Statistical regression for efficient high-dimensional modeling of analog and mixed-signal performance variations

ABSTRACT

The continuous technology scaling brings about high-dimensional performance variations that cannot be easily captured by the traditional response surface modeling. In this paper we propose a new statistical regression (STAR) technique that applies a novel strategy to address this high dimensionality issue. Unlike most traditional response surface modeling techniques that solve model coefficients from over-determined linear equations, STAR determines all unknown coefficients by moment matching. As such, a large number of (e.g., 10³~10⁵) model coefficients can be extracted from a small number of (e.g., 10²~10³) sampling points without over-fitting. In addition, a novel recursive estimator is proposed to accurately and efficiently predict the moment values. The proposed recursive estimator is facilitated by exploiting the interaction between different moment estimators and formulating the moment estimation problem into a special form that can be iteratively solved. Several circuit examples designed in commercial CMOS processes demonstrate that STAR achieves more than 20x runtime speedup compared with the traditional response surface modeling.

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INDEX TERMS

Primary Classification:
  B. Hardware
  B.7 INTEGRATED CIRCUITS
      B.7.2 Design Aids
          Subjects: Verification

General Terms:
Algorithms

Keywords:
circuits, process variations, response surface modeling