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 that was originally developed by Mueller and Müller for synchronization on pulse amplitude modulation over 1-D channels. This MIMO extension applies to joint detection of multiple signals with different timing offsets received over MIMO channels. We provide accurate theoretical expressions of the performance of the proposed scheme, and verify its applicability on a modern Two-Dimensional Magnetic Recording channel. Performance results show that the proposed timing error detector outperforms the conventional 1-D timing error detector that completely ignores the presence of crosstalk interference in MIMO channels.