A Two-Dimensional Extension of the Mueller and Müller Timing Error Detector

We present a 2-D extension of a timing error detector (TED) originally developed by Mueller and Muller for timing recovery on multilevel pulse amplitude modulation (PAM) over 1-D channels. We provide accurate theoretical expressions of the performance of the proposed scheme, and we verify its applicability by studying a particular case. The 2-D TED thus obtained is used as the engine of a 2-D phase locked loop (PLL) for timing recovery.