A Multiple-Input Multiple-Output Extension of the Mueller and Müller Timing Error Detector

We present a multiple-input multiple-output (MIMO) extension of the timing error detector (TED) that was originally developed by Mueller and Müller for synchronization on pulse-amplitude modulation over 1-D channels. This MIMO extension applies to the joint detection of multiple asynchronous tracks from one or more readback waveforms in a two-dimensional magnetic recording (TDMR) channel. We provide accurate theoretical expressions of the performance of the proposed scheme and verify its applicability on a modern MIMO TDMR channel. Performance results show that the proposed TED outperforms the conventional 1-D TED that completely ignores the presence of crosstalk interference in MIMO channels.