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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Functions of complex variables arise frequently in the formulation of signal processing problems. The basic calculus rules on differentiation and integration for functions of complex variables resemble, but are not identical to, the rules of their real variable counterparts. On the contrary, the standard calculus rules on differentiation, integration, series expansion, and so on are the special cases of the complex analysis with the restriction of the complex variable to the real line. The goal of this lect...
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In this paper, we analyze the performance of the Gaussian mixture probability hypothesis density (GM-PHD) filter in tracking multiple non-cooperative targets using a passive sensor network. Non-cooperative transmissions from illuminators of opportunity like GSM base stations, FM radio transmitters or digital broadcasters are exploited by non-directional separately located Doppler measuring sensors. Clutter, missed detections and multi-static Doppler variances are incorporated into a realistic multi-target s...
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.