Application of Sparse Polynomials Chaos Expansion Via Enhanced Compressive Sensing Method for Stochastic Analysis of Interconnects

Crosstalk in interconnects plays a crucial role in electromagnetic compatibility and signal integrity. Recently, growing attention has been devoted to studying the impact of potential uncertainties on crosstalk effects. This paper presents a novel approach to uncertainty quantification based on generalized polynomial chaos theory and compressed sensing theory to assess uncertainties effects on crosstalk on interconnects. The proposed method utilizes a hyperbolic truncation scheme and a Subspace Pursuit algorithm to efficiently address the curse of dimensionality. Additionally, the QR factorization method is incorporated to maintain the linear independence of the sample set, thereby improving the efficiency of coefficient computation. The effectiveness of this approach is demonstrated by comparing the uncertainty quantification results with those obtained using the Monte Carlo method and the Polynomial Chaos Expansion method based on least squares.