Extraction of timing error parameters from readback waveforms

In this paper, we consider the problem of modeling the timing error process in magnetic recording systems. We propose a discrete-valued Markov model for the timing error process, and design two methods (data-aided and nondata-aided), based on the Baum-Welch algorithm, to extract the model parameters from the readback waveforms. The channel model we consider is an intersymbol interference (ISI) channel with additive Gaussian noise. The continuous-time readback signal at the output of the channel is sampled at baud-rate. Simulation results show that the estimated parameters are close to the actual values and the convergence is attained in a few iterations of the Baum-Welch algorithm. We also demonstrate the usefulness of the accurate model extraction by comparing a fine-tuned Markov timing recovery loop to the standard Mueller and Muller detector with a tuned second-order loop filter.