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.

中文翻译：

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基于贝叶斯优化的高速通道最坏情况眼图分析

眼图分析是信号完整性评估的有利工具之一。传统上，这是通过冗长的瞬态仿真执行的，对于具有低误码率的复杂高速通道，这可能会非常耗时。存在用于眼睛估计的方法。但是，它们要么仅适用于线性时不变系统，要么缺乏准确性或效率。在本文中，提出了一种基于优化的方法来快速获得最坏情况下的眼图特征。该方法集中于符号间干扰，因为其影响可能跨越许多符号并包括串扰，这使得建模具有挑战性。在本文中，数据模式导致对应于高符号的最低电压，对应于低符号的最高电压，计算最小和最大水平交叉点的时间。然后，使用这些点估计眼睛的高度，眼睛的宽度和最坏情况下的眼睛张开。为了降低复杂度，提出的方法包括利用格雷码的映射算法。另外，使用贝叶斯优化是因为它在非线性和非凸问题上的效率和良好的性能。最后，通过数值实例对所提出的方法在高速SerDes通道以及系统级封装设计中的通道的应用进行了评估，结果表明了其准确性和效率。另外，使用贝叶斯优化是因为它在非线性和非凸问题上的效率和良好的性能。最后，通过数值实例对所提出的方法在高速SerDes通道以及系统级封装设计中的通道的应用进行了评估，结果表明了其准确性和效率。另外，使用贝叶斯优化是因为它在非线性和非凸问题上的效率和良好的性能。最后，通过数值实例对所提出的方法在高速SerDes通道以及系统级封装设计中的通道的应用进行了评估，结果表明了其准确性和效率。