| In future magnetic recording systems, with increasing areal densities, the signal-to-noise ratios (SNRs) will decrease and inter-symbol interference (ISI) will increase from current levels. New equalization and detection technologies such as iterative soft decoding and turbo equalization are being investigated to achieve acceptable bit error rates (BERs) in these challenging channels. However, most investigations of these advanced equalization, detection and decoding method assume perfect timing recovery, i.e., the readback signal is sampled at the optimum time instants. However, in low SNR, current timing recovery schemes do not work well and loss of lock (the event where the timing error is large enough to introduce too many errors for the error correction code to correct) occurs. Besides, future timing recovery systems must also cope with large frequency drifts and dropouts in magnetic tape recording systems.; In this thesis, we apply Kalman filtering methods for timing recovery. In the acquisition stage, we apply the Kalman filter with reduced implementation complexity to handle large frequency drift. We also develop closed form expressions for the Kalman filter's performance when it is used with imprecise prior information. These expressions can quantitatively determine how much mismatch the Kalman filter can tolerate. In the tracking stage, we apply the Kalman filter theory to determine optimal loop gains in the presence of loop delay. As a result, longer delay can be tolerated, and the loss of lock rate can be reduced. When the Kalman filter is applied to dropout compensation most of shallow and narrow dropouts can be compensated. Thus, the Kalman filter may prove to be an important tool for timing recovery in future high-density magnetic recording systems. |
