Optimal multiple hypothesis testing with an application in side lobe blanker design and invariance applications in detection and synchronization

Coşkun, Osman
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.


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In this study we investigate the problem of estimation and testing of hypotheses in multivariate linear regression models when the errors involved are assumed to be non-normally distributed. We consider the class of heavy-tailed distributions for this purpose. Although our method is applicable for any distribution in this class, we take the multivariate t-distribution for illustration. This distribution has applications in many fields of applied research such as Economics, Business, and Finance. For estimat...
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Performance of a non-linear adaptive beamformer algorithm for signal-of-interest extraction /
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In this thesis a non-linear adaptive beamforming technique, Adaptive Projections Subgradient Method [1] (APSM) is considered. This method uses projections over convex sets in Reproducing Kernel Hilbert Space. Main advantage of this method is observed if the signal-of-interest is due to digital modulation and when there are more jammers than the number of antennas. The performance of this non-linear beamforming technique is compared with well-known methods including Minimum Variance Distortionless Response [...
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In this paper we study the control problem and note that it is multi-objective by nature, and thus we develop an optimal multi-objective approach. Our approach includes formalizing components and identifying dimensions, resulting in few cases for concrete problem formulation. For a selected case, namely the finite control case, a single-objective from the literature and our multi-objective solutions are presented. It is demonstrated that the multi-objective solution avoids drawbacks of the single-objective ...
Citation Formats
O. Coşkun, “Optimal multiple hypothesis testing with an application in side lobe blanker design and invariance applications in detection and synchronization,” Ph.D. - Doctoral Program, Middle East Technical University, 2017.