基于深度学习的FDA-MIMO雷达协方差矩阵缺失数据恢复方法

丁梓航 谢军伟 王博

丁梓航, 谢军伟, 王博. 基于深度学习的FDA-MIMO雷达协方差矩阵缺失数据恢复方法[J]. 雷达学报, 2023, 12(5): 1112–1124. doi: 10.12000/JR23002
引用本文: 丁梓航, 谢军伟, 王博. 基于深度学习的FDA-MIMO雷达协方差矩阵缺失数据恢复方法[J]. 雷达学报, 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

基于深度学习的FDA-MIMO雷达协方差矩阵缺失数据恢复方法

doi: 10.12000/JR23002
基金项目: 国家自然科学基金(62001506)
详细信息
    作者简介:

    丁梓航,博士生,主要研究方向包括频控阵雷达抗干扰技术、波束优化理论、智能信号处理等

    谢军伟,博士,教授,主要研究方向包括雷达干扰与抗干扰技术、新体制雷达系统等

    王 博,博士,讲师,主要研究方向包括频控阵雷达波束设计、抗干扰应用等

    通讯作者:

    丁梓航 dingzihang0831@163.com

    谢军伟 xjw_xjw_123@163.com

  • 责任主编:朱圣棋 Corresponding Editor: ZHU Shengqi
  • 中图分类号: TN958

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

Funds: The National Natural Science Foundation of China (62001506)
More Information
  • 摘要: 频控阵-多输入多输出(FDA-MIMO)雷达通过波束形成技术实现抗干扰的研究已经十分丰富。然而,在实际工作中,受元器件老化和存储设备容量等硬件因素的影响,计算得到的信号协方差矩阵可能会出现数据缺失的情况。为了克服协方差矩阵数据缺失对波束形成算法性能的影响,该文提出了一种基于深度学习的FDA-MIMO雷达协方差矩阵数据恢复方法,并建立了协方差矩阵恢复-自适应波束形成的两阶段处理框架;提出了一种双通道生成对抗网络(GAN)来解决矩阵数据恢复问题,该网络主要由鉴别器(D)和生成器(G)两部分组成:生成器主要功能是输出完整的矩阵数据,鉴别器则是判别数据为真实数据还是填补数据。整个网络通过鉴别器和生成器之间相互对抗使生成器生成样本接近于真实数据的分布,从而实现对协方差矩阵缺失数据的恢复。此外,考虑到协方差矩阵数据为复数,分别构造两个独立的GAN网络以满足矩阵数据实部和虚部的训练。最后,数值实验结果表明,协方差矩阵真实数据与恢复后的数据平均均方根误差仅为0.01量级,验证了所提方法能够有效恢复协方差矩阵的缺失数据。

     

  • 图  1  双通道GAN网络的框架

    Figure  1.  The framework of dual channel GAN network

    图  2  鉴别器和生成器网络结构

    Figure  2.  The structure of D and G network

    图  3  协方差矩阵实部灰度图(单干扰源)

    Figure  3.  The grayscale image of the real part of covariance matrix (single interference)

    图  4  协方差矩阵虚部灰度图(单干扰源)

    Figure  4.  The grayscale image of the imaginary part of covariance matrix (single interference)

    图  5  矩阵恢复数据的RMSE在训练过程中的变化情况(不同损失率$\varepsilon $)

    Figure  5.  RMSE performance versus training process (different $ \varepsilon $)

    图  6  矩阵恢复数据的RMSE在训练过程中的变化情况(不同网络层数k)

    Figure  6.  RMSE performance versus training process (different k)

    图  7  基于不同协方差矩阵的FDA-MIMO雷达波束方向图(多干扰源)

    Figure  7.  FDA-MIMO radar beampattern based on different covariance matrices (single interference)

    图  8  协方差矩阵实部灰度图(多干扰源)

    Figure  8.  The grayscale image of the real part of covariance matrix (multiple interferences)

    图  9  协方差矩阵虚部灰度图(多干扰源)

    Figure  9.  The grayscale image of the imaginary part of covariance matrix (multiple interferences)

    图  10  基于不同协方差矩阵的FDA-MIMO雷达波束方向图(多干扰源)

    Figure  10.  FDA-MIMO radar beampattern based on different covariance matrices (multiple interferences)

