On Uniformly Most Powerful Decentralized Detection

The theory behind Uniformly Most Powerful (UMP) composite binary hypothesis testing is mature and well defined in centralized detection where all observations are directly accessible at one central node. However, within the area of decentralized detection, UMP tests have not been researched, even though tests of this nature have properties that are highly desirable. The purpose of this research is to extend the UMP concept into decentralized detection, which we define as UMP decentralized detection (UMP-DD). First, the standard parallel decentralized detection model with conditionally independent observations will be explored. This section will introduce theorems and corollaries that define when UMP-DD exists and provide counterintuitive examples where UMP-DD tests do not exist. Second, we explore UMP-DD for directed single-rooted trees of bounded height. We will show that a binary relay tree achieves a Type II error probability exponent that is equivalent to the parallel structure even if all the observations are not identically distributed. We then show that the optimal configuration can also achieve UMP-DD performance, while the tandem configuration does not achieve UMP-DD performance. Finally, we relax the assumption of conditional independence and show under specific constraints that both the parallel and binary relay tree configurations can still be UMP-DD. Throughout, examples will be provided that tie this theoretical work together with current research in fields such as Cognitive Radio.