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SCIENCE CHINA Information Sciences
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SCIENCE CHINA Information Sciences, Volume 63 , Issue 5 : 159206(2020) https://doi.org/10.1007/s11432-018-9635-0

Low-degree root-MUSIC algorithm for fast DOA estimation based on variable substitution technique

Fenggang YAN , Ming JIN , Hongjuan ZHOU *, Jun WANG , Shuai LIU
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  • ReceivedJul 2, 2018
  • AcceptedOct 31, 2018
  • PublishedDec 24, 2019
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Abstract

There is no abstract available for this article.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant No. 61871149).


References

[1] Li J, Li D, Jiang D. Extended-Aperture Unitary Root MUSIC-Based DOA Estimation for Coprime Array. IEEE Commun Lett, 2018, 22: 752-755 CrossRef Google Scholar

[2] Rao B D, Hari K V S. Performance analysis of Root-Music. IEEE Trans Acoust Speech Signal Processing, 1989, 37: 1939-1949 CrossRef Google Scholar

[3] Yan F G, Shen Y, Jin M. Fast DOA estimation based on a split subspace decomposition on the array covariance matrix. Signal Processing, 2015, 115: 1-8 CrossRef Google Scholar

[4] Hu A, Lv T, Gao H. An ESPRIT-Based Approach for 2-D Localization of Incoherently Distributed Sources in Massive MIMO Systems. IEEE J Sel Top Signal Process, 2014, 8: 996-1011 CrossRef ADS arXiv Google Scholar

[5] Yan F G, Liu S, Wang J. Unitary Direction of Arrival Estimation Based on A Second Forward/Backward Averaging Technique. IEEE Commun Lett, 2018, 22: 554-557 CrossRef Google Scholar

[6] Kitavi D M, Wong K T, Hung C C. An L-Shaped Array With Nonorthogonal Axes-Its Cramér-Rao Bound for Direction Finding. IEEE Trans Aerosp Electron Syst, 2018, 54: 486-492 CrossRef ADS Google Scholar

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    Figure 1

    (Color online) (a) Comparison of primary computational flops; (b) roots distribution, $8$ sensors ULA, SNR = 10 dB, 100 snapshots, $3$ sources at $10^{\circ}$, $20^{\circ}$, and $30^{\circ}$; (c) RMSE vs. the SNR, $11$ sensors ULA, 100 snapshots, $3$ sources at $20^{\circ}$, $23^{\circ}$, and $30^{\circ}$; (d) simulation time vs. the number of sensors, ULA, 100 snapshots, $2$ signals at $20^{\circ}$ and $30^{\circ}$.

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    Algorithm 1 Low-degree root-MUSIC algorithm

    Require:

    Output:

    Compute ${\boldsymbol~R}=\frac{1}{N}\sum^N_{t=1}{\boldsymbol~x}(t){\boldsymbol~x}^{\rm~H}(t)$, perform EVD on $\mathrm{Re}({\boldsymbol~R})$ to obtain the real matrix $\mathbb{E}_n$;

    Compute $\{b_k\}^{M-1}_{k=0}$ by (13a), obtain $h(\xi)$ by (12);

    Root $h(\xi)$ for $\{\xi_k\}^{M-1}_{k=1}$, get $\{{z}_{k},{z}^*_{k}\}^{M-1}_{k=1}$ by (15);

    Select among $\{{z}_{k},{z}^*_{k}\}^{M-1}_{k=1}$ for $\{{z}_{k},{z}^*_{k}\}^{L}_{k=1}$ by finding the $2L$ ones that lie closest to the unit circle;

    Compute the $2L$ possible DOAs $\{\pm{\theta}\}_{l=1}^L$ by (16), select among $\{\pm{\theta}\}_{l=1}^L$ for the $L$ true DOAs $\{{\theta}_l\}_{l=1}^{L}$ by maximizing $\Vert{\boldsymbol~a}^{\rm~H}(\theta){{\boldsymbol~R}}{\boldsymbol~a}(\theta)\Vert^2_\mathrm{F}$.