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非凸稀疏约束的多快拍压缩波束形成

丁飞龙 迟骋 李宇 黄海宁

丁飞龙, 迟骋, 李宇, 黄海宁. 非凸稀疏约束的多快拍压缩波束形成[J]. 电子与信息学报, 2022, 44(6): 2071-2079. doi: 10.11999/JEIT220017
引用本文: 丁飞龙, 迟骋, 李宇, 黄海宁. 非凸稀疏约束的多快拍压缩波束形成[J]. 电子与信息学报, 2022, 44(6): 2071-2079. doi: 10.11999/JEIT220017
DING Feilong, CHI Cheng, LI Yu, HUANG Haining. Multiple-snapshot Compressive Beamforming with Non-convex Sparse Constraints[J]. Journal of Electronics & Information Technology, 2022, 44(6): 2071-2079. doi: 10.11999/JEIT220017
Citation: DING Feilong, CHI Cheng, LI Yu, HUANG Haining. Multiple-snapshot Compressive Beamforming with Non-convex Sparse Constraints[J]. Journal of Electronics & Information Technology, 2022, 44(6): 2071-2079. doi: 10.11999/JEIT220017

非凸稀疏约束的多快拍压缩波束形成

doi: 10.11999/JEIT220017
基金项目: 国家自然科学基金(62001469)
详细信息
    作者简介:

    丁飞龙:男,1996年生,博士生,研究方向为阵列信号处理

    迟骋:男,1989年生,副研究员,研究方向为阵列信号处理

    李宇:男,1977年生,研究员,研究方向为阵列信号处理

    黄海宁:男,1969年生,研究员,研究方向为阵列信号处理

    通讯作者:

    李宇 ly@mail.ioa.ac.cn

  • 中图分类号: TN929.3; TB565

Multiple-snapshot Compressive Beamforming with Non-convex Sparse Constraints

Funds: The National Natural Science Foundation of China (62001469)
  • 摘要: 基于极小极大凹惩罚函数约束的压缩感知波束形成,相对于传统l1范数的压缩波束形成来说,可以增强信号的稀疏性,获得更精确的波达方向估计。然而,该算法在强噪声背景下,方位估计结果不稳定。针对这个问题,该文提出一种基于极小极大凹惩罚函数约束的多快拍压缩感知波束形成(MCP-MCSBF)算法。通过多个快拍的联合处理,提供更好的抗噪性能和更精准的波达方向估计结果。仿真结果表明与其他多快拍波达方向估计算法相比,该文算法提供了更优的精确性和更高的角度分辨率,湖试结果则进一步验证了所提算法的有效性。
  • 图  1  信噪比–10 dB下的DOA估计结果

