On the optimality of data-aided coarse timing with dirty templates

Rapid and accurate timing synchronization is a critical task in ultrawideband (UWB) systems. Yang and Giannakis introduced a promising algorithm, i.e., data-aided timing with dirty templates (TDT), which is known for low complexity and relaxed operation conditions in the presence of unknown time hopping and multipath channels. In this paper, we will explore the optimality of TDT. We develop a maximum-likelihood (ML) timing algorithm and obtain its optimum training sequence. It is shown that the optimum training sequence of the ML timing estimator coincides with that of the TDT algorithm. In addition, we prove that the ML algorithm can be simplified using this training sequence and that the simplified ML (SML) is equivalent to TDT.