Missing Covariance Matrix Recovery with the FDA-MIMO Radar Using Deep Learning Method

DING Zihang; XIE Junwei; WANG Bo

doi:10.12000/JR23002

Volume 12 Issue 5

Oct. 2023

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Journal of Radars > 2023 > 12(5): 1112-1124

DING Zihang, XIE Junwei, and WANG Bo. Missing covariance matrix recovery with the FDA-MIMO radar using deep learning method[J]. Journal of Radars, 2023, 12(5): 1112–1124. doi: 10.12000/JR23002

Citation:

DING Zihang, XIE Junwei, and WANG Bo. Missing covariance matrix recovery with the FDA-MIMO radar using deep learning method[J]. Journal of Radars, 2023, 12(5): 1112–1124. doi: 10.12000/JR23002

DING Zihang, XIE Junwei, and WANG Bo. Missing covariance matrix recovery with the FDA-MIMO radar using deep learning method[J]. Journal of Radars, 2023, 12(5): 1112–1124. doi: 10.12000/JR23002

Citation:

DING Zihang, XIE Junwei, and WANG Bo. Missing covariance matrix recovery with the FDA-MIMO radar using deep learning method[J]. Journal of Radars, 2023, 12(5): 1112–1124. doi: 10.12000/JR23002

PDF( 1448 KB)

Missing Covariance Matrix Recovery with the FDA-MIMO Radar Using Deep Learning Method

DOI: 10.12000/JR23002

DING Zihang^{1
,
,},
XIE Junwei^{1
,
,},
WANG Bo²

1.
Air and Missile Defense College, Air Force Engineering University, Xi’an 710051, China
2.
Air Traffic Control and Navigation College, Air Force Engineering University, Xi’an 710051, China

Funds: The National Natural Science Foundation of China (62001506)

More Information

Corresponding author: DING Zihang, dingzihang0831@163.com; XIE Junwei, xjw_xjw_123@163.com
Received Date: 2023-01-04
Rev Recd Date: 2023-03-17

Available Online: 2023-03-27

Publish Date: 2023-04-04

Abstract

Abstract

The realization of anti-jamming technologies via beamforming for applications in Frequency-Diverse Arrays and Multiple-Input and Multiple-Output (FDA-MIMO) radar is a field that is undergoing intensive research. However, because of limitations in hardware systems, such as component aging and storage device capacity, the signal covariance matrix data computed by the receiver system may be missing. To mitigate the impact of the missing covariance matrix data on the performance of the beamforming algorithm, we have proposed a covariance matrix data recovery method for FDA-MIMO radar based on deep learning and constructed a two-stage framework based on missing covariance matrix recovery-adaptive beamforming. Furthermore, a learning framework based on this two-stage framework and the Generative Adversarial Network (GAN) is constructed, which is mainly composed of a discriminator (D) and a generator (G). G is primarily used to output complete matrix data, while D is used to judge whether this data is real or filled. The entire network closes the gap between the samples generated by G and the distribution of the real data via a confrontation between D and G, consequently leading to the missing data of the covariance matrix being recovered. In addition, considering that the covariance matrix data is complex, two independent networks are constructed to train the real and imaginary parts of the matrix data. Finally, the numerical experiment results reveal that the difference in the root square mean error levels between the real and recovery data is 0.01 in magnitude.

