### Abstract

Level set estimation (LSE) is the process of using noisy observations of an unknown function to estimate the region(s) where the function values lie above a given threshold. It has a wide range of applications in many scientific and engineering areas, such as spectrum sensing or environment monitoring. In this paper, we study the optimum LSE of a time-varying random field under a total power constraint. A sensor performs uniform sampling of the random field and sends the samples to a fusion center, which estimates the level set by using distorted observations of the samples. Under a total power constraint, a higher sampling rate means less energy per sample, which may negatively impact the estimation performance, but also a stronger correlation between adjacent samples, which can improve the estimation accuracy. Thus it is critical to identify the optimum sampling rate that can minimize the LSE error provability. With the help of a Gaussian process (GP) prior model, we first develop an optimum LSE algorithm based on GP regression. The exact analytical LSE error probability of the LSE algorithm is then derived by considering a number of factors, such as the power consumptions of both sensing and transmission, the power constraint of the sensor, the sampling rate, and the probability distributions of the random field. To simplify analysis, we also obtain a closed-form upper bound of the LSE error probability. The optimum sampling rate is identified by using the analytical error probabilities.

Original language | English (US) |
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Title of host publication | 2015 IEEE Global Communications Conference, GLOBECOM 2015 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

ISBN (Electronic) | 9781479959525 |

DOIs | |

State | Published - Jan 1 2015 |

Event | 58th IEEE Global Communications Conference, GLOBECOM 2015 - San Diego, United States Duration: Dec 6 2015 → Dec 10 2015 |

### Publication series

Name | 2015 IEEE Global Communications Conference, GLOBECOM 2015 |
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### Other

Other | 58th IEEE Global Communications Conference, GLOBECOM 2015 |
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Country | United States |

City | San Diego |

Period | 12/6/15 → 12/10/15 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications
- Electrical and Electronic Engineering
- Communication

### Cite this

*2015 IEEE Global Communications Conference, GLOBECOM 2015*[7417745] (2015 IEEE Global Communications Conference, GLOBECOM 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/GLOCOM.2014.7417745

}

*2015 IEEE Global Communications Conference, GLOBECOM 2015.*, 7417745, 2015 IEEE Global Communications Conference, GLOBECOM 2015, Institute of Electrical and Electronics Engineers Inc., 58th IEEE Global Communications Conference, GLOBECOM 2015, San Diego, United States, 12/6/15. https://doi.org/10.1109/GLOCOM.2014.7417745

**Optimum level set estimation of a time-varying random field under a power constraint.** / Wang, Zuoen; Wu, Jingxian; Yang, Jing; Lin, Hai.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Optimum level set estimation of a time-varying random field under a power constraint

AU - Wang, Zuoen

AU - Wu, Jingxian

AU - Yang, Jing

AU - Lin, Hai

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Level set estimation (LSE) is the process of using noisy observations of an unknown function to estimate the region(s) where the function values lie above a given threshold. It has a wide range of applications in many scientific and engineering areas, such as spectrum sensing or environment monitoring. In this paper, we study the optimum LSE of a time-varying random field under a total power constraint. A sensor performs uniform sampling of the random field and sends the samples to a fusion center, which estimates the level set by using distorted observations of the samples. Under a total power constraint, a higher sampling rate means less energy per sample, which may negatively impact the estimation performance, but also a stronger correlation between adjacent samples, which can improve the estimation accuracy. Thus it is critical to identify the optimum sampling rate that can minimize the LSE error provability. With the help of a Gaussian process (GP) prior model, we first develop an optimum LSE algorithm based on GP regression. The exact analytical LSE error probability of the LSE algorithm is then derived by considering a number of factors, such as the power consumptions of both sensing and transmission, the power constraint of the sensor, the sampling rate, and the probability distributions of the random field. To simplify analysis, we also obtain a closed-form upper bound of the LSE error probability. The optimum sampling rate is identified by using the analytical error probabilities.

AB - Level set estimation (LSE) is the process of using noisy observations of an unknown function to estimate the region(s) where the function values lie above a given threshold. It has a wide range of applications in many scientific and engineering areas, such as spectrum sensing or environment monitoring. In this paper, we study the optimum LSE of a time-varying random field under a total power constraint. A sensor performs uniform sampling of the random field and sends the samples to a fusion center, which estimates the level set by using distorted observations of the samples. Under a total power constraint, a higher sampling rate means less energy per sample, which may negatively impact the estimation performance, but also a stronger correlation between adjacent samples, which can improve the estimation accuracy. Thus it is critical to identify the optimum sampling rate that can minimize the LSE error provability. With the help of a Gaussian process (GP) prior model, we first develop an optimum LSE algorithm based on GP regression. The exact analytical LSE error probability of the LSE algorithm is then derived by considering a number of factors, such as the power consumptions of both sensing and transmission, the power constraint of the sensor, the sampling rate, and the probability distributions of the random field. To simplify analysis, we also obtain a closed-form upper bound of the LSE error probability. The optimum sampling rate is identified by using the analytical error probabilities.

UR - http://www.scopus.com/inward/record.url?scp=84964858694&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964858694&partnerID=8YFLogxK

U2 - 10.1109/GLOCOM.2014.7417745

DO - 10.1109/GLOCOM.2014.7417745

M3 - Conference contribution

AN - SCOPUS:84964858694

T3 - 2015 IEEE Global Communications Conference, GLOBECOM 2015

BT - 2015 IEEE Global Communications Conference, GLOBECOM 2015

PB - Institute of Electrical and Electronics Engineers Inc.

ER -