Computationally efficient ESPRIT algorithm for direction-of-arrival estimation based on Nyström method

Cheng Qian; Lei Huang; H. C. So

doi:10.1016/j.sigpro.2013.05.007

Computationally efficient ESPRIT algorithm for direction-of-arrival estimation based on Nyström method

Cheng Qian, Lei Huang, H. C. So

Electrical and Computer Engineering

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

80 Scopus citations

Abstract

A low-complexity ESPRIT algorithm for direction-of-arrival (DOA) estimation is devised in this work. Unlike the conventional subspace based methods, the proposed scheme only needs to calculate two sub-matrices of the sample covariance matrix, that is, ^R11â̂̂CK× ^K and ^R21â̂̂C(M-^K)×K, avoiding its complete computation. Here, M is the number of sensors of the array, K satisfies P≤K≤min(M,N) with P being the number of source signals and N being the number of snapshots. Meanwhile, a Nyström-based approach is utilized to correctly compute the signal subspace which only requires O( ^MK2) flops. Thus, the proposed method has the advantage of computational attractiveness, particularly when Kâ ¡M. Furthermore, we derive the asymptotic variances of the estimated DOAs. Numerical results are included to demonstrate the effectiveness of the developed DOA estimator.

Original language	English (US)
Pages (from-to)	74-80
Number of pages	7
Journal	Signal Processing
Volume	94
Issue number	1
DOIs	https://doi.org/10.1016/j.sigpro.2013.05.007
State	Published - 2014

Bibliographical note

Funding Information:
The work described in this paper was in part supported by the NSFC/RGC Joint Research Scheme sponsored by the Research Grants Council of the Hong Kong and the National Natural Science Foundation of China (Project nos. N-CityU 104/11 , 61110229/61161160564 ), by the National Natural Science under Grants 61222106 and 61171187 and by the Shenzhen Kongqie talent program under Grant YFZZ20111013 .

Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

Keywords

Direction-of-arrival
ESPRIT
Eigenvalue decomposition
Signal subspace

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@article{64e0e9fc44e54cf6a57a3b23bb0d0c27,

title = "Computationally efficient ESPRIT algorithm for direction-of-arrival estimation based on Nystr{\"o}m method",

abstract = "A low-complexity ESPRIT algorithm for direction-of-arrival (DOA) estimation is devised in this work. Unlike the conventional subspace based methods, the proposed scheme only needs to calculate two sub-matrices of the sample covariance matrix, that is, R11{\^a}{\^̂}CK× K and R21{\^a}{\^̂}C(M-K)×K, avoiding its complete computation. Here, M is the number of sensors of the array, K satisfies P≤K≤min(M,N) with P being the number of source signals and N being the number of snapshots. Meanwhile, a Nystr{\"o}m-based approach is utilized to correctly compute the signal subspace which only requires O( MK2) flops. Thus, the proposed method has the advantage of computational attractiveness, particularly when K{\^a} ¡M. Furthermore, we derive the asymptotic variances of the estimated DOAs. Numerical results are included to demonstrate the effectiveness of the developed DOA estimator.",

keywords = "Direction-of-arrival, ESPRIT, Eigenvalue decomposition, Signal subspace",

author = "Cheng Qian and Lei Huang and So, {H. C.}",

note = "Funding Information: The work described in this paper was in part supported by the NSFC/RGC Joint Research Scheme sponsored by the Research Grants Council of the Hong Kong and the National Natural Science Foundation of China (Project nos. N-CityU 104/11 , 61110229/61161160564 ), by the National Natural Science under Grants 61222106 and 61171187 and by the Shenzhen Kongqie talent program under Grant YFZZ20111013 . Copyright: Copyright 2013 Elsevier B.V., All rights reserved.",

year = "2014",

doi = "10.1016/j.sigpro.2013.05.007",

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pages = "74--80",

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PY - 2014

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N2 - A low-complexity ESPRIT algorithm for direction-of-arrival (DOA) estimation is devised in this work. Unlike the conventional subspace based methods, the proposed scheme only needs to calculate two sub-matrices of the sample covariance matrix, that is, R11â̂̂CK× K and R21â̂̂C(M-K)×K, avoiding its complete computation. Here, M is the number of sensors of the array, K satisfies P≤K≤min(M,N) with P being the number of source signals and N being the number of snapshots. Meanwhile, a Nyström-based approach is utilized to correctly compute the signal subspace which only requires O( MK2) flops. Thus, the proposed method has the advantage of computational attractiveness, particularly when Kâ ¡M. Furthermore, we derive the asymptotic variances of the estimated DOAs. Numerical results are included to demonstrate the effectiveness of the developed DOA estimator.

AB - A low-complexity ESPRIT algorithm for direction-of-arrival (DOA) estimation is devised in this work. Unlike the conventional subspace based methods, the proposed scheme only needs to calculate two sub-matrices of the sample covariance matrix, that is, R11â̂̂CK× K and R21â̂̂C(M-K)×K, avoiding its complete computation. Here, M is the number of sensors of the array, K satisfies P≤K≤min(M,N) with P being the number of source signals and N being the number of snapshots. Meanwhile, a Nyström-based approach is utilized to correctly compute the signal subspace which only requires O( MK2) flops. Thus, the proposed method has the advantage of computational attractiveness, particularly when Kâ ¡M. Furthermore, we derive the asymptotic variances of the estimated DOAs. Numerical results are included to demonstrate the effectiveness of the developed DOA estimator.

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KW - Signal subspace

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Computationally efficient ESPRIT algorithm for direction-of-arrival estimation based on Nyström method

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Keywords

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