Distributed binary hypothesis testing with feedback

The problem of binary hypothesis testing is revisited in the context of distributed detection with feedback. Two basic distributed structures with decision feedback are considered. The first structure is the fusion center network, with decision feedback connections from the fusion center element to each one of the subordinate decisionmakers. The second structure consists of a set of detectors that are fully interconnected via decision feedback. Both structures are optimized in the Neyman-Pearson sense by optimizing each decision-maker individually. Then, the time evolution of the power of the tests is derived. Definite conclusions regarding the gain induced by the feedback process and direct comparisons between the two structures and the optimal centralized scheme are obtained through asymptotic studies (that is, assuming the presence of asymptotically many local detectors). The behavior of these structures is also examined in the presence of variations in the statistical description of the hypotheses. Specific robust designs are proposed and the benefits from robust operations are established. Numerical results provide additional support to the theoretical arguments