基于稀疏贝叶斯的阵列幅相和互耦误差联合校正方法

doi:10.11959/j.issn.1000-436x.2022175

摘要/Abstract

摘要：

实际阵列测向系统中往往存在幅相、互耦等多种误差，导致阵列测向性能出现严重恶化。为解决在低信噪比、小快拍、多种误差同时存在时的阵列测向失准问题，通过引入信号空域稀疏性，利用贝叶斯稀疏重构技术解决在幅相、互耦误差同时存在时的无源校正及阵列信号方位的联合估计问题，构建了误差存在时的接收信号的超完备模型，得到接收信号的后验概率密度函数。利用EM算法对概率密度函数进行迭代优化并对相应参数进行求解，同时还对阵列误差及信号方位的CRLB进行推导，实验仿真验证了所提方法的有效性。

关键词: 幅相误差, 互耦误差, 稀疏重构, 波达方向估计

Abstract:

In the actual array direction finding system, there are often a variety of errors such as amplitude and phase, mutual coupling, which lead to serious deterioration of array direction finding performance.In order to solve the problem of array direction finding misalignment in the presence of low signal-to-noise ratio, small snapshots and multiple errors, the spatial sparsity of signals were introduced, and Bayesian sparse reconstruction technology was used to solve the passive correction and joint estimation of array signal azimuth in the presence of amplitude-phase and mutual coupling errors.The over-complete model of the received signal with error was constructed, and the posterior probability density function of the received signal was obtained.The EM algorithm was used to iteratively optimize the probability density function to solve the corresponding parameters.At the same time, the CRLB of array error and signal azimuth was derived, and by experimental simulation verifies the effectiveness of the proposed method.

Key words: amplitude-phase error, mutual coupling error, sparse reconstruction, DOA estimation

中图分类号:

TN911

王鼎, 高卫港, 吴志东. 基于稀疏贝叶斯的阵列幅相和互耦误差联合校正方法[J]. 通信学报, 2022, 43(9): 112-120.

Ding WANG, Weigang GAO, Zhidong WU. Array amplitude-phase and mutual coupling error joint correction method based on sparse Bayesian[J]. Journal on Communications, 2022, 43(9): 112-120.

