A Simple Method for Evaluating the Probability Density Function of the Sample Number for the Optimum Sequential Detector

Sequential detectors are often used in PN-spread-spectrum systems to synchronize the incoming signal. In this paper it is shown that the probability density function (pdf) of the sample number for the optimum sequential detector can be computed recursively, provided that the samples from the envelope correlator are appropriately modeled as statistically independent. Furthermore, the error probabilities of this detector can be determined.