Statistical Analysis for Pulse Amplitude Modulation With N-Level (PAM-N) Signaling Considering Crosstalk in High-Speed Channels

In this article, we propose a novel statistical eye-diagram estimation method that accounts for crosstalk in high-speed channels utilizing pulse amplitude modulation N-level (PAM-N) signaling. In advanced packages, the increased electromagnetic coupling from finer interconnect pitches makes crosstalk a dominant factor in compromising the inherently low signal-to-noise ratio (SNR) of PAM-N serializer/de-serializer (SerDes) interfaces. The proposed method enables rapid and accurate statistical eye-diagram estimation in multi-level signaling without the need for transient simulations. The methodology successfully integrates inter-symbol interference (ISI), near-end crosstalk (NEXT), and far-end crosstalk (FEXT) into a unified probability density function (PDF), which enables the derivation of precise voltage bathtub curves at a target bit-error rate (BER). The validity of the proposed method is demonstrated by achieving eye-diagram contour results that show strong agreement with conventional transient simulations. Estimated results showed a high correlation with existing transient simulations, and even in a complex crosstalk environment, a speed improvement of at least 40 times was achieved while maintaining an error rate within 4.0%. Consequently, this article presents a verified, efficient, and accurate statistical analysis methodology for PAM-N signaling considering crosstalk in high-speed channels.