Theory of the stochastic resonance effect in signal detection: Part I - Fixed detectors

Hao Chen; Pramod K. Varshney; Steven M. Kay; James H. Michels

doi:10.1109/TSP.2007.893757

Theory of the stochastic resonance effect in signal detection: Part I - Fixed detectors

Hao Chen, Pramod K. Varshney, Steven M. Kay, James H. Michels

Department of Electrical Engineering & Computer Science

Research output: Contribution to journal › Article › peer-review

266 Scopus citations

Abstract

This paper develops the mathematical framework to analyze the stochastic resonance (SR) effect in binary hypothesis testing problems. The mechanism for SR noise enhanced signal detection is explored. The detection performance of a noise modified detector is derived in terms of the probability of detection P_D and the probability of false alarm P_FA. Furthermore, sufficient conditions are established to determine the improvability of a fixed detector using SR. The form of the optimal noise pdf is determined and the optimal stochastic resonance noise pdf which renders the maximum P_D without increasing P_FA is derived. Finally, an illustrative example is presented where performance comparisons are made between detectors where the optimal stochastic resonance noise, as well as Gaussian, uniform, and optimal symmetric noises are applied to enhance detection performance.

Original language	English (US)
Pages (from-to)	3172-3184
Number of pages	13
Journal	IEEE Transactions on Signal Processing
Volume	55
Issue number	7 I
DOIs	https://doi.org/10.1109/TSP.2007.893757
State	Published - Jul 2007

Keywords

Hypothesis testing
Non-Gaussian noise
Nonlinear systems
Signal detection
Stochastic resonance (SR)

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering

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10.1109/TSP.2007.893757

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@article{17ef8032ce9d4d068306067e0cf7c6a6,

title = "Theory of the stochastic resonance effect in signal detection: Part I - Fixed detectors",

abstract = "This paper develops the mathematical framework to analyze the stochastic resonance (SR) effect in binary hypothesis testing problems. The mechanism for SR noise enhanced signal detection is explored. The detection performance of a noise modified detector is derived in terms of the probability of detection PD and the probability of false alarm PFA. Furthermore, sufficient conditions are established to determine the improvability of a fixed detector using SR. The form of the optimal noise pdf is determined and the optimal stochastic resonance noise pdf which renders the maximum PD without increasing PFA is derived. Finally, an illustrative example is presented where performance comparisons are made between detectors where the optimal stochastic resonance noise, as well as Gaussian, uniform, and optimal symmetric noises are applied to enhance detection performance.",

keywords = "Hypothesis testing, Non-Gaussian noise, Nonlinear systems, Signal detection, Stochastic resonance (SR)",

author = "Hao Chen and Varshney, {Pramod K.} and Kay, {Steven M.} and Michels, {James H.}",

note = "Funding Information: Manuscript received December 14, 2005; revised July 24, 2006. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. L. Collins. This work was supported by AFOSR under contract FA9550-05-C-0139. This paper was presented in part at the 2006 International Conference on Acoustics, Speech, and Signal Processing, Toulouse, France, May 2006.",

year = "2007",

month = jul,

doi = "10.1109/TSP.2007.893757",

language = "English (US)",

volume = "55",

pages = "3172--3184",

journal = "IEEE Transactions on Signal Processing",

issn = "1053-587X",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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T2 - Part I - Fixed detectors

AU - Chen, Hao

AU - Varshney, Pramod K.

AU - Kay, Steven M.

AU - Michels, James H.

N1 - Funding Information: Manuscript received December 14, 2005; revised July 24, 2006. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. L. Collins. This work was supported by AFOSR under contract FA9550-05-C-0139. This paper was presented in part at the 2006 International Conference on Acoustics, Speech, and Signal Processing, Toulouse, France, May 2006.

PY - 2007/7

Y1 - 2007/7

N2 - This paper develops the mathematical framework to analyze the stochastic resonance (SR) effect in binary hypothesis testing problems. The mechanism for SR noise enhanced signal detection is explored. The detection performance of a noise modified detector is derived in terms of the probability of detection PD and the probability of false alarm PFA. Furthermore, sufficient conditions are established to determine the improvability of a fixed detector using SR. The form of the optimal noise pdf is determined and the optimal stochastic resonance noise pdf which renders the maximum PD without increasing PFA is derived. Finally, an illustrative example is presented where performance comparisons are made between detectors where the optimal stochastic resonance noise, as well as Gaussian, uniform, and optimal symmetric noises are applied to enhance detection performance.

AB - This paper develops the mathematical framework to analyze the stochastic resonance (SR) effect in binary hypothesis testing problems. The mechanism for SR noise enhanced signal detection is explored. The detection performance of a noise modified detector is derived in terms of the probability of detection PD and the probability of false alarm PFA. Furthermore, sufficient conditions are established to determine the improvability of a fixed detector using SR. The form of the optimal noise pdf is determined and the optimal stochastic resonance noise pdf which renders the maximum PD without increasing PFA is derived. Finally, an illustrative example is presented where performance comparisons are made between detectors where the optimal stochastic resonance noise, as well as Gaussian, uniform, and optimal symmetric noises are applied to enhance detection performance.

KW - Hypothesis testing

KW - Non-Gaussian noise

KW - Nonlinear systems

KW - Signal detection

KW - Stochastic resonance (SR)

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JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

IS - 7 I

ER -

Theory of the stochastic resonance effect in signal detection: Part I - Fixed detectors

Abstract

Keywords

ASJC Scopus subject areas

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