Optimum Synchronization of Ternary Preamble Sequences in Gaussian Noise

We consider synchronization based on the detection of a known sequence (preamble, unique word, or sync word), that is transmitted to delimit a frame of random data. Recently, preamble sequences with ternary symbols have been considered in ultrawide band (UWB) due to their improved (with respect to classical binary sequences) autocorrelation properties, and in particular to the need to allow the use of both coherent and noncoherent receivers. In this paper we consider preamble synchronization where the preamble symbols are ternary and data are random binary symbols, assuming a Gaussian channel and soft values available at the input of the synchronization device. We show that detection of preambles based on correlation is not optimal, and that a simple modification of the metric gives substantial improvements. More precisely, we derive the optimum test metric and a suboptimal low-complexity detector, and compare their performance with the usual correlation based preamble detector. Results show that the gap between the two metrics (optimal and suboptimal) is very small, and that both outperform the correlation based synchronizer.