    算法1 双通道GAN伪代码
    Alg. 1 Pseudocode of dual channels GAN network
     while 训练损失值未达到收敛条件 or 未达到预设的迭代次数 do
      1 鉴别器训练(${ {\rm{D} }_1}$和${ {\rm{D} }_2}$分别为实部和虚部网络的鉴别器)
      从训练数据集取出$ {J_{\text{D}}} $个样本作为一批量的数据$\left\{ {\left( { {\text{Re} }\left( {\tilde {\boldsymbol{x}}\left( j \right)} \right),{\boldsymbol{m} }\left( j \right)} \right)} \right\}_{j = 1}^{ {J_{\text{D} } } }$,$\left\{ {\left( { {\text{Im} }\left( {\tilde {\boldsymbol{x}}\left( j \right)} \right),{\boldsymbol{m} }\left( j \right)} \right)} \right\}_{j = 1}^{ {J_{\text{D} } } }$,并分别归一化处理。
      随机采样$ {J_{\text{D}}} $个样本$\left\{ {{\boldsymbol{z}}\left( j \right)} \right\}_{j = 1}^{ {J_{\text{D} } } }$, $\left\{ {{\boldsymbol{b}}\left( j \right)} \right\}_{j = 1}^{ {J_{\text{D} } } }$,并分别归一化处理。
      for $j = 1,2,\cdots,{J_{\text{D} } }$ do
       ${ {\rm{Re} } } \left( {\bar {\boldsymbol{x}}\left( j \right)} \right) \leftarrow {\text{G} }\left( { { {\rm{Re} } } \left( {\tilde {\boldsymbol{x}}\left( j \right)} \right),{\boldsymbol{m} }\left( j \right),{\boldsymbol{z} }\left( j \right)} \right)$, ${ {\rm{Im} } } \left( {\bar {\boldsymbol{x}}\left( j \right)} \right) \leftarrow {\text{G} }\left( { { {\rm{Im} } } \left( {\tilde {\boldsymbol{x}}\left( j \right)} \right),{\boldsymbol{m} }\left( j \right),{\boldsymbol{z} }\left( j \right)} \right)$
       ${ {\rm{Re} } } \left( {\hat {\boldsymbol{x}}\left( j \right)} \right) \leftarrow {\boldsymbol{m} }\left( j \right) \odot { {\rm{Re} } } \left( {\tilde {\boldsymbol{x} } \left( j \right)} \right) + \left( {1 - {\boldsymbol{m} }\left( j \right)} \right) \odot { {\rm{Re} } } \left( {\bar {\boldsymbol{x}}\left( j \right)} \right)$, ${ {\rm{Im} } } \left( {\hat {\boldsymbol{x}}\left( j \right)} \right) \leftarrow {\boldsymbol{m} }\left( j \right) \odot { {\rm{Im} } } \left( {\tilde {\boldsymbol{x} }\left( j \right)} \right) + \left( {1 - {\boldsymbol{m} }\left( j \right)} \right) \odot { {\rm{Im} } } \left( {\bar {\boldsymbol{x}}\left( j \right)} \right)$
       ${\boldsymbol{h} }\left( j \right) = {\boldsymbol{b} }\left( j \right) \odot {\boldsymbol{m} }\left( j \right) + 0.5\left( {1 - {\boldsymbol{b}}\left( j \right)} \right)$
      end for
      使用随机梯度下降(Stochastic Gradient Descent, SGD)算法, 分别更新$ {{\text{D}}_1} $和$ {{\text{D}}_2} $网络参数(固定$ {{\text{G}}_1} $和$ {{\text{G}}_2} $网络的参数)
       ${{\text{∇}} _{ { {\text{D} }_1} } } - \displaystyle\sum\limits_{j = 1}^{ {J_{\text{D} } } } { {\mathcal{L}_{\text{D} } }\left( { {\boldsymbol{m} }\left( j \right),{ {\text{D} }_1}\left( { {\text{Re} }\left( {\hat {\boldsymbol{x} }\left( j \right)} \right),{\boldsymbol{h} }\left( j \right)} \right),{\boldsymbol{b} }\left( j \right)} \right)}$
       ${{\text{∇}} _{ { {\text{D} }_2} } } - \displaystyle\sum\limits_{j = 1}^{ {J_{\text{D} } } } { {\mathcal{L}_{\text{D} } }\left( { {\boldsymbol{m} }\left( j \right),{ {\text{D} }_2}\left( { {\text{Im} }\left( {\hat {\boldsymbol{x} }\left( j \right)} \right),{\boldsymbol{h} }\left( j \right)} \right),{\boldsymbol{b} }\left( j \right)} \right)}$
       2 生成器训练(${ {\rm{G} }_1}$和${ {\rm{G} }_2}$分别为实部和虚部网络的生成器)
       从训练数据集取出$ {J_{\text{G}}} $个样本作为一批量的数据$\left\{ {\left( { {\text{Re} }\left( {\tilde {\boldsymbol{x}}\left( j \right)} \right),{\boldsymbol{m}}\left( j \right)} \right)} \right\}_{j = 1}^{ {J_{\text{G} } } }$,$\left\{ {\left( { {\text{Im} }\left( {\tilde {\boldsymbol{x}}\left( j \right)} \right),{\boldsymbol{m} }\left( j \right)} \right)} \right\}_{j = 1}^{ {J_{\text{G} } } }$
       随机采样$ {J_{\text{G}}} $个样本$\left\{ {{\boldsymbol{z}}\left( j \right)} \right\}_{j = 1}^{ {J_{\text{G} } } }$, $\left\{ {{\boldsymbol{b}}\left( j \right)} \right\}_{j = 1}^{ {J_{\text{G} } } }$
       for $j = 1,2,\cdots,{J_{\rm{D}}}$ do
       ${\boldsymbol{h} }\left( j \right) = {\boldsymbol{b} }\left( j \right) \odot {\boldsymbol{m} }\left( j \right) + 0.5\left( {1 - {\boldsymbol{b}}\left( j \right)} \right)$
      end for
      使用SGD算法更新$ {{\text{G}}_1} $和$ {{\text{G}}_2} $网络(固定$ {{\text{D}}_1} $和$ {{\text{D}}_2} $网络参数)
      ${{\text{∇}} _{ { {\text{G} }_1} } } - \displaystyle\sum\limits_{j = 1}^{ {J_{\text{G} } } } { {\mathcal{L}_{\text{G} } }\left( { {\boldsymbol{m} }\left( j \right),\hat {\boldsymbol{m} }\left( j \right),{\boldsymbol{b} }\left( j \right)} \right)} + \beta {\mathcal{L}_{\text{M} } }\left( { {\text{Re} }\left( {\hat {\boldsymbol{x} }\left( j \right)} \right),{\text{Re} }\left( {\tilde {\boldsymbol{x} }\left( j \right)} \right)} \right)$
      ${{\text{∇}} _{ { {\text{G} }_2} } } - \displaystyle\sum\limits_{j = 1}^{ {J_{\text{G} } } } { {\mathcal{L}_{\text{G} } }\left( { {\boldsymbol{m} }\left( j \right),\hat {\boldsymbol{m} }\left( j \right),{\boldsymbol{b} }\left( j \right)} \right)} + \beta {\mathcal{L}_{\text{M} } }\left( { {\text{Im} }\left( {\hat {\boldsymbol{x} }\left( j \right)} \right),{\text{Im} }\left( {\tilde {\boldsymbol{x} }\left( j \right)} \right)} \right)$
     end while
    下载: 导出CSV

