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适用于二维阵列的无格稀疏波达方向估计算法

王剑书 樊养余 杜瑞 吕国云

引用本文: 王剑书, 樊养余, 杜瑞, 吕国云. 适用于二维阵列的无格稀疏波达方向估计算法[J]. 电子与信息学报, 2019, 41(2): 447-454. doi: 10.11999/JEIT180340 shu
Citation:  Jianshu WANG, Yangyu FAN, Rui DU, Guoyun LÜ. Gridless Sparse Method for Direction of Arrival Estimation for Two-dimensional Array[J]. Journal of Electronics and Information Technology, 2019, 41(2): 447-454. doi: 10.11999/JEIT180340 shu

适用于二维阵列的无格稀疏波达方向估计算法

    作者简介: 王剑书: 男,1989年生,博士生,研究方向为阵列信号处理、DOA估计和波束形成等;
    樊养余: 男,1960年生,教授,主要研究方向为数字图像处理、数字信号处理理论与应用、无线光通信技术和虚拟现实技术等;
    杜瑞: 男,1988年生,博士生,研究方向为雷达信号处理和模式识别等;
    吕国云: 男,1975年生,副教授,主要研究方向为信号与信息处理、语音和图像处理、虚拟现实和嵌入式系统和高速信号处理等
    通讯作者: 王剑书,wangjs123@mail.nwpu.edu.cn
  • 基金项目: 水声对抗重点实验室基金(kmb5494)

摘要: 针对现有的适用于2维阵列的无格稀疏波达方向(DOA)估计方法性能不足的问题,该文提出一种新的方法。对2维阵列,从原子L0范数出发,证明其值等于一个以矩阵秩为目标函数的半定规划(SDP)问题的最优解。对该矩阵使用第1类有限阶贝塞尔函数近似表达,构造新的秩优化SDP问题。根据低秩矩阵恢复理论,对该SDP问题的目标函数使用log-det函数方法平滑替代,然后使用优化最小(MM)算法求解,最后通过(半)正定Toeplitz矩阵的范德蒙分解方法实现无格DOA估计。在MM算法求解模型时,使用样本协方差矩阵构造初始优化问题,减少算法迭代。仿真实验结果表明,相较于基于网格的MUSIC和其他无格DOA估计方法,该文方法具有更好的均方根误差(RMSE)性能与对相邻源的分辨能力;在快拍数充足且信噪比(SNR)较高时,适当的第1类贝塞尔函数阶数选择可以实现与较大阶数接近的RMSE性能,同时能减少运行时间。

English

    1. [1]

      QIN Si, ZHANG Yimin D, and AMIN M G. DOA estimation of mixed coherent and uncorrelated targets exploiting coprime MIMO radar[J]. Digital Signal Processing, 2017, 61: 26–34. doi: 10.1016/j.dsp.2016.06.006

    2. [2]

      SAUCAN A A, CHONAVEL T, SINTES C, et al. CPHD-DOA tracking of multiple extended sonar targets in impulsive environments[J]. IEEE Transactions on Signal Processing, 2016, 64(5): 1147–1160. doi: 10.1109/TSP.2015.2504349

    3. [3]

      HE Saijuan and CHEN Huawei. Closed-form DOA estimation using first-order differential microphone arrays via joint temporal-spectral-spatial processing[J]. IEEE Sensors Journal, 2017, 17(4): 1046–1060. doi: 10.1109/JSEN.2016.2641449

    4. [4]

      WAN Liangtian, HAN Guangjie, JIANG Jinfang, et al. A DOA estimation approach for transmission performance guarantee in D2D communication[J]. Mobile Networks and Applications, 2017, 22(6): 998–1009. doi: 10.1007/s11036-017-0820-2

    5. [5]

      CAPON J. High-resolution frequency-wavenumber spectrum analysis[J]. Proceedings of the IEEE, 1969, 57(8): 1408–1418. doi: 10.1109/PROC.1969.7278

    6. [6]

      SCHMIDT R. Multiple emitter location and signal parameter estimation[J]. IEEE Transactions on Antennas and Propagation, 1986, 34(3): 276–280. doi: 10.1109/TAP.1986.1143830

    7. [7]

      ROY R and KAILATH T. ESPRIT—Estimation of signal parameters via rotational invariance techniques[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1989, 37(7): 984–995. doi: 10.1109/29.32276

    8. [8]

      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

    9. [9]

      WIPF D P and RAO B D. An empirical Bayesian strategy for solving the simultaneous sparse approximation problem[J]. IEEE Transactions on Signal Processing, 2007, 55(7): 3704–3716. doi: 10.1109/TSP.2007.894265