FullText(HTML)

References(37)

References

[1]	WANG Wenqin. Overview of frequency diverse array in radar and navigation applications[J]. IET Radar, Sonar & Navigation, 2016, 10(6): 1001–1012. doi: 10.1049/iet-rsn.2015.0464
[2]	ANTONIK P, WICKS M C, GRIFFITHS H D, et al. Frequency diverse array radars[C]. The 2006 IEEE Conference on Radar, Verona, USA, 2006: 215–217.
[3]	WICKS M C and ANTONIK P. Frequency diverse array with independent modulation of frequency, amplitude, and phase[P]. US, 7319427, 2008.
[4]	WANG Wenqin and SHAO Huaizong. Range-angle localization of targets by a double-pulse frequency diverse array radar[J]. IEEE Journal of Selected Topics in Signal Processing, 2014, 8(1): 106–114. doi: 10.1109/JSTSP.2013.2285528
[5]	BASIT A, KHAN W, KHAN S, et al. Development of frequency diverse array radar technology: A review[J]. IET Radar, Sonar & Navigation, 2018, 12(2): 165–175. doi: 10.1049/iet-rsn.2017.0207
[6]	SECMEN M, DEMIR S, HIZAL A, et al. Frequency diverse array antenna with periodic time modulated pattern in range and angle[C]. The 2007 IEEE Radar Conference, Waltham, USA, 2007: 427–430.
[7]	SAMMARTINO P F, BAKER C J, and GRIFFITHS H D. Frequency diverse MIMO techniques for Radar[J]. IEEE Transactions on Aerospace and Electronic Systems, 2013, 49(1): 201–222. doi: 10.1109/TAES.2013.6404099
[8]	XU Jingwei, LIAO Guisheng, ZHU Shengqi, et al. Joint range and angle estimation using MIMO radar with frequency diverse array[J]. IEEE Transactions on Signal Processing, 2015, 63(13): 3396–3410. doi: 10.1109/TSP.2015.2422680
[9]	LAN Lan, ROSAMILIA M, AUBRY A, et al. Single-snapshot angle and incremental range estimation for FDA-MIMO radar[J]. IEEE Transactions on Aerospace and Electronic Systems, 2021, 57(6): 3705–3718. doi: 10.1109/TAES.2021.3083591
[10]	LAN Lan, LIAO Guisheng, XU Jingwei, et al. Transceive beamforming with accurate nulling in FDA-MIMO radar for imaging[J]. IEEE Transactions on Geoscience and Remote Sensing, 2020, 58(6): 4145–4159. doi: 10.1109/TGRS.2019.2961324
[11]	XU Jingwei, LIAO Guisheng, ZHU Shengqi, et al. Deceptive jamming suppression with frequency diverse MIMO radar[J]. Signal Processing, 2015, 113: 9–17. doi: 10.1016/j.sigpro.2015.01.014
[12]	LAN Lan, LIAO Guisheng, XU Jingwei, et al. Range-angle-dependent beamforming for FDA-MIMO radar using oblique projection[J]. Science China Information Sciences, 2022, 65(5): 152305. doi: 10.1007/s11432-020-3250-7
[13]	WEN Cai, PENG Jinye, ZHOU Yan, et al. Enhanced three-dimensional joint domain localized STAP for airborne FDA-MIMO radar under dense false-target jamming scenario[J]. IEEE Sensors Journal, 2018, 18(10): 4154–4166. doi: 10.1109/JSEN.2018.2820905
