基于稀疏阵列的电磁矢量传感器多输入多输出雷达高分辨角度和极化参数联合估计

谢前朋; 潘小义; 陈吉源; 肖顺平

doi:10.7498/aps.69.20191895

摘要

针对双基地电磁矢量传感器多输入多输出(electromagnetic vector sensors multiple-input multiple-output, EMVS-MIMO)雷达参数估计精度以及角度参数配对问题, 通过设计一种新的稀疏阵列和采用自动参数配对算法来实现高分辨的角度参数和极化参数联合估计. 首先, 通过设计稀疏的发射阵列和接收阵列来实现对EMVS-MIMO雷达阵列孔径的扩展; 然后, 提出平行因子-三线性分解算法对接收数据的三阶张量模型进行求解. 所提出的平行因子-三线性分解算法能够实现二维发射角、二维接收角、极化相位角和极化相位差的联合参数自动配对; 且针对估计得到的发射导向矢量矩阵和接收导向矢量矩阵, 根据旋转不变特性可以实现高精度的发射俯仰角和接收俯仰角测量. 在得到精确的发射俯仰角和接收俯仰角之后, 相应的发射和接收方位角、极化角和极化相位差可以通过矢量叉积算法来进行估计. 相比于现有算法, 所提出的算法能够避免高维数据奇异值分解以及额外的参数配对过程; 且通过稀疏阵列设计, 角度参数估计精度能够进一步地提升, 仿真结果表明所提出的算法具有优良的角度参数估计性能.

关键词:

Abstract

In this paper, a new sparse transmitting and receiving array is designed to improve the joint angle and polarization parameter estimation performance for bistatic electromagnetic vector sensors Multiple-Input Multiple-Output radar. Firstly, large array aperture can be obtained with the aid of the sparse transmitting and receiving array. Then, an effective third-order tensor model is constructed in order to make full use of the multidimensional space-time characteristics of output data after matching filtering. And, the Parallel Factor trilinear alternating least square algorithm is proposed to deal with the constructed third-order tensor model, which can yield closed-form automatically paired two dimensional Direction of Departure and two dimensional Direction of Departure estimation without additional angle pair matching process. Furthermore, two sets of high accuracy rotation invariance relationships corresponding to transmit elevation angle and receive elevation angle can be achieved by using the estimated transmit steering vector matrix and receive steering vector matrix. After the accuracy transmit elevation angle and receive angle are obtained, the corresponding transmitting and receiving azimuth angle, polarization angle and polarization phase difference can be accurately estimated by using the vector-cross-product algorithm. Compared with existing algorithms, the proposed algorithm can avoid high dimensional eigenvalue decomposition and additional parameter matching process. Moreover, the high estimation performance of the proposed can be further guaranteed by using the designed sparse array. Finally, simulation results demonstrate the effectiveness and superiority of the proposed method in terms of estimation accuracy and angle resolution.

Keywords:

PACS:

作者及机构信息

国防科技大学, 电子信息系统复杂电磁环境效应国家重点实验室, 长沙　410073

通信作者: 潘小义, mrpanxy@nudt.edu.cn

基金项目: 国家级-国家自然科学基金(61701507，61890542，61890540)

Authors and contacts

State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System, National University of Defense Technology, Changsha 410073, China

