基于稀疏恢复的快速高精度DOA估计算法

doi:10.12305/j.issn.1001-506X.2024.11.05

Abstract

Abstract:

The conventional direction of arrival (DOA) estimation algorithm based on sparse recovery uses dense sampling grids, resulting in significantly increased computational complexity and low estimation accuracy for adjacent signals. To address this issue, this manuscript proposes a fast and high accuracy DOA estimation algorithm. Firstly, starting from sparse grids, the grid evolution method is used to reduce the total number of grid points. Noise variance and signal power are estimated again, then use off-grid root sparse Bayesian learning (OGRSBL) technique to calculate the accurate estimation of incident angle. Simulation results show that compared to conventional sparse Bayesian learning algorithms, the proposed algorithm has higher computational efficiency with higher accuracy for closely spaced signals.

Key words: direction of arrival (DOA) estimation, off-grid, grid evolution, sparse Bayesian learning (SBL)

CLC Number:

TN911.7

Lutao LIU, Guoheng XU, Zhen WANG. Fast and high precision DOA estimation algorithm based on sparse recovery[J]. Systems Engineering and Electronics, 2024, 46(11): 3631-3638.

Figures/Tables 4

Table 1

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References 30

1	KRIM H , VIBERG M . Two decades of array signal processing research: the parametric approach[J]. IEEE Signal Processing Magazine, 1996, 13 (4): 67- 94. doi: 10.1109/79.526899
2	SCHMIDT R . Multiple emitter location and signal parameter estimation[J]. IEEE Trans.on Antennas & Propagation, 1986, 34 (3): 276- 280.
3	MALLAT S G , ZHANG Z . Matching pursuits with time-frequency dictionaries[J]. IEEE Trans.on Signal Processing, 1993, 41 (12): 3397- 3415. doi: 10.1109/78.258082
4	TROPP J A , GILBERT A C . Signal recovery from random measurements via orthogonal matching pursuit[J]. IEEE Trans.on Information Theory, 2007, 53 (12): 4655- 4666. doi: 10.1109/TIT.2007.909108
5	NEEDELL D , VERSHYNIN R . Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit[J]. IEEE Journal of Selected Topics in Signal Processing, 2010, 4 (2): 310- 316. doi: 10.1109/JSTSP.2010.2042412
6	KARABULUT G Z, KURT T, YONGACOGLU A. Angle of arrival detection by matching pursuit algorithm[C]//Proc. of the IEEE 60th Vehicular Technology Conference, 2004: 324-328.
7	MALIOUTOV D , CETIN M , WILLSKY A S . A sparse signal reconstruction perspective for source localization with sensor arrays[J]. IEEE Trans.on Signal Processing, 2005, 53 (8): 3010- 3022. doi: 10.1109/TSP.2005.850882
8	LU H T, LONG X Z, LV J Y. A fast algorithm for recovery of jointly sparse vectors based on the alternating direction methods[C]//Proc. of the 14th International Conference on Artificial Intelligence and Statistics, 2011, 15: 461-469.
9	王庚, 李浩, 何翼, 等. 最优冗余线阵欠定信号双重构DOA估计方法[J]. 系统工程与电子技术, 2023, 45 (1): 49- 55.
	WANG G , LI H , HE Y , et al. Underdetermined DOA estimation of optimal redundancy array via double reconstruction[J]. Systems Engineering and Electronics, 2023, 45 (1): 49- 55.
10	曹若石, 赵永波, 邱雨铖. 基于改进SP算法的多目标DOA估计方法[J]. 系统工程与电子技术, 2024, 46 (7): 2294- 2300.
	CAO R S , ZHAO Y B , QIU Y C . Multi-target DOA estimation method based on improved SP algorithm[J]. Systems Engineering and Electronics, 2024, 46 (7): 2294- 2300.
11	唐军奎, 刘峥, 冉磊, 等. 基于稀疏和低秩先验的雷达前视超分辨成像方法[J]. 雷达学报, 2023, 12 (2): 332- 342.
	TANG J K , LIU Z , RAN L , et al. Radar forward-looking super-resolution imaging method based on sparse and low-rank priors[J]. Journals of Radars, 2023, 12 (2): 332- 342.
12	TIPPING M E . Sparse Bayesian learning and the relevance vector machine[J]. Journal of Machine Learning Research, 2001, 1 (3): 211- 244.
13	TIPPING M E, FAUL A C. Fast marginal likelihood maximisation for sparse bayesian models[C]//Proc. of the 9th International Workshop on Artificial Intelligence & Statistics, 2003
14	JI S , XUE Y , CARIN L . Bayesian compressive sensing[J]. IEEE Trans.on Signal Processing, 2008, 56 (6): 2346- 2356.
15	JI S , DUNSON D , CARIN L . Multitask compressive sensing[J]. IEEE Trans.on Signal Processing, 2009, 57 (1): 92- 106.
16	BABACAN S D, MOLINA R, KATSAGGELOS A K. Fast Bayesian compressive sensing using Laplace priors[C]//Proc. of the IEEE International Conference on Acoustics, 2009.
17	LIU Z M , HUANG Z T , ZHOU Y Y . An efficient maximum likelihood method for direction-of-arrival estimation via sparse Bayesian learning[J]. IEEE Trans.on Wireless Communications, 2012, 11 (10): 1- 11.
18	YANG Z , XIE L H , ZHANG C S . Off-grid direction of arrival estimation using sparse Bayesian inference[J]. IEEE Trans.on Signal Processing, 2013, 61 (1): 38- 43.
19	DAI J S , BAO X , XU W C , et al. Root sparse Bayesian learning for off-grid DOA estimation[J]. IEEE Signal Processing Letters, 2016, 24 (1): 46- 50.
20	SHAO Y Y, MA H, LIU H W. A study and comparison of different sparse Bayesian learning algorithms in DOA estimation[C]//Proc. of the IEEE International Conference on Information Communication and Signal Processing, 2022.
21	YU D , WANG X , FANG W W , et al. DOA estimation based on root sparse Bayesian learning under gain and phase error[J]. Journal of Communications and Information Networks, 2022, 7 (2): 202- 213.
22	DAS A . Real-valued sparse Bayesian learning for off-grid direction-of-arrival (DOA) estimation in ocean acoustics[J]. IEEE Journal of Oceanic Engineering, 2021, 46 (1): 172- 182.
23	DAI J S , SO H C . Real-valued sparse Bayesian learning for DOA estimation with arbitrary linear arrays[J]. IEEE Trans.on Signal Processing: a publication of the IEEE Signal Processing Society, 2021, 69 (1): 4977- 4990.
24	GUO L M, XIAO S Q, GUO M R. Off-grid sparse Bayesian learning algorithm for compressed sparse array[C]//Proc. of the CIE International Conference on Radar, 2021.
25	WANG Q S , YU H , LI J , et al. Sparse Bayesian learning using generalized double pareto prior for DOA estimation[J]. IEEE Signal Processing Letters, 2021, 28, 1744- 1748.
26	FU H S, WANG Y Y, DAI F Z. Off-grid error calibration for single snapshot DOA estimation based on sparse Bayesian learning[C]//Proc. of the 5th International Conference on Information Communication and Signal Processing, 2022.
27	WANG Q , ZHAO Z , CHEN Z M , et al. Grid evolution method for DOA estimation[J]. IEEE Trans.on Signal Processing, 2018, 66 (9): 2374- 2383.
28	王琦森, 余华, 李杰, 等. 基于稀疏贝叶斯学习的空间紧邻信号DOA估计算法[J]. 电子与信息学报, 2021, 43 (3): 708- 716.
	WANG Q S , YU H , LI J , et al. Sparse Bayesian learning based algorithm for DOA estimation of closely spaced signals[J]. Journal of Electronics & Information Technology, 2021, 43 (3): 708- 716.
29	BRESLER Y , MACOVSKI A . On the number of signals resolvable by a uniform linear array[J]. IEEE Trans. Acoustic. Speech, Signal Processing, 2003, 34 (6): 1361- 1375.
30	WU X H , ZHU W P , YAN J . Direction of arrival estimation for off-grid signals based on sparse Bayesian learning[J]. IEEE Sensors Journal, 2016, 16 (7): 2004- 2016.