[14]	BASIT A, WANG Wenqin, NUSENU S Y, et al. Cognitive FDA-MIMO with channel uncertainty information for target tracking[J]. IEEE Transactions on Cognitive Communications and Networking, 2019, 5(4): 963–975. doi: 10.1109/TCCN.2019.2928799
[15]	HUANG Bang, WANG Wenqin, BASIT A, et al. Bayesian detection in Gaussian clutter for FDA-MIMO Radar[J]. IEEE Transactions on Vehicular Technology, 2022, 71(3): 2655–2667. doi: 10.1109/TVT.2021.3139894
[16]	LAN Lan, MARINO A, AUBRY A, et al. GLRT-based adaptive target detection in FDA-MIMO radar[J]. IEEE Transactions on Aerospace and Electronic Systems, 2021, 57(1): 597–613. doi: 10.1109/TAES.2020.3028485
[17]	WANG Keyi, LIAO Guisheng, XU Jingwei, et al. Clutter rank analysis in airborne FDA-MIMO radar with range ambiguity[J]. IEEE Transactions on Aerospace and Electronic Systems, 2022, 58(2): 1416–1430. doi: 10.1109/TAES.2021.3122822
[18]	WEN Cai, HUANG Yan, PENG Jinye, et al. Slow-time FDA-MIMO technique with application to STAP radar[J]. IEEE Transactions on Aerospace and Electronic Systems, 2022, 58(1): 74–95. doi: 10.1109/TAES.2021.3098100
[19]	WEN Cai, TAO Mingliang, PENG Jinye, et al. Clutter suppression for airborne FDA-MIMO radar using multi-waveform adaptive processing and auxiliary channel STAP[J]. Signal Processing, 2019, 154: 280–293. doi: 10.1016/j.sigpro.2018.09.016
[20]	WEN Cai, MA Changzheng, PENG Jinye, et al. Bistatic FDA-MIMO radar space-time adaptive processing[J]. Signal Processing, 2019, 163: 201–212. doi: 10.1016/j.sigpro.2019.05.025
[21]	DING Zihang, XIE Junwei, WANG Bo, et al. Robust adaptive null broadening method based on FDA-MIMO radar[J]. IEEE Access, 2020, 8: 177976–177983. doi: 10.1109/ACCESS.2020.3025602
[22]	WANG Yuzhuo and ZHU Shengqi. Main-beam range deceptive jamming suppression with simulated annealing FDA-MIMO radar[J]. IEEE Sensors Journal, 2020, 20(16): 9056–9070. doi: 10.1109/JSEN.2020.2982194
[23]	JAMSHIDIAN M and BENTLER P M. ML estimation of mean and covariance structures with missing data using complete data routines[J]. Journal of Educational and Behavioral Statistics, 1999, 24(1): 21–24. doi: 10.3102/10769986024001021
[24]	WU C F J. On the convergence properties of the EM algorithm[J]. The Annals of Statistics, 1983, 11(1): 95–103. doi: 10.1214/aos/1176346060
[25]	AUBRY A, DE MAIO A, MARANO S, et al. Structured covariance matrix estimation with missing-(complex) data for radar applications via expectation-maximization[J]. IEEE Transactions on Signal Processing, 2021, 69: 5920–5934. doi: 10.1109/TSP.2021.3111587
