SPC10-3: Performance Measures for Frame Synchronization Techniques

We study sequential frame synchronization based on markers (or sync words), where the received samples are observed over a window of length equal to the marker length. A decision variable is derived over the observation window. A marker is declared if the decision variable exceeds a threshold; otherwise the observation window is time-shifted by one sample. This detection strategy can be characterized by the probabilities of false alarm and of correct detection, usually represented in terms of the receiver operating characteristic (ROC). However, once the detector (and hence its ROC) is given, it is crucial from a design perspective to select an optimal operating point on the ROC. In this paper we propose a general framework to connect the ROC to the performance of frame synchronization in terms of the probability of correct acquisition in an arbitrarily long time period, valid both for constant and variable length frames. This framework can also be used to compare different marker detectors for frame synchronization.