Optimal Multiple Hypothesis Testing With An Application In Side Lobe Blanker Design And Invariance Applications In Detection And Synchronization
This thesis aims to study two problems, namely optimal hypothesis testing in the sense of Neyman-Pearson in the presence of multiple hypotheses and optimal hypothesis testing in the presence of non-random unknown parameters (nuisance parameters). Both problems occur frequently in different applications and their optimal solution involves some fine details. In the first part of the thesis, the multiple hypothesis testing problem is examined and the results are applied on the problem of radar sidelobe blanker system design. The goal of this part is two folds: To examine and compare the performance of Maisel system (the conventional sidelobe blanking systems) with the optimal system and determine the conditions for the Maisel system to approach the optimal blanker performance so as to assist the design of practical Maisel sidelobe blankers. In the second part of the thesis, uniformly most powerful invariant (UMPI) tests are examined. UMPI tests are applicable when there are unknown non-random constants in the hypothesis testing. UMPI tests retain the optimality properties of uniformly most powerful tests (UMP) in a restricted setting of transform invariance with respect to the unknown parameters. Many practical problems do not have UMP tests and for these problems the general approach is to apply generalized likelihood ratio test (GLRT) which does not have any optimality properties apart from asymptotic ones. Similar to the first part of the thesis, our goal is to study the UMPI tests and examine their performance with respect to well-known GLRT test. After a brief description of UMPI tests, we study two problems namely the problem of low probability of intercept signal detection and the problem of frame synchronization word detection problem. UMPI and GLRT approach based tests are derived for both problems and it is shown that for some operating conditions the invariant detector provides a better performance than GLRT, the performance difference is not significant.
Prof. Dr. Çağatay Candan