[26]	LOUNICI K. High-dimensional covariance matrix estimation with missing observations[J]. Bernoulli, 2014, 20(3): 1029–1058. doi: 10.3150/12-BEJ487
[27]	HIPPERT-FERRER A, EL KORSO M N, BRELOY Y A, et al. Robust low-rank covariance matrix estimation with a general pattern of missing values[J]. Signal Processing, 2022, 195: 108460. doi: 10.1016/j.sigpro.2022.108460
[28]	XU Danlei, DU Lan, LIU Hongwei, et al. Compressive sensing of stepped-frequency radar based on transfer learning[J]. IEEE Transactions on Signal Processing, 2015, 63(12): 3076–3087. doi: 10.1109/TSP.2015.2421473
[29]	JI Yuanjie, WEN Cai, HUANG Yan, et al. Robust direction-of-arrival estimation approach using beamspace-based deep neural networks with array imperfections and element failure[J]. IET Radar, Sonar & Navigation, 2022, 16(11): 1761–1778. doi: 10.1049/rsn2.12295
[30]	ZOOGHBY A H E, CHRISTODOULOU C G, and GEORGIOPOULOS M. Neural network-based adaptive beamforming for one- and two-dimensional antenna arrays[J]. IEEE Transactions on Antennas and Propagation, 1998, 46(12): 1891–1893. doi: 10.1109/8.743843
[31]	SALLAM T, ABDEL-RAHMAN A B, ALGHONIEMY M, et al. A neural-network-based beamformer for phased array weather radar[J]. IEEE Transactions on Geoscience and Remote Sensing, 2016, 54(9): 5095–5104. doi: 10.1109/TGRS.2016.2554116
[32]	ZHAO Zhonghui, ZHAO Huiling, WANG Zhaoping, et al. Radial basis function neural network optimal modeling for phase-only array pattern nulling[J]. IEEE Transactions on Antennas and Propagation, 2021, 69(11): 7971–7975. doi: 10.1109/TAP.2021.3083787
[33]	SALLAM T and ATTIYA A M. Convolutional neural network for 2D adaptive beamforming of phased array antennas with robustness to array imperfections[J]. International Journal of Microwave and Wireless Technologies, 2021, 13(10): 1096–1102. doi: 10.1017/S1759078721001070
[34]	TAN Ming, WANG Chunyang, and LI Zhihui. Correction analysis of frequency diverse array radar about time[J]. IEEE Transactions on Antennas and Propagation, 2021, 69(2): 834–847. doi: 10.1109/TAP.2020.3016508
[35]	CAPON J. High-resolution frequency-wavenumber spectrum analysis[J]. Proceedings of the IEEE, 1969, 57(8): 1408–1418. doi: 10.1109/PROC.1969.7278
[36]	YOON J, JORDON J, and VAN DER SCHAAR M. GAIN: Missing data imputation using generative adversarial nets[C]. The 35th International Conference on Machine Learning, Stockholm, Sweden, 2018: 5675–5684.
[37]	STEKHOVEN D J and BÜHLMANN P. MissForest-non-parametric missing value imputation for mixed-type data[J]. Bioinformatics, 2012, 28(1): 112–118. doi: 10.1093/bioinformatics/btr597

