Trellis-Based Baud-rate Timing Recovery Loop for Magnetic Recording Channels

Timing recovery is crucial for magnetic recording systems. A conventional timing recovery loop (also known as the phase-locked loop) consists of a timing error detector (TED), a loop filter, and a voltage controlled oscillator (VCO), all of which process the samples 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 using a discrete Markov model that does not confine the timing error to only small fractions of the bit interval. By utilizing such a model, we derive an optimal baud-rate processing unit that does not perform tasks in sequence, but jointly. The derived unit has a similar structure as the classical first-order phase-locked loop (PLL). Simulation results show that the new detector outperforms the standard Mueller and Muller phase-locked loop. This performance gain is substantial if the timing error process is extremely noisy or if there is residual frequency-offset. For moderately low-noise timing errors without residual frequency-offset, the improvement over the Mueller and M?ller phase-locked loop is just marginal.