Timing-recovery and gain-control play important role in communication systems. In this paper, we propose reliable acquisition, tracking and gain control algorithms for fixed delay tree search with decision feedback (FDTS/DF) detector on magnetic recording channel. First, we propose a modified Mueller and Muller algorithm for timing recovery during tracking period, which is based on selective transitions in the samples at the detector input. Next, we give the modified threshold detection scheme that quickly converges to the correct sampling phase without hang-up problems during acquisition period. Bit-by-bit simulations are included first to show the reliability in tracking performance of the timing-recovery and gain-control loops, and then to show the robustness and accuracy of the fast acquisition algorithm.

The study of error-burst statistics is important for all detection systems, and more so for the decision feedback class. In data storage applications, many detection systems use decision feedback in one form or another. Fixed-delay tree search with decision feedback (FDTS/DF) and decision feedback equalization (DFE) are the direct forms, whereas the partial response detectors such as the reduced state sequence estimator (RSSE) and noise predictive maximum likelihood (NPML) detectors are the other forms. Although DF reduces the system complexity, it is inevitably linked with error propagation (EP), which can be quantified using error-burst statistics. Analytical evaluation of these statistics is difficult, if not impossible, because of the complexity of the problem. Hence, the usual practice is to use computer simulations. However, the computational time in traditional bit-by-bit simulations can be prohibitive at meaningful signal-to-noise ratios. In this paper, we propose a novel approach for fast estimation of error-burst statistics in FDTS/DF detectors, which is also applicable to other detection systems. In this approach, error events are initiated more frequently than natural by artificially injecting noise samples. These noise samples are generated using a transformation that results in significant reduction in computational complexity. Simulation studies show that the EP performance obtained by the proposed method matches closely with those obtained by bit-by-bit simulations, while saving as much as 99% of simulation time.