Fast Estimation of a Statistical Eye Diagram for Nonlinear High-Speed Links Based on the Minimum Required Order of the Multiple Edge Response Method

With the increase in nonlinear effects of high-speed links, the higher order multiple edge response (MER) method is widely used to accurately evaluate high-speed link performance by computing the statistical eye diagram at the price of massive edge responses. The computational complexity of the MER algorithm exponentially increases with the order. In this article, the estimation method for the minimum order of the MER method is proposed based on the last time of nonlinearity in high-speed links. The edge responses are divided into nonlinear and linear sections according to the minimum order of MER. To further improve the computational efficiency of the convolution operation of higher order MERs, a hybrid method is proposed that combines the double edge response (DER) method and statistical data of the edge response. The DER convolution is used to obtain the probability density distribution in the linear section, and the probability density distribution in the nonlinear section is obtained by the statistics of the rising and falling edge responses with different leading bits, which can greatly reduce the computation time. The accuracy and efficiency of the proposed method are verified by comparison with the higher order MER method.