Genralized Serial Search Code Acquisition: The Equivalent Circular State Diagram Approach

Abstract

A simple circular state-diagram method has been recently proposed [1], [2] for the modeling, analysis, and optimization of straight serial search code acquisition in spread-spectrum systems. Herein, the approach is generalized to arbitrary serial strategies, such as the Z -search expanding window search, etc., and arbitrary a priori probability distributions for the code phase uncertainty. The basic idea is the construction of equivalent circular state diagrams, wherefrom the transform domain description, i.e., the generating or characteristic function of the stochastic acquisition process is derived. This general method is readily systematized, circumvents the need for complicated time-domain combinatorial arguments, and allows past results [3], [4] to be obtained as particular examples. In principle, the generating function can be used to calculate any moment of the acquisition process; here, however, due to complexity considerations, we restrict our attention to the first moment and its associated performance measure, the mean acquisition time. Based on the derived analytical expressions for the mean acquisition time, an expanding-window single-dwell search strategy has been optimized in terms of the required number of partial windows, parameterized by the prior distribution of the phase uncertainty.