基于L型阵列酉变换矩阵重构的二维DOA估计

doi:10.11959/j.issn.1000-0801.2018208

摘要/Abstract

摘要：

二维空间信号波达方向（DOA）的估计是阵列信号处理的一个关键研究问题。经典的二维 MUSIC算法固然精度高，但此算法需要二维谱峰搜索，运算较为复杂。提出一种用于L型阵列的二维DOA估计算法，通过矩阵重构使得阵列输出矩阵变为中心对称矩阵，再利用酉变换矩阵将其由复值矩阵变为实值矩阵。该方法可以直接得到目标参数，不需要谱峰搜索，使得运算量大大降低。相比于 L 型阵列适用的增广矩阵束（MEMP）算法，该算法可以估计更多信源的DOA，并能获得较高的分辨率。计算机仿真结果表明，该算法具有较高的DOA估计精度。

关键词: 波达方向, L型阵列, 酉变换矩阵, 特征值, 增广矩阵束算法

Abstract:

The estimation of the direction of arrival of two-dimensional space signals is the key problem in the field of array antennas.Although the traditional two-dimensional MUSIC algorithm has high precision,it needs two dimensional spectrum peak search and has a large amount of operation.A two-dimensional DOA estimation algorithm for L-shaped array was proposed.The output matrix was transformed from a complex value matrix to a real value matrix by matrix reconstruction and a unitary transformation matrix.This method could directly get the elevation angle of the target without conversion,which greatly reduced the amount of operation.Compared with the matrix enhancement and matrix pencil algorithm for L-shaped array,this algorithm could estimate more targets’DOA.The results of simulation show that the algorithm has a high accuracy of DOA estimation.

Key words: direction of arrival, L-shaped array, unitary transformation matrix, eigenvalue, matrix enhancement and, matrix pencil algorithm

王秀,常青,王耀力. 基于L型阵列酉变换矩阵重构的二维DOA估计[J]. 电信科学, 2018, 34(7): 110-117.

Xiu WANG,Qing CHANG,Yaoli WANG. Two-dimensional DOA estimation of unitary transformation matrix reconstruction based on L-shaped array[J]. Telecommunications Science, 2018, 34(7): 110-117.

图/表 8

图1

图2

图3

图4

图5

图6

图7

表1

参考文献 16

[1]	JUNG T J , LEE K K . Closed-form algorithm for 3-D single-source localization with uniform circular array[J]. IEEE Antennas Wireless Propagation Letters, 2014,13(1): 1096-1099.
[2]	李婷 . 二维谱估计算法的空间探测性能分析及验证[J]. 电信科学, 2016,32(5): 173-178. LI T . Analysis and verification on space probe performance of 2-D spectrum estimation algorithm[J]. Telecommunications Science, 2016,32(5): 173-178.
[3]	吴秀芬 . 宽带阵列信号 DOA 估计方法研究[D]. 南京:南京大学, 2013. WU X F . Research on wideband array signal DOA estimation[D]. Nanjing:Nanjing University, 2013.
[4]	GU J F , ZHU W P , SWAMY M N S . Joint 2-D DOA estimation via sparse L-shaped array[J]. IEEE Transactions on Signal Processing, 2015,63(5): 1171-1182.
[5]	ZHANG W , LIU W , WANG J ,et al. Computationally efficient 2-D DOA estimation for uniform rectangular arrays[J]. Multidimensional Systems ＆ Signal Processing, 2014,25(4): 847-857.
[6]	穆昌, 姚俊良, 蔡振合 . 三维MIMO阵列空间相关性分析[J]. 电信科学, 2015,31(1): 1-6. MU C , YAO J L , CAI Z H . Spatial correlation analysis of 3D MIMO array[J]. Telecommunications Science, 2015,31(1): 1-6.
[7]	张小飞, 张立岑, 孙华普 ,等. 双平行线阵中基于 Euler 变换传播算子的二维DOA估计算法[J]. 南京航空航天大学学报, 2015,47(3): 324-331. ZHANG X F , ZHANG L C , SUN H P ,et al. Two-dimensional DOA estimation algorithm for two parallel linear arrays via Euler transformation and propagator method[J]. Journal of Nanjing University of Aeronautics ＆ Astronautics, 2015,47(3): 324-331.
[8]	GU J F , ZHU W P , SWAMY M N S . Performance analysis of 2-D DOA estimation via L-shaped array[C]// 2012 25th IEEE Canadian Conference on Electrical ＆ Computer Engineering (CCECE),April 29-May 2,2012,Montreal,Canada. Piscataway:IEEE Press, 2012: 1-4.
[9]	金梁, 殷勤业 . 时空 DOA 矩阵方法[J]. 电子学报, 2000,28(6): 8-12. JIN L , YIN Q Y . Space-time DOA matrix method[J]. Acta Electronica Sinica, 2000,28(6): 8-12.
[10]	金梁, 殷勤业 . 时空 DOA 矩阵法的分析与推广[J]. 电子学报, 2001,29(3): 300-303. JIN L , YIN Q Y . Analysis and generalization of space-time DOA matrix method[J]. Acta Electronica Sinica, 2001,29(3): 300-303.
[11]	TAYEM N , KWON H M . L-shape2-dimensional arrival angle estimation with propagator method[C]// VTC-2005,May 30-June 1,2005,Stockholm,Sweden. Piscataway:IEEE Press, 2005: 1622-1630.
[12]	KIKUCHI S,TSUJIH , SANO A . Pair-matching method for estimating 2-D angle of arrival with a cross-correlation matrix[J]. IEEE Antennas and Wireless Propagation Letters, 2006,5(1): 35-40.
[13]	WEI Y S , GUO X J . Pair-matching method by signal covariance matrices for 2D-DOA estimation[J]. IEEE Antennas Wireless Propagation.Letters, 2014(13): 1199-1202.
[14]	TIAN Y , LIAN Q S , XU H . Sparse-reconstruction-based 2-D angle of arrival estimation with L-shaped array[J]. International Journal of Electronics and Communications, 2017(72): 162-165.
[15]	YLIMAZER N , SARKAR Y K . 2-D unitary matrix pencilmethod for efficient direction of arrival estimation[J]. Digital Signal Processing:A Review Journal, 2006,16(6): 767-781.
[16]	陈建 . 二维波达方向估计理论研究[D]. 长春:吉林大学, 2006. CHEN J . Theoretical study on two-dimensional direction of arrival estimation[D]. Changchun:Jilin University, 2006.

阵元数	2D-MUSIC算法	增广矩阵束算法	本文算法
5	2.027 892	0.078 909	0.078 768
6	2.396 772	0.079 336	0.079 868
7	3.033 217	0.080 563	0.082 112
8	3.203 651	0.088 141	0.086 562
9	3.588 295	0.089 568	0.089 135
10	3.692 880	0.090 666	0.090 001
20	6.114 345	0.102 475	0.140 633
30	8.572 638	0.163 838	0.397 243
40	10.016 099	0.394 133	1.325 503
50	16.969 983	0.915 499	4.474 533