Relative Articles

[1]	WANG Zhirui, ZHAO Liangjin, WANG Yuelei, ZENG Xuan, KANG Jian, YANG Jian, SUN Xian. AIR-PolSAR-Seg-2.0: Polarimetric SAR Ground Terrain Classification Dataset for Large-scale Complex Scenes[J]. Journal of Radars, 2025, 14(2): 353-365. doi: 10.12000/JR24237
[2]	YIN Junjun, LUO Jiahao, LI Xiang, DAI Xiaokang, YANG Jian. Ship Detection Based on Polarimetric SAR Gradient and Complex Wishart Classifier[J]. Journal of Radars, 2024, 13(2): 396-410. doi: 10.12000/JR23198
[3]	DING Jinshan, ZHONG Chao, WEN Liwu, XU Zhong. Joint Detection of Moving Target in Video Synthetic Aperture Radar[J]. Journal of Radars, 2022, 11(3): 313-323. doi: 10.12000/JR22036
[4]	HUANG Zhongling, YAO Xiwen, HAN Junwei. Progress and Perspective on Physically Explainable Deep Learning for Synthetic Aperture Radar Image Interpretation（in English）[J]. Journal of Radars, 2022, 11(1): 107-125. doi: 10.12000/JR21165
[5]	YAN Hua, ZHANG Lei, LU Jinwen, XING Xiaoyu, LI Sheng, YIN Hongcheng. Frequency-dependent Factor Expression of the GTD Scattering Center Model for the Arbitrary Multiple Scattering Mechanism[J]. Journal of Radars, 2021, 10(3): 370-381. doi: 10.12000/JR21005
[6]	QUAN Sinong, FAN Hui, DAI Dahai, WANG Wei, XIAO Shunping, WANG Xuesong. Recognition of Ships and Chaff Clouds Based on Sophisticated Polarimetric Target Decomposition[J]. Journal of Radars, 2021, 10(1): 61-73. doi: 10.12000/JR20123
[7]	CUI Xingchao, SU Yi, CHEN Siwei. Polarimetric SAR Ship Detection Based on Polarimetric Rotation Domain Features and Superpixel Technique[J]. Journal of Radars, 2021, 10(1): 35-48. doi: 10.12000/JR20147
[8]	WEI Yangkai, ZENG Tao, CHEN Xinliang, DING Zegang, FAN Yujie, WEN Yuhan. Parametric SAR Imaging for Typical Lines and Surfaces[J]. Journal of Radars, 2020, 9(1): 143-153. doi: 10.12000/JR19077
[9]	WANG Xuesong, CHEN Siwei. Polarimetric Synthetic Aperture Radar Interpretation and Recognition: Advances and Perspectives[J]. Journal of Radars, 2020, 9(2): 259-276. doi: 10.12000/JR19109
[10]	HU Cheng, DENG Yunkai, TIAN Weiming, ZENG Tao. A Compensation Method of Nonlinear Atmospheric Phase Applied for GB-InSAR Images[J]. Journal of Radars, 2019, 8(6): 831-840. doi: 10.12000/JR19073
[11]	Hu Dingsheng, Qiu Xiaolan, Lei Bin, Xu Feng. Analysis of Crosstalk Impact on the Cloude-decomposition-based Scattering Characteristic[J]. Journal of Radars, 2017, 6(2): 221-228. doi: 10.12000/JR16129
[12]	Tao Chensong, Chen Siwei, Li Yongzhen, Xiao Shunping. Polarimetric SAR Terrain Classification Using Polarimetric Features Derived from Rotation Domain[J]. Journal of Radars, 2017, 6(5): 524-532. doi: 10.12000/JR16131
[13]	Wu Jiani, Chen Yongguang, Dai Dahai, Pang Bo, Wang Xuesong. Scattering Mechanism Identification Based on Polarimetric HRRP of Manmade Target[J]. Journal of Radars, 2016, 5(2): 174-181. doi: 10.12000/JR16026
[14]	Sun Xun, Huang Pingping, Tu Shangtan, Yang Xiangli. Polarimetric SAR Image Classification Using Multiple-feature Fusion and Ensemble Learning[J]. Journal of Radars, 2016, 5(6): 692-700. doi: 10.12000/JR15132
[15]	Huang Xiaojing, Yang Xiangli, Huang Pingping, Yang Wen. Prototype Theory Based Feature Representation for PolSAR Images[J]. Journal of Radars, 2016, 5(2): 208-216. doi: 10.12000/JR15071
[16]	Yang Ruliang, Dai Bowei, Li Haiying. Polarization Hierarchy and System Operating Architecture for Polarimetric Synthetic Aperture Radar[J]. Journal of Radars, 2016, 5(2): 132-142. doi: 10.12000/JR16013
[17]	Yan Jian, Li Yang, Yin Qiang, Hong Wen. Freeman-Durden Decomposition with Oriented Dihedral Scattering[J]. Journal of Radars, 2014, 3(5): 574-582. doi: 10.3724/SP.J.1300.2014.14057
[18]	Chong Jin-song, Zhou Xiao-zhong. Survey of Study on Internal Waves Detection in Synthetic Aperture Radar Image[J]. Journal of Radars, 2013, 2(4): 406-421. doi: 10.3724/SP.J.1300.2013.13012
[19]	Wu Yi-rong. Concept on Multidimensional Space Joint-observation SAR[J]. Journal of Radars, 2013, 2(2): 135-142. doi: 10.3724/SP.J.1300.2013.13047

Supplements(0)

Cited By

Cited by

Periodical cited type(23)

