DesignCon 2014 Method for analytically calculating BER ( bit error rate ) in presence of non - linearity

Methods for calculating bit error rate (BER) using probability density function (PDF) of impairments (ISI, crosstalk, jitter etc.) have been studied and presented in the past. These approaches calculate PDF of the signal & impairments at the decision point based on linear system analysis and deduce the BER from tail probability. A typical high speed system also has significant non linearity in the signal path. We present a method to modify the probability distribution function to account for non-linearity in the path. Once the PDF is correctly modified, the tail probability methods to determine BER can be applied. This way we can combine any linear system(s) with a non-linear system(s) and predict its BER based on knowledge of channel and impairments. Static, memory-less non-linearity polynomials are considered in this paper. The methodology can also be adapted for time varying, frequency dependent non linearity.