Statistical Method for Eye Diagram Simulation in High-Speed Link Nonlinear System Applications

Due to the rapid expansion of high-speed systems and the escalating complexity of circuits in recent decades, relying on linearity and applying the superposition concept in high-speed signaling systems results in an underestimation of the influence of nonlinear effects within circuits. Consequently, the traditional fast simulation method, which assumes linearity, is no longer adequate for accurately analyzing high-speed link nonlinear systems. Therefore, a fast and accurate statistical eye diagram analysis dedicated to nonlinear systems is proposed. The proposed method uses the Volterra-Wiener model identification to decompose the system into a linear time-invariant (LTI) system and a static nonlinear system represented by the polynomial function. The 2D probability density function (PDF) or statistical eye diagram of the LTI system is estimated by the direct statistical analysis of the single-bit response (SBR). Subsequently, the nonlinear statistical eye is estimated by applying nonlinear density transformation with polynomial-based weights. The eye height (EH) and eye width (EW) are determined based on the voltage PDF and time PDF using statistical information. The accuracy and efficiency of the proposed method are verified using three examples: the ideal nonlinearity Wiener model, the differential FinFET buffer, and the high-speed link with nonlinear equalization.