Method for Accurate and Efficient Eye Diagram Prediction of Nonlinear High-Speed Links

Signaling analysis of nonlinear high-speed circuits is challenging because it cannot rely on linear time-invariant principles, whereas an exhaustive nonlinear simulation is computationally prohibitive for low bit error rates. To find the worst-case eye, an exhaustive approach requires nonlinear simulations of
$2^m$
bit patterns for a channel of
$m$
-bit memory. In this article, we represent the nonlinear responses to the
$2^m$
inputs by a rank-
$k$
matrix, where
$k$
denotes the number of distinct waveforms in the responses for a prescribed accuracy, which is much smaller than
$2^m$
. We further develop a fast full cross approximation algorithm to find the rank-
$k$
model with a low complexity independent of
$2^m$
. Simulations of large-scale real-world nonlinear circuits with an over 100-bit channel memory demonstrate the accuracy, efficiency, and capacity of the proposed work.