Corresponding author: Pan Xiao-Yi, mrpanxy@nudt.edu.cn

文章全文

参考文献

[1]	Wang X P, Wang L Y, Li X M, Bi G A 2017 Signal Process. 135 147 Google Scholar
[2]	Wang X P, Wan L T, Huang M X, Shen C, Zhang K 2019 IEEE J. Sel. Topics Signal Process. 13 1001 Google Scholar
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[6]	Zhang X F, Xu D Z 2010 Electron. Lett. 12 860
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[9]	Bencheikh M L, Wang Y D, He H Y 2010 Signal Process. 90 2723
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[12]	Wang X P, Wang W, Liu J, Liu Q, Wang B 2015 Signal Process. 116 152 Google Scholar
[13]	Wen F Q, Xiong X D, Su J, Zhang Z J 2017 Signal Process. 134 261 Google Scholar
[14]	Xu B Q, Zhao Y B 2019 Signal Process. 157 88 Google Scholar
[15]	Li L, Younan N H, Shi X F 2019 Sensors 19 1 Google Scholar
[16]	Chen J L, Zhou Q G, Li J Q, Zhu Y P 2019 IET Radar Sonar Navigat. 13 1180 Google Scholar
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[22]	Sidiropoulos N D, Bro R, Giannakis G B 2000 IEEE Trans. Signal Process. 48 2377 Google Scholar
[23]	Stoica P, Nehorai A 1989 IEEE Trans. Acoust. Speech Signal Process. 37 720 Google Scholar

图 1 稀疏阵列EMVS-MIMO雷达系统

Fig. 1. EMVS-MIMO radar system with sparse linear array.

下载: 全尺寸图片幻灯片

图 2 不同算法的计算复杂度随快拍数的变化

Fig. 2. Comparison of computational complexity versus different snapshots number.

下载: 全尺寸图片幻灯片

图 3 所提算法角度参数和极化参数估计星座图　(a) 发射俯仰角和接收俯仰角; (b) 发射方位角和接收方位角; (c) 发射俯仰角和发射方位角; (d) 发射极化角和极化相位差; (e) 接收俯仰角和接收方位角; (f) 接收极化角和极化相位差

Fig. 3. Scatter plot of the angle parameters and polarization parameters by using the proposed method: (a) Scatter plot of the transmit elevation angle and receive elevation angle; (b) scatter plot of the transmit azimuth angle and receive azimuth angle; (c) scatter plot of the transmit elevation angle and azimuth angle; (d) scatter plot of the transmit polarization angle and polarization phase difference; (e) scatter plot of the receive elevation angle and azimuth angle; (f) scatter plot of the receive polarization angle and polarization phase difference.

下载: 全尺寸图片幻灯片

图 4 信噪比对算法的影响　(a) 均方误差随信噪比的变化; (b) 检测概率随信噪比的变化

Fig. 4. The effect of the SNR for different methods: (a) Curves of RMSE versus SNR; (b) curves of PSD versus SNR.

下载: 全尺寸图片幻灯片

图 5 快拍数对算法的影响　(a) 均方误差随快拍数的变化; (b) 检测概率随快拍数的变化

Fig. 5. The effect of the snapshot for different methods: (a) Curves of RMSE versus snapshot; (b) curves of PSD versus snapshot.

下载: 全尺寸图片幻灯片

图 6 不同算法的目标分辨力比较　(a) 均方误差随角度间隔的变化; (b) 检测概率随角度间隔的变化

Fig. 6. Comparison of target resolution ability of different methods: (a) curves of RMSE versus angular separation; (b) curves of PSD versus angular separation.

下载: 全尺寸图片幻灯片

表 1 不同算法的计算复杂度对比

Table 1. Computational complexity comparison of different methods.

算法类型	计算复杂度	计算时间/s
ESPRIT-Like算法 [19]	$\begin{aligned}& o((6 M)^2(6N)^2L + (6 M)^3(6 N)^3 + 2K^26(N + M - 2) + 6{K^3} \\ & + 7(M + N){K^2} + 12 K + 36 MN(36 MN - K) + (36 MN - K){K^2}) \end{aligned}$	28.332
PM-Like算法 [20]	$\begin{aligned}& o((6M)^2(6N)^2L + 72MN{K^2} + 2{K^2}6 (N + M - 2) + 6{K^3} \\& + 7( {M + N} ) {K^2} + 12K + 36MN({36MN - K}) + (36MN - K){K^2})\end{aligned}$	2.0698
Tensor子空间算法 [21]	$\begin{aligned} & o((6 M)^2(6N)^2L + 4(6M)^3(6N)^3 + 2K^2 6(N + M - 2) + 6{K^3} \\& + 7( {M + N} ) K^2 + 12 K + 36 MN( {36 MN - K} ) + (36 MN - K)K^2) \end{aligned}$	109.880
所提算法	$\begin{aligned}& o(\kappa ( 3K^3+ 108 MNKL + 3K^2) + \kappa (3K^2(36 MN + 6 NL + 6 ML)) \\ & + 2{K^2}6({N + M - 2} ) + 6{K^3} + 7(M + N){K^2} + 12K) \end{aligned}$	0.5684

