A Two-Dimensional Extension of the Mueller & M¨ uller Timing Error Detector Kevin M. Whelan ∗ Student Member, IEEE, F´ elix Balado Member, IEEE, Gu´ enol´ e C.M. Silvestre Member, IEEE, and Neil J. Hurley Abstract A timing error detector (TED) forms an integral part of feedback symbol timing recovery systems in digital communications. We present here a two-dimensional (2-D) extension of a TED originally developed by Mueller and M¨ uller for multi-level pulse amplitude modulation (PAM) over one-dimensional (1-D) channels. Our detector extracts bidimensional timing information (i.e., bidimensional sampling information) from the output of a noisy channel with bidimensional transfer function and subject to sampling errors. Applications for such a scenario include synchronization in multi-level 2-D bar code systems and synchronization in spatial domain image data-hiding. To our knowledge, our proposal is the first one of its kind for this type of scenario. We provide accurate theoretical expressions of the performance of the proposed scheme, and we verify its applicability by studying a particular case with a minimal set of parameters. The 2-D TED thus obtained is used as the engine of a 2-D phase locked loop (PLL) for timing recovery in that scenario, in which we also show the performance gain obtained by the bidimensional approach with respect to the application of standard 1-D TED. EDICS Category: IMD-MDSP, COM-ESTI *Corresponding author. E-mail: kevin.whelan@ihl.ucd.ie; Phone: +353 1 716 2454; Fax: +353 1 269 7262 All the authors are with the School of Computer Science and Informatics at University College Dublin (National University of Ireland). Common address: University College Dublin, School of Computer Science and Informatics, Belfield Campus, Dublin 4, Ireland. E-mails: F´ elix Balado: fiz@ihl.ucd.ie; Gu´ enol´ e C.M. Silvestre: guenole.silvestre@ihl.ucd.ie; Neil J. Hurley: neil.hurley@ucd.ie. Their phone and fax numbers are the same as for the corresponding author. This work was kindly supported by Enterprise Ireland under the research grant ATRP-2002/230 and by the European Commission through the IST Programme under Contract IST-2002-507609 SIMILAR. May 23, 2006 DRAFT