Probability of frame synchronisation failure for binary and complex-valued sequences

Several different sequences for frame synchronisation have been published in the literature. Recently, even sequences using complex signal alphabets have been specified. Whether binary or complex, they are always chosen according to the properties of their autocorrelation function. However, the probability of being out of synchronisation has not as such been considered sufficiently. The paper serves as a compendium of derivations of such probability formulas for various applications and conditions, including both binary and complex signal constellations. Hard quantisation as well as the continuous case are treated.<>