Worst-Case Eye Analysis of High-Speed Channels Based on Bayesian Optimization

One of the favorable tools for signal integrity evaluation is eye diagram analysis. This is traditionally performed with a lengthy transient simulation, which can be prohibitively time consuming for complex high-speed channels with a low bit error rate. Methods for eye estimation exist; however, they are either only applicable to linear time-invariant systems or have lack in accuracy or efficiency. In this article, an optimization-based approach is proposed to quickly obtain the worst-case eye diagram characteristics. This approach focuses on the inter-symbol interference since its effect can span over many symbols and include crosstalk, making it challenging to model. In this article, the data patterns leading to the lowest voltage corresponding to a high symbol, the highest voltage corresponding to a low symbol, and the times of minimum and maximum level crossing points are calculated. Then, eye height, eye width, and the worst-case eye opening are estimated using these points. To reduce complexity, the proposed approach includes a mapping algorithm that exploits the Gray code. Additionally, Bayesian optimization is used because of its efficiency and good performance on non-linear and non-convex problems. Finally, the application of the proposed approach to high-speed SerDes channels, and channels in system-on-package designs is evaluated with numerical examples, where the results show its accuracy and efficiency.