Noise enhanced hypothesis-testing in the restricted Bayesian framework

Suat Bayram, Sinan Gezici, H. Vincent Poor

Research output: Contribution to journalArticle

51 Scopus citations

Abstract

Performance of some suboptimal detectors can be enhanced by adding independent noise to their observations. In this paper, the effects of additive noise are investigated 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.

Original languageEnglish (US)
Article number5446401
Pages (from-to)3972-3989
Number of pages18
JournalIEEE Transactions on Signal Processing
Volume58
Issue number8
DOIs
StatePublished - Aug 1 2010

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering

Keywords

  • Composite hypotheses
  • M-ary hypothesis-testing
  • noise enhanced detection
  • restricted Bayes
  • stochastic resonance

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