Fast and Accurate Estimation of Statistical Eye Diagram for Nonlinear High-Speed Links

A fast and accurate statistical eye diagram estimation method for high-speed nonlinear links is proposed in this article. Probability density functions (PDFs) of output responses are derived based on multiple edge responses (MERs). According to the property that the influence of nonlinearity will not propagate for a long time in high-speed links, a new scheme for calculating the PDFs of responses is presented, in which the convolution process is divided into nonlinear section, transition section, and linear section. Convolutions via high-order of MERs are only used for the nonlinear section, low-order of MERs are used for the transition section, and double edge responses are used for the linear section. The new scheme can drastically reduce the amount of computation. The proposed method is verified by comparing the probability density distributions of the statistical eye diagram, the bathtub curves, and the simulation time with that of the traditional total MER-based statistical eye diagram. Results show that the simulation speed of the proposed method has been improved by more than ten times, and the accuracy is almost the same as the traditional statistical eye diagram for nonlinear links. This method provides an efficient and accurate solution for estimating the statistical and BER eye diagrams for serious nonlinear links.