Differentiable Machine Learning-Based Modeling for Directly-Modulated Lasers

TL;DR

This work tackles the difficulty of differentiable channel modeling for directly modulated lasers in large-signal operation, which is essential for end-to-end optimization but hindered by nonlinear laser dynamics. It develops and compares data-driven surrogate models—including a convolutional attention transformer (CAT), TDNN, Volterra, and LSTM—trained to reproduce laser output from input current sequences and evaluated within a numerical equalization setup against laser-rate-equation ground truth. The CAT model achieves the best combination of low $NRMSE$ and fast inference across symbol rates, while other models show varying deficits at higher rates. The study demonstrates that differentiable surrogates can substitute expensive ODE solvers in gradient-based link optimization for DML-based systems, enabling practical end-to-end design of optical transceivers.

Abstract

End-to-end learning has become a popular method for joint transmitter and receiver optimization in optical communication systems. Such approach may require a differentiable channel model, thus hindering the optimization of links based on directly modulated lasers (DMLs). This is due to the DML behavior in the large-signal regime, for which no analytical solution is available. In this paper, this problem is addressed by developing and comparing differentiable machine learning-based surrogate models. The models are quantitatively assessed in terms of root mean square error and training/testing time. Once the models are trained, the surrogates are then tested in a numerical equalization setup, resembling a practical end-to-end scenario. Based on the numerical investigation conducted, the convolutional attention transformer is shown to outperform the other models considered.

Figures (5)

• Figure 1: Block diagrams of a) data acquisition and b) model setup
• Figure 2: NRMSE scores of the studied models
• Figure 3: Time elapsed (per epoch) by the presented models
• Figure 4: Eye diagram of a 4PAM Gaussian pulse train at $R_s \approx f_R$ for a) ODE solver, b) TDNN, c) Volterra filter, d) LSTM and e) CAT.
• Figure 5: Equalization NRMSE tested on a) surrogate models b) ODE solver