Asymptotic analysis of maximum search based code synchronization probabilities

The aim of this paper is to determine the probability that the decision variable of a maximum search based direct sequence synchronization procedure exceeds also a signal detection threshold set by the generalized likelihood ratio detector. The required distribution is derived independent of the signal presence or absence. Neither has the investigated code phase be the correct one. The derived novel probability is required in the analysis and threshold setting of synchronization processes of systems that have uncertainty on the existence of the signal. These include all random access type systems. Also other required probabilities, like the more familiar probability that the correct bin is the maximum, are determined using the same asymptotic analysis method. The analyzed results are compared to the simulated ones. It can be concluded that the analyzed results predict very well the points where the probability is high, near to one. These are typically the points that the system designers like to know.