A lower bound for optimum frame synchronization on AWGN channels

We present a new tight lower bound for evaluating the performance of sync word based frame synchronization algorithms, in the periodically embedded case, i.e. for fixed length frames where a synchronization word has to be searched. The optimal search technique, based on maximum likelihood criterion, consists in this case in finding the position where a metric, evaluated in a proper window, is maximal. The performance of such synchronizer has never been evaluated analytically given its complexity. In this work we provide an analytical lower bound for the correct synchronization probability, that will be shown to be very close to results obtained through simulation for commonly used channel conditions and ratios frame length/sync word length.