1.	肖敏睿，王巍，尤明懿，陈新. 存在时频统误差条件下的联合时频差定位与观测站航迹优化方法. 信号处理. 2025(01): 150-160 .
2.	Xin Yang，Hongming Liu，Xiaoke Wang，Wen Yu，Jingqiu Liu，Sipei Zhang. A Fusion Localization Method Based on Target Measurement Error Feature Complementarity and Its Application. Journal of Beijing Institute of Technology. 2024(01): 75-88 .
3.	任洋，姚金杰，赵昶淳，邹宇，薛晓东. 卫星导航多干扰源直接定位方法. 计算机测量与控制. 2024(04): 159-165+173 .
4.	罗军，张顺生. 联合自适应LASSO与块稀疏贝叶斯直接定位方法. 雷达科学与技术. 2024(03): 265-274 .
5.	万鹏武，李文杰，彭康. 混合信道下基于到达时间的快速直接定位算法. 西安邮电大学学报. 2024(02): 20-26 .
6.	Dandan Li，Deyi Wang，Hao Huan. LFM Radar Source Passive Localization Algorithm Based on Range Migration. Journal of Beijing Institute of Technology. 2024(02): 130-140 .
7.	李俊霞，王欣，黄高见，徐勇军，郝万明，朱政宇，李兴旺. 无源定位技术发展及其展望. 无线电工程. 2024(08): 1825-1846 .
8.	陈梁栋，黄知涛，王翔，吴癸周. 基于角速度信息先验的固定无源单站直接定位方法. 电子学报. 2024(07): 2190-2200 .
9.	任洋，姚金杰，赵昶淳. 一种自适应网格细化的卫星干扰源定位方法. 火力与指挥控制. 2024(08): 152-158+165 .
10.	张炜，杨秋，李昊. 一种分布式一体化传感器异步纯方位跟踪管理方法. 指挥控制与仿真. 2024(06): 43-48 .
11.	王雨琦，吴楠，张旭，刘丹，王海强，韩笑冬，仲小清，王宁远. 多星分布式无源相干定位方法. 中国空间科学技术. 2023(01): 63-68 .
12.	陈志坤，翁一鸣，彭冬亮，吴美婵. 基于VEPPSO-EXTRA混合算法的分布式直接定位技术. 电子与信息学报. 2023(02): 664-671 .
13.	罗迪，尹灿斌，李智. 双星对地面未知辐射源直接定位方法研究. 指挥控制与仿真. 2023(01): 136-143 .
14.	刘云天，史鑫磊. 多基站非圆信号直接定位：降维PM与泰勒补偿. 太赫兹科学与电子信息学报. 2023(06): 725-733 .
15.	夏楠，高丹阳，邢宝辉，王亚宁. 基于外辐射源的空中目标直接定位算法. 通信学报. 2023(06): 117-124 .
16.	唐元春，陈端云，夏炳森. 基于传播算子的卫星导航系统干扰源直接定位方法. 太赫兹科学与电子信息学报. 2023(08): 985-991 .
17.	张怡霄，王怀习，姚云龙，常超，康凯. 基于聚类与霍夫变换的同型雷达多目标定位算法. 电讯技术. 2023(12): 1885-1893 .
18.	刘清，谢坚，王伶，王秋红，张兆林. 卫星导航欺骗式干扰源高精度直接定位方法. 电子学报. 2022(05): 1117-1122 .
19.	韦卓. 基于单站干涉仪测向法的未知辐射源定位技术. 舰船电子工程. 2022(07): 159-161 .
20.	王裕旗，孙光才，邢孟道，张子敬. 合成孔径无源定位性能分析与参数设计. 电子与信息学报. 2022(09): 3155-3162 .
21.	刘振，苏晓龙，刘天鹏，彭勃，陈鑫，刘永祥. 基于矩阵差分的远场和近场混合源定位方法. 雷达学报. 2021(03): 432-442 . 本站查看
22.	金峥嵘，王洁，陈丹彤，赵翼，朱秋明，段洪涛. 基于频谱测绘的辐射源定位. 通信技术. 2021(12): 2644-2649 .
23.	张国鑫，易伟，孔令讲. 基于1比特量化的大规模MIMO雷达系统直接定位算法. 雷达学报. 2021(06): 970-981 . 本站查看

Other cited types(22)

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Get Citation

PDF

XML

Article views(1117) PDF downloads(255)