Neyman-Pearson detection of Gauss-Markov signals in noise: Closed-form error exponent and properties

Youngchul Sung; Lang Tong; H. Vincent Poor

doi:10.1109/TIT.2006.871599

Neyman-Pearson detection of Gauss-Markov signals in noise: Closed-form error exponent and properties

Youngchul Sung, Lang Tong, H. Vincent Poor

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62 Scopus citations

Abstract

The performance of Neyman-Pearson detection of correlated random signals using noisy observations is considered. Using the large deviations principle, the performance is analyzed via the error exponent for the miss probability with a fixed false-alarm probability. Using the state-space structure of the signal and observation model, a closed-form expression for the error exponent is derived using the innovations approach, and the connection between the asymptotic behavior of the optimal detector and that of the Kalman filter is established. The properties of the error exponent are investigated for the scalar case. It is shown that the error exponent has distinct characteristics with respect to correlation strength: for signal-to-noise ratio (SNR) ≥ 1 the error exponent is monotonically decreasing as the correlation becomes strong whereas for < 1 there is an optimal correlation that maximizes the error exponent for a given SNR.

Original language	English (US)
Pages (from-to)	1354-1365
Number of pages	12
Journal	IEEE Transactions on Information Theory
Volume	52
Issue number	4
DOIs	https://doi.org/10.1109/TIT.2006.871599
State	Published - Apr 2006

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

Keywords

Autoregressive process
Correlated signal
Error exponent
Gauss-Markov model
Neyman-Pearson detection

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10.1109/TIT.2006.871599

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title = "Neyman-Pearson detection of Gauss-Markov signals in noise: Closed-form error exponent and properties",

abstract = "The performance of Neyman-Pearson detection of correlated random signals using noisy observations is considered. Using the large deviations principle, the performance is analyzed via the error exponent for the miss probability with a fixed false-alarm probability. Using the state-space structure of the signal and observation model, a closed-form expression for the error exponent is derived using the innovations approach, and the connection between the asymptotic behavior of the optimal detector and that of the Kalman filter is established. The properties of the error exponent are investigated for the scalar case. It is shown that the error exponent has distinct characteristics with respect to correlation strength: for signal-to-noise ratio (SNR) ≥ 1 the error exponent is monotonically decreasing as the correlation becomes strong whereas for < 1 there is an optimal correlation that maximizes the error exponent for a given SNR.",

keywords = "Autoregressive process, Correlated signal, Error exponent, Gauss-Markov model, Neyman-Pearson detection",

author = "Youngchul Sung and Lang Tong and Poor, {H. Vincent}",

note = "Funding Information: Manuscript received November 18, 2004; revised December 30, 2005. This work was supported in part by the Multidisciplinary University Research Initiative (MURI) under the Office of Naval Research Contract N00014-00-1-0564. This work was prepared through collaborative participation in the Communications and Networks Consortium sponsored by the U. S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The work of H. V. Poor was also supported in part by the Office of Naval Research under Grant N00014-03-1-0102. The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Adelaide, Australia, September, 2005.",

year = "2006",

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doi = "10.1109/TIT.2006.871599",

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AU - Sung, Youngchul

AU - Tong, Lang

AU - Poor, H. Vincent

N1 - Funding Information: Manuscript received November 18, 2004; revised December 30, 2005. This work was supported in part by the Multidisciplinary University Research Initiative (MURI) under the Office of Naval Research Contract N00014-00-1-0564. This work was prepared through collaborative participation in the Communications and Networks Consortium sponsored by the U. S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The work of H. V. Poor was also supported in part by the Office of Naval Research under Grant N00014-03-1-0102. The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Adelaide, Australia, September, 2005.

PY - 2006/4

Y1 - 2006/4

N2 - The performance of Neyman-Pearson detection of correlated random signals using noisy observations is considered. Using the large deviations principle, the performance is analyzed via the error exponent for the miss probability with a fixed false-alarm probability. Using the state-space structure of the signal and observation model, a closed-form expression for the error exponent is derived using the innovations approach, and the connection between the asymptotic behavior of the optimal detector and that of the Kalman filter is established. The properties of the error exponent are investigated for the scalar case. It is shown that the error exponent has distinct characteristics with respect to correlation strength: for signal-to-noise ratio (SNR) ≥ 1 the error exponent is monotonically decreasing as the correlation becomes strong whereas for < 1 there is an optimal correlation that maximizes the error exponent for a given SNR.

AB - The performance of Neyman-Pearson detection of correlated random signals using noisy observations is considered. Using the large deviations principle, the performance is analyzed via the error exponent for the miss probability with a fixed false-alarm probability. Using the state-space structure of the signal and observation model, a closed-form expression for the error exponent is derived using the innovations approach, and the connection between the asymptotic behavior of the optimal detector and that of the Kalman filter is established. The properties of the error exponent are investigated for the scalar case. It is shown that the error exponent has distinct characteristics with respect to correlation strength: for signal-to-noise ratio (SNR) ≥ 1 the error exponent is monotonically decreasing as the correlation becomes strong whereas for < 1 there is an optimal correlation that maximizes the error exponent for a given SNR.

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Neyman-Pearson detection of Gauss-Markov signals in noise: Closed-form error exponent and properties

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