    图  2  信噪比–10 dB下多快拍的DOA估计结果

    图  3  –10 dB下不同算法的DOA估计结果对比

    图  4  不同算法的性能比较

    图  5  成功分辨率随SNR和角度间隔的变化

    图  6  方位历程图

    表  1  基于MCP函数约束的压缩波束形成算法步骤

     输入:观测数据${\boldsymbol{y}}$,参数$ \varepsilon $,超参数$ \gamma $,最大迭代次数$ Q $,终止条
        件${\rm{tol}} = {10^{ - 3} }$。参数向量$ {t_0} = 1 $,${{\boldsymbol{u}}^0}$和${{\boldsymbol{s}}^0}$的初始值均设为
        ${ {\textit{0}}}$向量,且${{\boldsymbol{u}}^0} = {{\boldsymbol{u}}^1}$, ${{\boldsymbol{s}}^0} = {{\boldsymbol{s}}^1}$。
     (1) 当$ q \le Q $时:
     (2)   根据式(14)和式(13)更新$ w_u^q $,
     (3)   获得变量${\tilde {\boldsymbol{u}}^q}$,并按照式(9)更新变量为${{\boldsymbol{u}}^{q + 1} }$,
     (4)   根据式(14)和式(13)更新$ w_s^q $,
     (5)   同理获得变量${\tilde {\boldsymbol{s}}^q}$,并按照式(12)更新变量为${{\boldsymbol{s}}^{q + 1} }$。
     (6)   如果${{\boldsymbol{s}}^{q + 1} }$和${{\boldsymbol{s}}^q}$的变化$ \le {\rm{tol}} $:
     (7)    那么停止迭代,且最优估计${{\boldsymbol{s}}^ * } = {{\boldsymbol{s}}^{q + 1} }$,
     (8)    找到${{\boldsymbol{s}}^ * }$的峰值,并将其对应到DOA估计的角度${{\boldsymbol{\theta}} ^ * }$。
     (9)   结束
     (10) 结束
     输出:DOA估计的角度${{\boldsymbol{\theta}} ^ * }$。
    下载: 导出CSV

