Differentiable Machine Learning-Based Modeling for Directly-Modulated Lasers

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.

Low-complexity Samples versus Symbols-based Neural Network Receiver for Channel Equalization

Low-complexity neural networks (NNs) have successfully been applied for digital signal processing (DSP) in short-reach intensity-modulated directly detected optical links, where chromatic dispersion-induced impairments significantly limit the transmission distance. The NN-based equalizers are usually optimized independently from other DSP components, such as matched filtering. This approach may result in lower equalization performance. Alternatively, optimizing a NN equalizer to perform functionalities of multiple DSP blocks may increase transmission reach while keeping the complexity low. In this work, we propose a low-complexity NN that performs samples-to-symbol equalization, meaning that the NN-based equalizer includes match filtering and downsampling. We compare it to a samples-to-sample equalization approach followed by match filtering and downsampling in terms of performance and computational complexity. Both approaches are evaluated using three different types of NNs combined with optical preprocessing. We numerically and experimentally show that the proposed samples-to-symbol equalization approach applied for 32 GBd on-off keying (OOK) signals outperforms the samples-domain alternative keeping the computational complexity low. Additionally, the different types of NN-based equalizers are compared in terms of performance with respect to computational complexity.

Addressing Data Scarcity in Optical Matrix Multiplier Modeling Using Transfer Learning

We present and experimentally evaluate using transfer learning to address experimental data scarcity when training neural network (NN) models for Mach-Zehnder interferometer mesh-based optical matrix multipliers. Our approach involves pre-training the model using synthetic data generated from a less accurate analytical model and fine-tuning with experimental data. Our investigation demonstrates that this method yields significant reductions in modeling errors compared to using an analytical model, or a standalone NN model when training data is limited. Utilizing regularization techniques and ensemble averaging, we achieve < 1 dB root-mean-square error on the matrix weights implemented by a photonic chip while using only 25% of the available data.

Rate Adaptive Geometric Constellation Shaping Using Autoencoders and Many-To-One Mapping

A many-to-one mapping geometric constellation shaping scheme is proposed with a fixed modulation format, fixed FEC engine and rate adaptation with an arbitrarily small step. An autoencoder is used to optimize the labelings and constellation points' positions.

Data-Driven Modeling of Directly-Modulated Lasers

The end-to-end optimization of links based on directly-modulated lasers may require an analytically differentiable channel. We overcome this problem by developing and comparing differentiable laser models based on machine learning techniques.

Data-efficient Modeling of Optical Matrix Multipliers Using Transfer Learning

We demonstrate transfer learning-assisted neural network models for optical matrix multipliers with scarce measurement data. Our approach uses <10\% of experimental data needed for best performance and outperforms analytical models for a Mach-Zehnder interferometer mesh.

Reservoir Computing-based Multi-Symbol Equalization for PAM 4 Short-reach Transmission

We propose spectrum-sliced reservoir computer-based (RC) multi-symbol equalization for 32-GBd PAM4 transmission. RC with 17 symbols at the output achieves an order of magnitude reduction in multiplications/symbol versus single output case while maintaining simple training.

Geometric Constellation Shaping for Fiber-Optic Channels via End-to-End Learning

End-to-end learning has become a popular method to optimize a constellation shape of a communication system. When the channel model is differentiable, end-to-end learning can be applied with conventional backpropagation algorithm for optimization of the shape. A variety of optimization algorithms have also been developed for end-to-end learning over a non-differentiable channel model. In this paper, we compare gradient-free optimization method based on the cubature Kalman filter, model-free optimization and backpropagation for end-to-end learning on a fiber-optic channel modeled by the split-step Fourier method. The results indicate that the gradient-free optimization algorithms provide a decent replacement to backpropagation in terms of performance at the expense of computational complexity. Furthermore, the quantization problem of finite bit resolution of the digital-to-analog and analog-to-digital converters is addressed and its impact on geometrically shaped constellations is analysed. Here, the results show that when optimizing a constellation with respect to mutual information, a minimum number of quantization levels is required to achieve shaping gain. For generalized mutual information, the gain is maintained throughout all of the considered quantization levels. Also, the results implied that the autoencoder can adapt the constellation size to the given channel conditions.

End-to-end Learning of a Constellation Shape Robust to Channel Condition Uncertainties

Vendor interoperability is one of the desired future characteristics of optical networks. This means that the transmission system needs to support a variety of hardware with different components, leading to system uncertainties throughout the network. For example, uncertainties in signal-to-noise ratio and laser linewidth can negatively affect the quality of transmission within an optical network due to e.g. mis-parametrization of the transceiver signal processing parameters. In this paper, we propose to geometrically optimize a constellation shape that is robust to uncertainties in the channel conditions by utilizing end-to-end learning. In the optimization step, the channel model includes additive noise and residual phase noise. In the testing step, the channel model consists of laser phase noise, additive noise and blind phase search as the carrier phase recovery algorithm. Two noise models are considered for the additive noise: white Gaussian noise and nonlinear interference noise model for fiber communication. The latter models the behavior of an optical fiber channel more accurately because it considers the nonlinear effects of the optical fiber. For this model, the uncertainty in the signal-to-noise ratio can be divided between amplifier noise figures and launch power variations. For both noise models, our results indicate that the learned constellations are more robust to uncertainties in channel conditions compared to a standard constellation scheme such as quadrature amplitude modulation and more importantly standard geometric constellation shaping techniques.

End-to-end Learning of a Constellation Shape Robust to Variations in SNR and Laser Linewidth

We propose an autoencoder-based geometric shaping that learns a constellation robust to SNR and laser linewidth estimation errors. This constellation maintains shaping gain in mutual information (up to 0.3 bits/symbol) with respect to QAM over various SNR and laser linewidth values.