算法	计算复杂度
本文算法	第1次迭代: $\begin{gathered}O\left(M N_{\max } L+M N_{\max }^2+M^2 N_{\max }+M^3+L K^2=\right. \\ \left.N_{\max } K^2+M N_{\max } K\right)\end{gathered}$
本文算法	第2次迭代: $\begin{gathered}O\left(M N_{\max } L+M N_{\max }^2+M^2 N_{\max }+M^3+\right. \\ \left.M\left(N_{\max }-1\right) L\right)\end{gathered}$
OGSBI	$\begin{gathered}O\left(M N L+M N^2+M^2 N+M^3+\right. \\ \left.L K^2+N K^2+M N K\right)\end{gathered}$
OGRSBL	$\begin{gathered}O\left(M N L+M N^2+M^2 N+M^3+\right. \\ M(N-1) L)\end{gathered}$
PSBL	$\begin{gathered}O\left(M(N-1) L+M(N-1)^2+M^2(N-1)+\right. \\ \left.M^3+L K^2+(N-1) K^2+M(N-1) K\right)\end{gathered}$
GE-OGSBI	$\begin{gathered}O\left(M N_{\max } L+M N_{\max }^2+M^2 N_{\max }+M^3+L K^2+\right. \\ \left.N_{\max } K^2+M N_{\max } K\right)\end{gathered}$
GI-MSBL	第1次迭代: O(MNL+MN+M²N+M³+LK²)
	第2次迭代: $O\left(\overline{M N L}+\overline{M N}+M^2 \bar{N}+M^3+L K^2\right) $
	计算离网误差: (2M²+2M)N₀K

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Fast and high precision DOA estimation algorithm based on sparse recovery

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