    表  1  测试集矩阵恢复数据的平均RMSE(不同损失率${\boldsymbol{\varepsilon}} $)

    Table  1.   Average RMSE of the missing data recovery (different $ {\boldsymbol{\varepsilon}} $)

    损失率平均RMSE损失率平均RMSE
    $ \varepsilon = 0.2 $1.43E–02$ \varepsilon = 0.4 $2.20E–02
    $ \varepsilon = 0.3 $1.59E–02$ \varepsilon = 0.5 $2.33E–02
    下载: 导出CSV

    表  2  测试集矩阵恢复数据的平均RMSE(不同网络层数k)

    Table  2.   Average RMSE of the missing data recovery (different k)

    网络层数平均RMSE
    31.92E–02
    61.59E–02
    91.63E–02
    下载: 导出CSV

    表  3  测试集矩阵恢复数据的平均RMSE(不同方法)

    Table  3.   Average RMSE of the missing data recovery (different methods)

    矩阵缺失数据恢复方法平均RMSE
    EM3.66E–02
    随机森林2.87E–02
    降噪自编码器3.08E–02
    本文所提算法1.59E–02
    下载: 导出CSV
  • [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
  • 加载中
图(10) / 表(4)
计量
  • 文章访问数:  751
  • HTML全文浏览量:  433
  • PDF下载量:  208
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-01-04
  • 修回日期:  2023-03-17
  • 网络出版日期:  2023-04-04
  • 刊出日期:  2023-10-28

目录

    /

    返回文章
    返回