下载: 导出CSV

表 2 目标回波参数表

Table 2. Parameters of target signals.

目标	方位角θ/(°)	俯仰角ϕ/(°)	极化角γ/(°)	极化相位差η/(°)
1	$40/24$	$15/21$	$10/42$	$38/17$
2	$20/38$	$25/32$	$22/33$	$48/27$
3	$30/16$	$35/55$	$45/60$	$56/39$

下载: 导出CSV

map

[1]	Wang X P, Wang L Y, Li X M, Bi G A 2017 Signal Process. 135 147 Google Scholar
[2]	Wang X P, Wan L T, Huang M X, Shen C, Zhang K 2019 IEEE J. Sel. Topics Signal Process. 13 1001 Google Scholar
[3]	Xie Q P, Pan X Y, Huang M, Chen J Y, Xiao S P 2019 IEEE Access 7 107805 Google Scholar
[4]	Li J, Stoica P 2007 IEEE Signal Process. Mag. 5 106
[5]	Zhang X F, Xu L Y, Xu L, Xu D Z 2010 IEEE Commun. Lett. 14 1161 Google Scholar
[6]	Zhang X F, Xu D Z 2010 Electron. Lett. 12 860
[7]	Chen D F, Chen B X, Qin G D 2008 Electron. Lett. 44 770 Google Scholar
[8]	Chen J L, Gu H, Song W M 2008 Electron. Lett. 44 1422 Google Scholar
[9]	Bencheikh M L, Wang Y D, He H Y 2010 Signal Process. 90 2723
[10]	Xia T Q 2015 Signal Process. 108 159 Google Scholar
[11]	Xia T Q 2015 Signal Process. 116 7 Google Scholar
[12]	Wang X P, Wang W, Liu J, Liu Q, Wang B 2015 Signal Process. 116 152 Google Scholar
[13]	Wen F Q, Xiong X D, Su J, Zhang Z J 2017 Signal Process. 134 261 Google Scholar
[14]	Xu B Q, Zhao Y B 2019 Signal Process. 157 88 Google Scholar
[15]	Li L, Younan N H, Shi X F 2019 Sensors 19 1 Google Scholar
[16]	Chen J L, Zhou Q G, Li J Q, Zhu Y P 2019 IET Radar Sonar Navigat. 13 1180 Google Scholar
[17]	Chen J L, Zhang T X, Li J Q, Chen X 2019 IEEE Sensors J. 19 5384 Google Scholar
[18]	Wong K T, Zoltowski M D 1997 IEEE Trans. Antennas Propag. 45 1467 Google Scholar
[19]	Chintagunta S, Ponnusamy P 2018 Signal Process. 147 163 Google Scholar
[20]	Liu T T, Wen F Q, Shi J P, Gong Z H, Xu H 2019 IEEE Access 7 120533 Google Scholar
[21]	Mao C X, Shi J P, Wen F Q 2019 IEEE Access 7 163119 Google Scholar
[22]	Sidiropoulos N D, Bro R, Giannakis G B 2000 IEEE Trans. Signal Process. 48 2377 Google Scholar
[23]	Stoica P, Nehorai A 1989 IEEE Trans. Acoust. Speech Signal Process. 37 720 Google Scholar

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