Use of second order Markov chains to model digital symbol synchroniser performance

A second order Markov chain model is used to evaluate the performance of a binary quantised data transition tracking loop (DTTL). At small and moderate signal-to-noise ratios (SNRs), where a first order model is inaccurate for some common pulse shapes, the second order model closely approximates simulated results. The effects of two common loop filters (LFs) on the DTTL performance is also investigated. A first order model accurately predicts performance for moderate and large K for an accumulating LF, which sums K successive timing error estimates. However, an example shows that for a random walk LF with K states, the first and second order models can predict increasingly different performance as K becomes larger