    表  2  MCP-MCSBF算法步骤

     输入:多快拍观测数据矩阵${\boldsymbol{Y}}$。
     (1) 根据式(16)和式(17)计算降噪后的观测矩阵${{\boldsymbol{Y}}_{\hat K} }$,
     (2) 构造加权向量$\hat {\boldsymbol{w}}$,满足$ {\hat w_1} + {\hat w_2} + \cdots + {\hat w_{\hat K}} = 1 $,
     (3) 根据式(25)计算${{\boldsymbol{y}}_{\hat K} }$,
     (4)  将${{\boldsymbol{y}}_{\hat K} }$代入式(26)中得到全新的目标函数,
     (5)  根据表1的算法得到DOA估计角度${{\boldsymbol{\theta}} ^ * }$。
     输出:DOA估计的角度${{\boldsymbol{\theta}} ^ * }$。
    下载: 导出CSV
  • [1] MALIOUTOV D, CETIN M, and WILLSKY A S. A sparse signal reconstruction perspective for source localization with sensor arrays[J]. IEEE Transactions on Signal Processing, 2005, 53(8): 3010–3022. doi: 10.1109/TSP.2005.850882
    [2] WANG Shuo, CHI Cheng, JIN Shenglong, et al. Fast compressive beamforming with a modified fast iterative shrinkage-thresholding algorithm[J]. The Journal of the Acoustical Society of America, 2021, 149(5): 3437–3448. doi: 10.1121/10.0004997
    [3] XENAKI A, GERSTOFT P, and MOSEGAARD K. Compressive beamforming[J]. The Journal of the Acoustical Society of America, 2014, 136(1): 260–271. doi: 10.1121/1.4883360
    [4] BARANIUK R G, CANDES E, ELAD M, et al. Applications of sparse representation and compressive sensing [scanning the issue][J]. Proceedings of the IEEE, 2010, 98(6): 906–909. doi: 10.1109/JPROC.2010.2047424
    [5] SELESNICK I W and BAYRAM İ. Sparse signal estimation by maximally sparse convex optimization[J]. IEEE Transactions on Signal Processing, 2014, 62(5): 1078–1092. doi: 10.1109/TSP.2014.2298839
    [6] QIAO Baijie, AO Chunyan, MAO Zhu, et al. Non-convex sparse regularization for impact force identification[J]. Journal of Sound and Vibration, 2020, 477: 115311. doi: 10.1016/j.jsv.2020.115311
    [7] LIU Lutao and RAO Zejing. An adaptive Lp norm minimization algorithm for direction of arrival estimation[J]. Remote Sensing, 2022, 14(3): 766. doi: 10.3390/rs14030766
    [8] TAUSIESAKUL B. Iteratively reweighted least squares minimization with nonzero index update[C]. 2021 Smart Technologies, Communication and Robotics (STCR), Sathyamangalam, India, 2021: 1–6.
    [9] SELESNICK I. Sparse regularization via convex analysis[J]. IEEE Transactions on Signal Processing, 2017, 65(17): 4481–4494. doi: 10.1109/TSP.2017.2711501
    [10] YANG Yixin, DU Zhaohui, WANG Yong, et al. Convex compressive beamforming with nonconvex sparse regularization[J]. The Journal of the Acoustical Society of America, 2021, 149(2): 1125–1137. doi: 10.1121/10.0003373
    [11] SHAW A, SMITH J, and HASSANIEN A. MVDR beamformer design by imposing unit circle roots constraints for uniform linear arrays[J]. IEEE Transactions on Signal Processing, 2021, 69: 6116–6130. doi: 10.1109/TSP.2021.3121630
    [12] DIAS U V. Extremely sparse co-prime acquisition: Low latency estimation using MUSIC algorithm[C]. 2021 Sixth International Conference on Wireless Communications, Signal Processing and Networking (WiSPNET), Chennai, India, 2021: 225–229.
    [13] GERSTOFT P, XENAKI A, and MECKLENBRÄUKER C F. Multiple and single snapshot compressive beamforming[J]. The Journal of the Acoustical Society of America, 2015, 138(4): 2003–2014. doi: 10.1121/1.4929941
    [14] BOYD S and VANDENBERGHE L. Convex Optimization[M]. Cambridge: Cambridge University Press, 2004: 23–25.
    [15] BECK A and TEBOULLE M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems[J]. SIAM Journal on Imaging Sciences, 2009, 2(1): 183–202. doi: 10.1137/080716542
    [16] GRANT M C and BOYD S P. Graph Implementations for Nonsmooth Convex Programs[M]. BLONDEL V D, BOYD S P, and KIMURA H. Recent Advances in Learning and Control. London: Springer, 2008: 95–110.
    [17] HUBER P J. Robust estimation of a location parameter[J]. The Annals of Mathematical Statistics, 1964, 35(1): 73–101. doi: 10.1214/aoms/1177703732
    [18] XU Yangyang and YIN Wotao. Block stochastic gradient iteration for convex and nonconvex optimization[J]. SIAM Journal on Optimization, 2015, 25(3): 1686–1716. doi: 10.1137/140983938
    [19] COMBETTES P L and PESQUET J C. Proximal Splitting Methods in Signal Processing[M]. BAUSCHKE H H, BURACHIK R S, COMBETTES P L, et al. Fixed-Point Algorithms for Inverse Problems in Science and Engineering. New York: Springer, 2011: 185–212.
    [20] TANG Wengen, JIANG Hong, and ZHANG Qi. One-bit gridless DOA estimation with multiple measurements exploiting accelerated proximal gradient algorithm[J]. Circuits, Systems, and Signal Processing, 2022, 41(2): 1100–1114. doi: 10.1007/s00034–021-01829-z
    [21] LI Ping, WANG Hua, LI Xuemei, et al. An image denoising algorithm based on adaptive clustering and singular value decomposition[J]. IET Image Processing, 2021, 15(3): 598–614. doi: 10.1049/ipr2.12017
    [22] BAUSCHKE H H and COMBETTES P L. Convex Analysis and Monotone Operator Theory in Hilbert Spaces[M]. Cham: Springer International Publishing, 2017: 413–447.
    [23] LU Hongtao, LONG Xianzhong, and LV Jingyuan. A fast algorithm for recovery of jointly sparse vectors based on the alternating direction methods[J]. Journal of Machine Learning Research, 2011, 15(6): 461–469.
    [24] POCK T and SABACH S. Inertial proximal alternating linearized minimization (iPALM) for nonconvex and nonsmooth problems[J]. SIAM Journal on Imaging Sciences, 2016, 9(4): 1756–1787. doi: 10.1137/16M1064064
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出版历程
  • 收稿日期:  2022-01-06
  • 修回日期:  2022-05-24
  • 网络出版日期:  2022-05-26
  • 刊出日期:  2022-06-21

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