As data rates in wireless communications systems continue to increase, as networks become more populated with users, and as these networks of communications nodes are operated in increasingly harsh environments such as indoor and densely populated urban areas, the effects of multipath will become increasingly significant. Therefore a thorough understanding of its effects on communication systems will be necessary. One key element required in communication systems is synchronization, which produces alignment of transmitter and receiver clocks so that information can be accurately exchanged. Here the process of synchronization is studied in the presence of dense multipath for ultra-wideband (UWB) signals. The analytic framework developed for this purpose is applicable to a number of different problems involving synchronization in multipath and is not restricted to the case of the ultra-wideband signals considered herein. In fact, these analysis techniques are applicable to any problem involving a group of observers searching for a group of objects in some arbitrary fashion.; The mathematical framework developed here for search analysis is based upon graphical techniques. Specifically, a generalized signal flow graph is introduced which is well suited for acquisition in multipath. This graph produces a complete statistical description of the search time, as well as the acquisition probability. Hybrid serial/parallel acquisition of UWB signals, as well as sequential detection schemes, can also be examined using these graphical techniques. Efficient search permutations are found for hybrid acquisition in multipath, specifically the bit reversal search is introduced. This search permuation significantly reduces the mean acquisition time in the presence of multipath without any additional complexity versus traditional linear search permutations. The process of acquisition is divided into two main parts, coarse acquisition followed by fine acquisition. The coarse acquisition process attempts to locate the group of paths which, because of the multipath channel, tend to cluster together. Fine acquisition attempts to locate the strongest paths within the multipath cluster of arriving paths, effectively combining the processes of verification and channel estimation. A combined graphical structure, termed a self-similar signal flow graph, has been developed to study the combined coarse/fine acquisition process.
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