Performance analysis of coarray-based MUSIC and the Cramér-Rao bound

Mianzhi Wang; Zhen Zhang; Arye Nehorai

doi:10.1109/ICASSP.2017.7952719

Performance analysis of coarray-based MUSIC and the Cramér-Rao bound

Mianzhi Wang
, Zhen Zhang
, Arye Nehorai

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

11 Scopus citations

Abstract

Sparse linear arrays, such as co-prime and nested arrays, can identify up to O(M²) sources with only O(M) sensors by using co-array based MUSIC. We conduct analytical performance analysis of two coarray based MUSIC algorithms, namely the direct augmentation based MUSIC, and the spatial smoothing based MUSIC. In addition, we analyze the Cramér-Rao bound for sparse linear arrays, and show that for co-prime and nested arrays, it can decrease at a rate of O(M^-5) as the number of sensors M goes to infinity, in contrast to O(M^-3) in the ULA case. We use numerical examples to demonstrate our analytical results.

Original language	English
Title of host publication	2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3061-3065
Number of pages	5
ISBN (Electronic)	9781509041176
DOIs	https://doi.org/10.1109/ICASSP.2017.7952719
State	Published - Jun 16 2017
Event	2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - New Orleans, United States Duration: Mar 5 2017 → Mar 9 2017

Publication series

Name	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)	1520-6149

Conference

Conference	2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
Country/Territory	United States
City	New Orleans
Period	03/5/17 → 03/9/17

Keywords

Cramer-Rao bound
mean-square error
MUSIC
performance analysis
sparse linear arrays

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10.1109/ICASSP.2017.7952719

Cite this

Wang, M., Zhang, Z., & Nehorai, A. (2017). Performance analysis of coarray-based MUSIC and the Cramér-Rao bound. In 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings (pp. 3061-3065). Article 7952719 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2017.7952719

Wang, Mianzhi ; Zhang, Zhen ; Nehorai, Arye. / Performance analysis of coarray-based MUSIC and the Cramér-Rao bound. 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 3061-3065 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

@inproceedings{a1c3bd0d5b70482183848dfc678eb108,

title = "Performance analysis of coarray-based MUSIC and the Cram{\'e}r-Rao bound",

abstract = "Sparse linear arrays, such as co-prime and nested arrays, can identify up to O(M2) sources with only O(M) sensors by using co-array based MUSIC. We conduct analytical performance analysis of two coarray based MUSIC algorithms, namely the direct augmentation based MUSIC, and the spatial smoothing based MUSIC. In addition, we analyze the Cram{\'e}r-Rao bound for sparse linear arrays, and show that for co-prime and nested arrays, it can decrease at a rate of O(M-5) as the number of sensors M goes to infinity, in contrast to O(M-3) in the ULA case. We use numerical examples to demonstrate our analytical results.",

keywords = "Cramer-Rao bound, mean-square error, MUSIC, performance analysis, sparse linear arrays",

author = "Mianzhi Wang and Zhen Zhang and Arye Nehorai",

note = "Funding Information: This work was supported by the ONR Grant N000141310050. Publisher Copyright: {\textcopyright} 2017 IEEE.; 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 ; Conference date: 05-03-2017 Through 09-03-2017",

year = "2017",

month = jun,

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doi = "10.1109/ICASSP.2017.7952719",

language = "English",

series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",

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Wang, M, Zhang, Z & Nehorai, A 2017, Performance analysis of coarray-based MUSIC and the Cramér-Rao bound. in 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings., 7952719, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 3061-3065, 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017, New Orleans, United States, 03/5/17. https://doi.org/10.1109/ICASSP.2017.7952719

Performance analysis of coarray-based MUSIC and the Cramér-Rao bound. / Wang, Mianzhi; Zhang, Zhen; Nehorai, Arye.
2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2017. p. 3061-3065 7952719 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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

TY - GEN

T1 - Performance analysis of coarray-based MUSIC and the Cramér-Rao bound

AU - Wang, Mianzhi

AU - Zhang, Zhen

AU - Nehorai, Arye

PY - 2017/6/16

Y1 - 2017/6/16

N2 - Sparse linear arrays, such as co-prime and nested arrays, can identify up to O(M2) sources with only O(M) sensors by using co-array based MUSIC. We conduct analytical performance analysis of two coarray based MUSIC algorithms, namely the direct augmentation based MUSIC, and the spatial smoothing based MUSIC. In addition, we analyze the Cramér-Rao bound for sparse linear arrays, and show that for co-prime and nested arrays, it can decrease at a rate of O(M-5) as the number of sensors M goes to infinity, in contrast to O(M-3) in the ULA case. We use numerical examples to demonstrate our analytical results.

AB - Sparse linear arrays, such as co-prime and nested arrays, can identify up to O(M2) sources with only O(M) sensors by using co-array based MUSIC. We conduct analytical performance analysis of two coarray based MUSIC algorithms, namely the direct augmentation based MUSIC, and the spatial smoothing based MUSIC. In addition, we analyze the Cramér-Rao bound for sparse linear arrays, and show that for co-prime and nested arrays, it can decrease at a rate of O(M-5) as the number of sensors M goes to infinity, in contrast to O(M-3) in the ULA case. We use numerical examples to demonstrate our analytical results.

KW - Cramer-Rao bound

KW - mean-square error

KW - MUSIC

KW - performance analysis

KW - sparse linear arrays

UR - https://www.scopus.com/pages/publications/85023758465

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DO - 10.1109/ICASSP.2017.7952719

M3 - Conference contribution

AN - SCOPUS:85023758465

T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

SP - 3061

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BT - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017

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Wang M, Zhang Z, Nehorai A. Performance analysis of coarray-based MUSIC and the Cramér-Rao bound. In 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2017. p. 3061-3065. 7952719. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP.2017.7952719

Performance analysis of coarray-based MUSIC and the Cramér-Rao bound

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