Trellis-Based Optimal Baud-Rate Timing Recovery Loops for Magnetic Recording Systems

The advent of iteratively decodable codes has allowed a decrease in tolerable signal-to-noise ratios (SNRs) in magnetic recording systems, which typically translates into an increase in the recording densities. However, at such low SNRs, conventional timing recovery loops suffer from frequent cycle slips. Typical timing recovery loops in magnetic recording applications perform data detection, timing error detection, and loop filtering in a sequential manner. This sequence of operations in the timing recovery loop performs well if the timing error is a small fraction of the bit interval. However, in the cycle-slip regions, the timing error is comparable to the bit interval, and the loop fails. In this paper, we represent the timing error in magnetic recording systems by using a Markov model that does not confine the timing error to only small fractions of the bit interval. By utilizing such a model, we give a trellis representation of the timing error process. The trellis representation permits the formulations of two optimal baud-rate timing recovery loops, according to two optimality criteria. We prove that both optimality criteria lead to solutions similar to the classical first-order phase-locked loop. The new loops do not perform data detection, timing error detection, and loop filtering in a sequential manner. Instead, the loops perform data detection and timing error detection jointly on a trellis, without the need for a loop filter. Simulation results show that the new timing recovery loops outperform the standard second-order baud-rate Mueller and Muller phase-locked loop with fine-tuned loop parameters. This performance gain is substantial if the timing error process is extremely noisy or if there is residual frequency offset resulting from inaccurate acquisition from the sector preamble on a disk drive.