be done for example by considering the split-step method (SSM) for numerically solving the nonlinear Schrödinger equation (NLSE). By viewing all chromatic-dispersion steps as general linear functions, one obtains a parameterized model similar to a multi-layer NN [8]. Compared to standard "black-box" models, this approach has several advantages: it leads to clear hyperparameter choices (such as the number of layers/steps); it provides good initializations for a gradient-based optimization; and it allows one to inspect the learned solutions in order to understand why they work well, thereby providing significant insight into the problem [8][9][10].…”

What Can Machine Learning Teach Us about Communications?

“…However, this typically leads to poor parameter efficiency (i.e., it requires relatively long filters) because truncation errors pile up coherently. We have shown in [22], [23] that this truncation error problem can be controlled effectively by performing a joint optimization of all filter coefficients in the entire DBP algorithm. In particular, the computation graph of the SSFM is optimized via SGD by simply interpreting all matrices A δ as tunable parameters corresponding to the FIR filters, similar to the weight matrices in a deep NN.…”