图/表 10

图1

图2

图3

图4

图5

图6

图7

图8

表1

表2

参考文献 26

[1]	STEEG M , EXNER F , TEBART J ,et al． OFDM joint communication-radar with leaky-wave antennas［J］． Electronics Letters, 2020,56(21): 1139-1141．
[2]	KHALIFE J , SHAMAEI K , KASSAS Z M ． Navigation with cellular CDMA signals—part I:signal modeling and software-defined receiver design［J］． IEEE Transactions on Signal Processing, 2018,66(8): 2191-2203．
[3]	DAI W S , ZHENG E M , BAO K K ． A method of line spectrum extraction based on target radiated spectrum feature and its postprocessing［J］． Journal of Systems Engineering and Electronics, 2021,32(6): 1381-1393．
[4]	HEMMATEENEJAD B , TASHKHOURIAN J , BORDBAR M M ,et al． Development of colorimetric sensor array for discrimination of herbal medicine［J］． Journal of the Iranian Chemical Society, 2017,14(3): 595-604．
[5]	ZHAO J F , ZOU L , JIANG R K ． Hybrid antenna arrays with high angular resolution for 77 GHz automotive radars［J］． IEICE Electronics Express, 2020,17(2): 1-6．
[6]	SCHMIDT R ． Multiple emitter location and signal parameter estimation［J］． IEEE Transactions on Antennas and Propagation, 1986,34(3): 276-280．
[7]	FILHO G L , REZENDE A , CRUZ L F ,et al． 2-D DOA estimation in a cuboid array based on metaheuristic algorithms and maximum likelihood［J］． International Journal of Communications,Network and System Sciences, 2020,13(8): 121-137．
[8]	QIN Z J , FAN J C , LIU Y W ,et al． Sparse representation for wireless communications:a compressive sensing approach［J］． IEEE Signal Processing Magazine, 2018,35(3): 40-58．
[9]	GERSTOFT P , MECKLENBR?UKER C F , XENAKI A ,et al． Multisnapshot sparse Bayesian learning for DOA［J］． IEEE Signal Processing Letters, 2016,23(10): 1469-1473．
[10]	KASEM H M , SELIM M M , MOHAMED E M ,et al． DRCS-SR:deep robust compressed sensing for single image super-resolution［J］． IEEE Access, 2020,8: 170618-170634．
[11]	MCPHERSON E , PARK B , ITO T A ． The role of prototype matching in science pursuits:perceptions of scientists that are inaccurate and diverge from self-perceptions predict reduced interest in a science career［J］． Personality ＆ Social Psychology Bulletin, 2018,44(6): 881-898．
[12]	李双, 刘骁, 胡顺仁 ,等．加权稀疏信号重构的近场源定位方法［J］．声学技术, 2017,36(1): 75-80．
	LI S , LIU X , HU S R ,et al． Near-field source localization based on weighted sparse signal recovery［J］． Technical Acoustics, 2017,36(1): 75-80．
[13]	LIU Q , WANG X P , HUANG M X ,et al． DOA and range estimation for FDA-MIMO radar with sparse Bayesian learning［J］． Remote Sensing, 2021,13(13): 2553．
[14]	TIPPING M E ． Sparse Bayesian learning and the relevance vector machine［J］． Journal of Machine Learning Research, 2001,1(3): 211-244．
[15]	PANG X J , ZHAO Y B , CAO C H ,et al． STAP method based on atomic norm minimization with array amplitude-phase error calibration［J］． Journal of Systems Engineering and Electronics, 2021,32(1): 21-30．
[16]	ELBIR A M ． Direction finding in the presence of direction-dependent mutual coupling［J］． IEEE Antennas and Wireless Propagation Letters, 2017,16: 1541-1544．
[17]	CHEN P , YANG Y X , WANG Y ,et al． Adaptive beamforming with sensor position errors using covariance matrix construction based on subspace bases transition［J］． IEEE Signal Processing Letters, 2019,26(1): 19-23．
[18]	王鼎, 吴瑛．均匀线阵互耦和幅相误差有源校正改进算法［J］．系统工程与电子技术, 2009,31(9): 2076-2081．
	WANG D , WU Y ． Improved active array calibration algorithm for mutual coupling and amplitude-phase error of uniform linear array［J］． Systems Engineering and Electronics, 2009,31(9): 2076-2081．
[19]	王鼎, 邬钧霆, 叶国华 ,等．一种均匀线阵互耦和幅相误差校正算法［J］．信号处理, 2010,26(1): 38-45．
	WANG D , WU J T , YE G H ,et al． A mutual coupling and gain-phase errors calibration algorithm for uniform linear array［J］． Signal Processing, 2010,26(1): 38-45．
[20]	王鼎, 姚晖, 吴瑛．基于协方差匹配技术的互耦和幅相误差联合校正算法［J］．电子学报, 2012,40(3): 580-586．
	WANG D , YAO H , WU Y ． The joint calibration algorithms of mutual coupling and gain-and-phase errors based on covariance matching technique［J］． Acta Electronica Sinica, 2012,40(3): 580-586．
[21]	杨守国, 李勇, 张昆辉 ,等．基于降维的双基地MIMO雷达收发阵列互耦和幅相误差校正算法［J］．系统工程与电子技术, 2018,40(12): 2668-2674．
	YANG S G , LI Y , ZHANG K H ,et al． Reduced dimensional calibration method for bistatic MIMO radar with mutual coupling and gain-phase errors of transmitting and receiving arrays［J］． Systems Engineering and Electronics, 2018,40(12): 2668-2674．
[22]	YANG Z , XIE L H , ZHANG C S ． Off-grid direction of arrival estimation using sparse Bayesian inference［J］． IEEE Transactions on Signal Processing, 2013,61(1): 38-43．
[23]	WU C F J ． On the convergence properties of the EM algorithm［J］． The Annals of Statistics, 1983,11(1): 95-103．
[24]	SMITH S T ． Statistical resolution limits and the complexified Crame-Rao bound［J］． IEEE Transactions on Signal Processing, 2005,53(5): 1597-1609．
[25]	姚康泽, 梁甸农．模型误差对阵列信号特征结构的影响及一种校准方法［J］．系统工程与电子技术, 1996(8): 44-47,76．
	YAO K Z , LIANG D N ． The influnce of model error to array signal eigenstructure and a calibration method［J］． Systems Engineering and Electronics, 1996(8): 44-47,76．
[26]	DAI J , BAO X , XU W ,et al. Root sparse bayesian learning for off-grid DOA estimation［J］． IEEE Siganl Processing Letters, 2017,24(1): 46-50．

互偶系数	真实值	估计值
互耦系数1	0.6+j0.4	0.590 9+j0.377 6
互耦系数2	0.2+j0.1	0.2015+j0.109 9

幅相系数	真实值	估计值
幅相系数1	1.080 6-j0.393 3	1.054 8-j0.382 9
幅相系数2	1.125 8-j0.650 0	1.103 6-j0.553 3
幅相系数3	0.919 3-j0.7713	0.906 2-j0.718 7
幅相系数4	1.023 9+j0.717 0	0.976 7+j0.712 5
幅相系数5	0.725 0+j0.3381	0.696 3+j0.373 5
幅相系数6	0.7518+j0.273 6	0.726 3+j0.297 9
幅相系数7	0.536 2+j0.450 0	0.504 6+j0.527 2