Cramer-Rao bound and approximate maximum likelihood estimation for non-coherent direction of arrival problem

Wei Jiang; Alexander M. Haimovich

doi:10.1109/CISS.2016.7460554

Cramer-Rao bound and approximate maximum likelihood estimation for non-coherent direction of arrival problem

Wei Jiang, Alexander M. Haimovich

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

7 Scopus citations

Abstract

In previous work we proposed a direction of arrival (DOA) estimation method from non-coherent measurements taken by an array of sensors. Here, it is shown that the non-coherent measurements in the form of magnitude squared of array observations measured in the presence of additive white Gaussian noise are distributed according to a non-central chisquare distribution. It is further shown that, under certain conditions, the non-coherent measurements may be approximated by a Gaussian distribution. With this approximation, we develop the Cramer-Rao bound (CRB) on the non-coherent DOA estimation of a single source as well as an analytical expression of the maximum likelihood estimation (MLE) of the DOA. Numerical examples are presented to illustrate the performance of the non-coherent DOA estimator. For example, non-coherent DOA estimation outperforms coherent DOA when the standard deviation of the phase errors exceeds 15 degrees and the signal to noise ratio (SNR) exceeds 5 dB.

Original language	English (US)
Title of host publication	2016 50th Annual Conference on Information Systems and Sciences, CISS 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	506-510
Number of pages	5
ISBN (Electronic)	9781467394574
DOIs	https://doi.org/10.1109/CISS.2016.7460554
State	Published - Apr 26 2016
Event	50th Annual Conference on Information Systems and Sciences, CISS 2016 - Princeton, United States Duration: Mar 16 2016 → Mar 18 2016

Other

Other	50th Annual Conference on Information Systems and Sciences, CISS 2016
Country/Territory	United States
City	Princeton
Period	3/16/16 → 3/18/16

All Science Journal Classification (ASJC) codes

Computer Networks and Communications
Information Systems

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10.1109/CISS.2016.7460554

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title = "Cramer-Rao bound and approximate maximum likelihood estimation for non-coherent direction of arrival problem",

abstract = "In previous work we proposed a direction of arrival (DOA) estimation method from non-coherent measurements taken by an array of sensors. Here, it is shown that the non-coherent measurements in the form of magnitude squared of array observations measured in the presence of additive white Gaussian noise are distributed according to a non-central chisquare distribution. It is further shown that, under certain conditions, the non-coherent measurements may be approximated by a Gaussian distribution. With this approximation, we develop the Cramer-Rao bound (CRB) on the non-coherent DOA estimation of a single source as well as an analytical expression of the maximum likelihood estimation (MLE) of the DOA. Numerical examples are presented to illustrate the performance of the non-coherent DOA estimator. For example, non-coherent DOA estimation outperforms coherent DOA when the standard deviation of the phase errors exceeds 15 degrees and the signal to noise ratio (SNR) exceeds 5 dB.",

author = "Wei Jiang and Haimovich, {Alexander M.}",

year = "2016",

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doi = "10.1109/CISS.2016.7460554",

language = "English (US)",

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booktitle = "2016 50th Annual Conference on Information Systems and Sciences, CISS 2016",

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

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note = "50th Annual Conference on Information Systems and Sciences, CISS 2016 ; Conference date: 16-03-2016 Through 18-03-2016",

}

Jiang, W & Haimovich, AM 2016, Cramer-Rao bound and approximate maximum likelihood estimation for non-coherent direction of arrival problem. in 2016 50th Annual Conference on Information Systems and Sciences, CISS 2016., 7460554, Institute of Electrical and Electronics Engineers Inc., pp. 506-510, 50th Annual Conference on Information Systems and Sciences, CISS 2016, Princeton, United States, 3/16/16. https://doi.org/10.1109/CISS.2016.7460554

Cramer-Rao bound and approximate maximum likelihood estimation for non-coherent direction of arrival problem. / Jiang, Wei; Haimovich, Alexander M.
2016 50th Annual Conference on Information Systems and Sciences, CISS 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 506-510 7460554.

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

TY - GEN

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AU - Jiang, Wei

AU - Haimovich, Alexander M.

PY - 2016/4/26

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N2 - In previous work we proposed a direction of arrival (DOA) estimation method from non-coherent measurements taken by an array of sensors. Here, it is shown that the non-coherent measurements in the form of magnitude squared of array observations measured in the presence of additive white Gaussian noise are distributed according to a non-central chisquare distribution. It is further shown that, under certain conditions, the non-coherent measurements may be approximated by a Gaussian distribution. With this approximation, we develop the Cramer-Rao bound (CRB) on the non-coherent DOA estimation of a single source as well as an analytical expression of the maximum likelihood estimation (MLE) of the DOA. Numerical examples are presented to illustrate the performance of the non-coherent DOA estimator. For example, non-coherent DOA estimation outperforms coherent DOA when the standard deviation of the phase errors exceeds 15 degrees and the signal to noise ratio (SNR) exceeds 5 dB.

AB - In previous work we proposed a direction of arrival (DOA) estimation method from non-coherent measurements taken by an array of sensors. Here, it is shown that the non-coherent measurements in the form of magnitude squared of array observations measured in the presence of additive white Gaussian noise are distributed according to a non-central chisquare distribution. It is further shown that, under certain conditions, the non-coherent measurements may be approximated by a Gaussian distribution. With this approximation, we develop the Cramer-Rao bound (CRB) on the non-coherent DOA estimation of a single source as well as an analytical expression of the maximum likelihood estimation (MLE) of the DOA. Numerical examples are presented to illustrate the performance of the non-coherent DOA estimator. For example, non-coherent DOA estimation outperforms coherent DOA when the standard deviation of the phase errors exceeds 15 degrees and the signal to noise ratio (SNR) exceeds 5 dB.

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ER -

Cramer-Rao bound and approximate maximum likelihood estimation for non-coherent direction of arrival problem

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