Asynchronous Partial-Response Equalization to Time-Varying Target for Multitrack Detection of Asynchronous Tracks

Multitrack detection improves areal density and throughput in magnetic recording systems. Almost all multitrack detection algorithms assume that the tracks being detected are written synchronously to one another [1] , [2] . In practice, however, variations in disk rotational speeds can lead to slightly different bit rates from one track to the next. In conventional single-track detection, synchronization can precede detection without any interaction. In multitrack detection, however, it is impossible to simultaneously synchronize the readback waveforms to more than one track, the fact that prevents the read channel from separating the synchronization and detection functions. For this reason, in a previous work, we proposed the ROTAR algorithm that combines the functions of synchronization and detections into a joint Viterbi algorithm that works on a time-varying target [3] . In this work we complete the read channel by proposing a partial-response equalization scheme, namely an asynchronous partial-response (APR) equalization to time-varying target, that equalizes the unsynchronized ADC outputs to a time-varying target that the ROTAR detector [3] is designed to work on. The proposed equalizer outputs are then fed to the ROTAR detector to help achieve efficient multitrack detection. In essence, the new read channel extends the partial-response maximum-likelihood (PRML) paradigm to the joint detection of multiple asynchronous tracks. In jointly detecting K asynchronous tracks from N waveforms, the resulted branch metric for the transition from state p to state q at time k is ${\gamma _k}(p,q) = {\left\| {{{\mathbf{y}}_k} - {{\mathbf{o}}_k}(p,q)} \right\|^2}$ where y k is the noisy version of the vector collecting the N noiseless equalized outputs at time k given by