Alternative Approaches and Noise Benefits in Hypothesis-testing Problems in the Presence of Partial Information

ALTERNATIVE APPROACHES AND NOISE BENEFITS IN HYPOTHESIS-TESTING PROBLEMS IN THE PRESENCE OF PARTIAL INFORMATION Suat Bayram Ph.D. in Electrical and Electronics Engineering Supervisor: Asst. Prof. Dr. Sinan Gezici July 2011 Performance of some suboptimal detectors can be enhanced by adding independent noise to their observations. In the first part of the dissertation, the effects of additive noise are studied according to the restricted Bayes criterion, which provides a generalization of the Bayes and minimax criteria. Based on a generic M -ary composite hypothesis-testing formulation, the optimal probability distribution of additive noise is investigated. Also, sufficient conditions under which the performance of a detector can or cannot be improved via additive noise are derived. In addition, simple hypothesis-testing problems are studied in more detail, and additional improvability conditions that are specific to simple hypotheses are obtained. Furthermore, the optimal probability distribution of the additive noise is shown to include at most M mass points in a simple M -ary hypothesis-testing problem under certain conditions. Then, global optimization, analytical and convex relaxation approaches are considered to obtain the optimal noise distribution. Finally, detection examples are presented to investigate the theoretical results.