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

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  • ReceivedJul 2, 2018
  • AcceptedOct 31, 2018
  • PublishedDec 24, 2019


There is no abstract available for this article.


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


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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 $30^{\circ}$.


    Algorithm 1 Low-degree root-MUSIC algorithm



    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 $\Vert{\boldsymbol~a}^{\rm~H}(\theta){{\boldsymbol~R}}{\boldsymbol~a}(\theta)\Vert^2_\mathrm{F}$.