一种用于矩形阵列的二维波达方向估计方法

doi:10.19665/j.issn1001-2400.2019.04.017

摘要/Abstract

摘要：

针对现有使用均匀矩形阵列或稀疏矩形阵列的二维无格波达方向估计方法的性能欠佳的问题,提出一种基于二阶特普利茨矩阵重构和二维旋转不变参数估计技术的无格波达方向估计方法。使用均匀矩形阵列或稀疏矩形阵列,对其接收信号的协方差矩阵进行二阶特普利茨结构表达,通过log-det稀疏测度与正定约束构造约束优化问题,并使用优化最小算法求解,最后通过二维旋转不变参数估计技术估计源的二维波达方向,即方位角与俯仰角。这种方法需要多次求解半定规划问题,计算复杂度相对较高,但能获得更好的波达方向估计性能。在仿真实验中,这种方法在均匀矩形阵列或稀疏矩形阵列条件下均有非常低的均方根误差,接近克拉美罗界,证明了其良好的波达方向估计性能。

关键词: 二维波达方向估计, 无格, 矩形阵列, 半定规划, 优化最小

Abstract:

To improve the performance of existing two-dimensional (2-D) grid-less irection of arrival(DOA) estimation methods using the uniform rectangular array(URA) or sparse rectangular array(SRA), a novel 2-D grid-less DOA estimation method based on doubly Toeplitz matrix reconstruction and 2-D ESPRIT is proposed. First, using URA or SRA, the doubly Toeplitz structure of the associated covariance matrix is established. Second, by applying the log-det sparse metric and semi-definite positive constraints, the constrained optimization problem is presented and solved by the majorization-minimization (MM) algorithm. Finally, the azimuth angles and elevation angles are estimated by the 2-D ESPRIT method. The proposed method needs to solve semi-definite programming (SDP) problems repeatedly, which results in a high complexity, while it always provides a superior performance of DOA estimation. In simulations, the proposed method has a very small root-mean-square error (RMSE) in the case of URA and SRA, which can approach the Crammer-Rao bound. Simulation results prove the good performance of the proposed method.

Key words: 2-D direction of arrival estimation, grid-less, rectangular array, semi-definite programming, majorization-minimization

中图分类号:

TN911.7

王剑书,樊养余,杜瑞,吕国云. 一种用于矩形阵列的二维波达方向估计方法[J]. 西安电子科技大学学报, 2019, 46(4): 122-129.

WANG Jianshu,FAN Yangyu,DU Rui,LV Guoyun. Method for estimation of the two-dimensional direction of wave arrival using the rectangular array[J]. Journal of Xidian University, 2019, 46(4): 122-129.

