Analysis of an Optimum Sync Search Procedure

Synchronization of communications receivers can require lengthy sync search procedures. In order to establish theoretical guideposts for evaluating synchronization systems, an idealized model is assumed in which: 1) Sync exists in one, and only one, of a large number of discrete time cells, 2) the a priori probability distribution of sync position is known and 3) samples taken from any time cell are normally distributed. An optimum search procedure samples at any instant the cell most likely to contain sync based on all previous samples. This minimizes the average synchronization time, or, for a fixed synchronization time, it minimizes the probability of missing sync. The minimum theoretical average sync time is obtained for Gaussian and uniform a priori distributions. For a fixed synchronization time, the minimum theoretical probability of error is given as a function of sync time for the Gaussian and uniform a priori distributions. An equation for the average search time for a practical nonoptimum search procedure is derived which can be applied to any symmetric unimodal a priori distribution. For a Gaussian a priori distribution the expected value of search time for this procedure converges rapidly to optimum.