Neural networks for optical links nonlinear equalization

The continuously increasing Internet traffic demand, driven by modern technologies such as cloud services Internet of Things and 5G, is posing the request for an upgrade in the Data Center Interconnects (DCI) above their current maximum capacity. Current DCI commercial solutions are based on Intensity Modulation and Direct Detection optical links, able to transmit up to 28 Gbps per lane over nearly 100 m, using Multi-Modal Fiber and low-cost Vertical-Cavity Emitting Surface Lasers (VCSEL). The next step is then to achieve 100 Gbps per lane, but this target seems unfeasible using the current technologies. At high bitrates indeed, several impairments distort the transmitted signals: bandwidth limitations at receiver and transmitter side, modal and chromatic dispersion along with the fiber, and nonlinear effects introduced by components such as the VCSEL. The work of this Thesis aims therefore to overcome these limitations, by designing and studying the Artificial Neural Networks (ANN) to use them as nonlinear post- and pre- equalizers on PAM-4 modulated optical signals. As a first step, the work started by testing several ANN-based post-equalizers structures, used at the receiver side on a simulated optical system, exploiting two different VCSEL models provided by CISCO. We studied what the ANN models learned, developing a Python code for training the neural nets, and we selected an optimization strategy based on variants of the Gradient Descent algorithm that resulted to be effective for the physical system under analysis. We then compared the performances in terms of Bit Error Rate (BER) against different linear and nonlinear models, such as the adaptive Feed-Forward equalizers, or the Volterra-based and MLSE equalizers. We derived moreover from the simulated system a theoretical benchmark (Eb/N0), to assess how far the performances of the equalizers were distant from the ideal bounds. We then studied the use of an ANN-based Digital Predistortion (DPD) at the transmitter side of the simulated system. By following the so-called “Indirect Learning Approach”, we trained the models as post-distorters at receiver side, placing them after the optimization at the transmitter side. We studied the issues in applying this method: from the correct way to place the trained nonlinear predistorter in the system, to the physical limitations of the system, such as the limited dynamics of the Digital-to-analog converter. Analyzing the effects on the signals and exploiting techniques such as clipping, we present how to overcome these problems. We then present the results obtained in the simulated system using pre- and/or post- equalization, assessing the advantages of using DPD. Finally, we applied the nonlinear post-equalizers and pre-distorters on two different experimental optical systems. We report therefore the problematics that arise when using DPD in real transmission systems, and we illustrate the performances obtained with the nonlinear equalizers. By considering the results obtained during this Thesis to be a starting point, we suggest then possible future works related to nonlinear equalization. The next step in this study could consist in mastering more advanced techniques for using neural networks as nonlinear equalizer: for instance, a Direct Learning Approach could be the next step for training nonlinear predistorters, or the End-to-end Learning could be applied to jointly train the equalizers at transmitter and receiver side.