A Generalized Signal Flow Graph Approach for Hybrid Acquisition of Ultra-Wideband Signals

Abstract

This paper establishes a general framework for the study of various search procedures in which a group of observers is searching for a group of items in some arbitrary manner. A generalized signal flow graph approach yields a complete statistical description of the search time as well as the probability of correctly terminating the search. The motivation for this study comes from the acquisition of an ultra-wideband (UWB) signal in a dense multipath channel. In this particular problem many resolvable paths tend to cluster at a receiver containing multiple correlators allowing for a hybrid serial/parallel search. This hybrid search, as well as a bound on a sorted hybrid search, is analyzed using the generalized signal flow graph approach. Rapid code and frame acquisition at the receiver is desired and it is shown that a specific nonconsecutive search, the bit reversal search, yields an optimum hybrid search procedure under certain conditions. The acquisition of UWB signals also leads to the concept of a self-similar signal flow graph, in which a new search is initiated upon the completion of the previous one.