This article proposes an accelerated statistical eye diagram estimation method for efficient signal integrity (SI) analysis. An eye diagram is a critical metric in the SI analysis, however obtaining an eye diagram is time-consuming in simulation. The required time might be a few weeks depending on the complexity. Because the eye diagram is obtained by superposition of the received waveforms. Statistical eye diagram estimation methods were proposed to make the eye diagram acquisition efficient, however, it still has a limited improvement due to a large number of convolution operations. To address this limitation, the proposed method includes two approaches: (i) an increased voltage step in the amplitude PDF with a compensation factor and (ii) skippable and replaceable convolution operations. The efficiency of the proposed method is verified by comparing the derived result with that of a conventional transient simulation. The previous estimation method requires 1,065 s while approaches (i) and (ii) reduce the required time to 88 and 510 s, respectively. When both approaches are applied, the required time is reduced to 17 s in comparison to the simulation time of 259,200 s required for a transient simulation. Approach (ii) reduces the number of convolution operations from 768,000 to 103,000. Therefore, the proposed method successfully reduces the required simulation time and the required number of convolutions to obtain a statistical eye diagram.


Electrical and Computer Engineering


National Science Foundation, Grant IIP-1916535

Keywords and Phrases

Electromagnetic compatibility (EMC); eye diagram; eye diagram estimation method; high-speed systems; signal integrity (SI); single-bit response (SBR)

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2023 The Authors, All rights reserved.

Publication Date

01 Jan 2023