Noise enhanced M-ary composite hypothesis-testing in the presence of partial prior information
Author
Bayram, S.
Gezici, Sinan
Date
2010-12-06Source Title
IEEE Transactions on Signal Processing
Print ISSN
1053-587X
Publisher
IEEE
Volume
59
Issue
3
Pages
1292 - 1297
Language
English
Type
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Abstract
In this correspondence, noise enhanced detection is studied for M-ary composite hypothesis-testing problems in the presence of partial prior information. Optimal additive noise is obtained according to two criteria, which assume a uniform distribution (Criterion 1) or the least-favorable distribution (Criterion 2) for the unknown priors. The statistical characterization of the optimal noise is obtained for each criterion. Specifically, it is shown that the optimal noise can be represented by a constant signal level or by a randomization of a finite number of signal levels according to Criterion 1 and Criterion 2, respectively. In addition, the cases of unknown parameter distributions under some composite hypotheses are considered, and upper bounds on the risks are obtained. Finally, a detection example is provided in order to investigate the theoretical results.