图/表 5

参考文献 26

[1]	SCHMIDT R O . Multiple Emitter Location and Signal Parameter Estimation[J]. IEEE Transactions on Antennas and Propagation, 1986,34(3):276-280.
[2]	ROY R, KAILATH T . ESPRIT—Estimation of Signal Parameters via Rotational Invariance Techniques[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1989,37(7):984-995.
[3]	MALIOUTOV D, CETIN M, WILLSKY A S . A Sparse Signal Reconstruction Perspective for Source Localization with Sensor Arrays[J]. IEEE Transactions on Signal Processing, 2005,53(8):3010-3022.
[4]	WU X H, ZHU W P, YAN J , et al. Two Sparse-based Methods for Off-grid Direction-of-arrival Estimation[J]. Signal Processing, 2018,142:87-95.
[5]	韦娟, 计永祥, 牛俊儒 . 一种新的稀疏重构的DOA估计算法[J]. 西安电子科技大学学报, 2018,45(5):19-24.
	WEI Juan, JI Yongxiang, NIU Junru . Novel Algorithm for DOA Estimation Based on the Sparse Reconstruction[J]. Journal of Xidian University, 2018,45(5):19-24.
[6]	DAI J S, SO H C . Sparse Bayesian Learning Approach for Outlier-resistant Direction-of-arrival Estimation[J]. IEEE Transactions on Signal Processing, 2018,66(3):744-756.
[7]	ZOLTOWSKI M D, HAARDT M, MATHEWS C P . Closed-form 2-D Angle Estimation with Rectangular Arrays in Element Space or Beamspace via Unitary ESPRIT[J]. IEEE Transactions on Signal Processing, 1996,44(2):316-328.
[8]	MATHEWS C P, ZOLTOWSKI M D . Eigenstructure Techniques for 2-D Angle Estimation with Uniform Circular Arrays[J]. IEEE Transactions on Signal Processing, 1994,42(9):2395-2407.
[9]	ZOLTOWSKI M D, MATHEWS C P. Closed-form 2D Angle Estimation with Uniform Circular Array via Phase Mode Excitation and ESPRIT [C]// Conference Record of the 1993 Twenty-seventh Asilomar Conference on Signals, Systems and Computers. Los Alamitos: IEEE, 1993: 169-173.
[10]	DONG Y Y, DONG C X, LIU W , et al. 2-D DOAEstimation for L-shaped Array with Array Aperture and Snapshots Extension Techniques[J]. IEEE Signal Processing Letters, 2017,24(4):495-499.
[11]	WANG Q, YANG H, CHEN H , et al. A Low-complexity Method for Two-dimensional Direction-of-arrival Estimation Using an L-shaped Array[J]. Sensors, 2017,17(1):190-204.
[12]	CHEN H, HOU C, LIU W , et al. Efficient Two-dimensional Direction-of-arrival Estimation for a Mixture of Circular and Noncircular Sources[J]. IEEE Sensors Journal, 2016,16(8):2527-2536.
[13]	WU X H, ZHU W P, YAN J . A Fast Gridless Covariance Matrix Reconstruction Method for One-and Two-dimensional Direction-of-arrival Estimation[J]. IEEE Sensors Journal, 2017,17(15):4916-4927.
[14]	TIAN X Y, LEI J, DU L . A Generalized 2-D DOA Estimation Method Based on Low-rank Matrix Reconstruction[J]. IEEE Access, 2018,6:17407-17414.
[15]	QIAN T, TIAN J, ZHANG X. et al. Atomic Norm Method for DOA Estimation in Random Sampling Condition [C]//Proceedings of the 2016 CIE International Conference on Radar. Piscataway: IEEE, 2016: 8059530.
[16]	ZHANG Y, ZHANG G, WANG X. Array Covariance Matrix-based Atomic Norm Minimization for Off-grid Coherent Direction-of-arrival Estimation [C]//Proceedings of the 2017 IEEE International Conference on Acoustics, Speech and Signal Processing. Piscataway: IEEE, 2017: 3196-3200.
[17]	MHATA K, HYDER M M . Grid-less T.V Minimization for DOA Estimation[J]. Signal Processing, 2017,132:155-164.
[18]	YANG Z, XIE L . Enhancing Sparsity and Resolution via Reweighted Atomic Norm Minimization[J]. IEEE Transactions on Signal Processing, 2016,64(4):995-1006.
[19]	YANG Z, XIE L . On Gridless Sparse Methods for Multi-snapshot Direction of Arrival Estimation[J]. Circuits, Systems, and Signal Processing, 2017,36(8):3370-3384.
[20]	ZHANG Y W, HONG X, WANG Y. et al. Gridless SPICE Applied to Parameter Estimation of Underwater Acoustic Frequency Hopping Signals [C]//Proceedings of the 2016 IEEE/OES China Ocean Acoustics Symposium. Piscataway: IEEE, 2016: 7535747.
[21]	YANG Z, LI J, STOICA P , et al . Sparse Methods for Direction-of-arrival Estimation[EB/OL]. [ 2018- 12- 11]. http://cn.arxiv.org/pdf/1609.09596v2.
[22]	SAHNOUN S, USEVICH K, COMON P . Multidimensional ESPRIT for Damped and Undamped Signals: Algorithm, Computations, and Perturbation Analysis[J]. IEEE Transactions on Signal Processing, 2017,65(22):5897-5910.
[23]	ZHANG F . The Schur Complement and Its Applications[M]. Heidelberg: Springer, 2006: 34-37.
[24]	SUN Y, BABU P, PALOMAR D P . Majorization-minimization Algorithms in Signal Processing, Communications, and Machine Learning[J]. IEEE Transactions on Signal Processing, 2017,65(3):794-816.
[25]	STURM J F. . Using SeDuMi 1.02, a MATLABToolbox for Optimization over Symmetric Cones[J]. Optimization Methods and Software, 1999,11(1):625-653.
[26]	LOFBERG J. YALMIP:a Toolbox for Modeling and Optimization in MATLAB [C]//Proceedings of the 2004 IEEE International Symposium on Computer Aided Control Systems Design. Piscataway: IEEE, 2004: 284-289.