有效的矩估计与极小的样本量通过贝叶斯推理模拟/混合信号验证

Chenjie Gu, E. Chiprout, Xin Li
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引用次数: 21

摘要

在模拟/混合信号电路的预硅和后硅验证中,一个关键问题是估计电路性能的分布,由此可以估计所有电路配置和角落的故障概率和参数良率。对于极小的样本量,传统的估计器只能达到非常低的置信水平,从而导致过度验证或验证不足。在本文中,我们提出了一种多总体矩估计方法,该方法在小样本量下显著提高了估计精度。实际上,所提出的估计量在理论上保证优于通常的矩估计量。其关键思想是利用在不同电路配置和角落采集的仿真和测量数据可以相互关联,并且是条件独立的这一事实。我们通过采用贝叶斯框架来利用不同种群之间的这种相关性,即通过学习先验分布并使用先验应用最大后验估计。我们将提出的方法应用于几个数据集,包括商业高速I/O链路的硅后测量,并证明平均误差减少高达2倍,这可以等效地转化为验证时间和成本的显着减少。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Efficient moment estimation with extremely small sample size via bayesian inference for analog/mixed-signal validation
A critical problem in pre-Silicon and post-Silicon validation of analog/mixed-signal circuits is to estimate the distribution of circuit performances, from which the probability of failure and parametric yield can be estimated at all circuit configurations and corners. With extremely small sample size, traditional estimators are only capable of achieving a very low confidence level, leading to either over-validation or under-validation. In this paper, we propose a multi-population moment estimation method that significantly improves estimation accuracy under small sample size. In fact, the proposed estimator is theoretically guaranteed to outperform usual moment estimators. The key idea is to exploit the fact that simulation and measurement data collected under different circuit configurations and corners can be correlated, and are conditionally independent. We exploit such correlation among different populations by employing a Bayesian framework, i.e., by learning a prior distribution and applying maximum a posteriori estimation using the prior. We apply the proposed method to several datasets including post-silicon measurements of a commercial highspeed I/O link, and demonstrate an average error reduction of up to 2×, which can be equivalently translated to significant reduction of validation time and cost.
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