    10. [10]

      LIU Zhangmeng, HUANG Zhitao, and ZHOU Yiyu. An efficient maximum likelihood method for direction-of-arrival estimation via sparse Bayesian learning[J]. IEEE Transactions on Wireless Communications, 2012, 11(10): 1–11. doi: 10.1109/TWC.2012.090312.111912

    11. [11]

      BHASKAR B N, TANG Gongguo, and RECHT B. Atomic norm denoising with applications to line spectral estimation[J]. IEEE Transactions on Signal Processing, 2013, 61(23): 5987–5999. doi: 10.1109/TSP.2013.2273443

    12. [12]

      QIAN Tong, TIAN Jing, ZHANG Xu, et al. Atomic norm method for DOA estimation in random sampling condition[C]. 2016 CIE International Conference on Radar (RADAR), Guangzhou, China, 2016: 1–4.

    13. [13]

      ZHANG Yu, ZHANG Gong, and WANG Xinhai. Array covariance matrix-based atomic norm minimization for off-grid coherent direction-of-arrival estimation[C]. 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, USA, 2017: 3196–3200. doi: 10.1109/ICASSP.2017.7952746.

    14. [14]

      CHEN Yuxin and CHI Yuejie. Robust spectral compressed sensing via structured matrix completion[J]. IEEE Transactions on Information Theory, 2014, 60(10): 6576–6601. doi: 10.1109/TIT.2014.2343623

    15. [15]

      YANG Zai, LI Jian, STOICA P, et al. Sparse methods for direction-of-arrival estimation[OL]. http://cn.arxiv.org/pdf/1609.09596v2, 2017.3.

    16. [16]

      YANG Zai, XIE Lihua, and ZHANG Cishen. A discretization-free sparse and parametric approach for linear array signal processing[J]. IEEE Transactions on Signal Processing, 2014, 62(19): 4959–4973. doi: 10.1109/TSP.2014.2339792

    17. [17]

      YANG Zai and XIE Lihua. On gridless sparse methods for multi-snapshot direction of arrival estimation[J]. Circuits, Systems, and Signal Processing, 2017, 36(8): 3370–3384. doi: 10.1007/s00034-016-0462-9

    18. [18]

      ZHANG Youwen, HONG Xiaoping, WANG Yonggang, et al. Gridless SPICE applied to parameter estimation of underwater acoustic frequency hopping signals[C]. 2016 IEEE/OES Chian Ocean Acoustics (COA), Harbin, China, 2016: 1–6.

    19. [19]

      MAHATA K and HYDER M M. Grid-less TV minimization for DOA estimation[J]. Signal Processing, 2017, 132: 155–164. doi: 10.1016/j.sigpro.2016.09.018

    20. [20]

      RAO B D and HARI K V S. Performance analysis of root-MUSIC[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1989, 37(12): 1939–1949. doi: 10.1109/29.45540

    21. [21]

      TANG Gongguo, BHASKAR B N, SHAH P, et al. Compressed sensing off the grid[J]. IEEE Transactions on Information Theory, 2013, 59(11): 7465–7490. doi: 10.1109/TIT.2013.2277451

    22. [22]

      MOHAN K and FAZEL M. Iterative reweighted algorithms for matrix rank minimization[J]. Journal of Machine Learning Research, 2012, 13(11): 3441–3473.

    23. [23]

      SUNDIN M, ROJAS C R, JANSSON M, et al. Relevance singular vector machine for low-rank matrix reconstruction[J]. IEEE Transactions on Signal Processing, 2016, 64(20): 5327–5339. doi: 10.1109/TSP.2016.2597121

    24. [24]

      SUN Ying, BABU P, and PALOMAR D P. Majorization-minimization algorithms in signal processing, communications, and machine learning[J]. IEEE Transactions on Signal Processing, 2017, 65(3): 794–816. doi: 10.1109/TSP.2016.2601299

    25. [25]

      HORN R A and JOHNSON C R. Matrix Analysis[M]. Cambridge: Cambridge University Press, 2013: 495–497.

    26. [26]

      LANDAU H J. The classical moment problem: Hilbertian proofs[J]. Journal of Functional Analysis, 1980, 38(2): 255–272. doi: 10.1016/0022-1236(80)90065-8

    27. [27]

      STOICA P and MOSES R L. Spectral Analysis of Signals[M]. Upper Saddle River, NJ: Pearson Prentice Hall, 2005: 172–177.

    28. [28]

      YANG Zai and XIE Lihua. Enhancing sparsity and resolution via reweighted atomic norm minimization[J]. IEEE Transactions on Signal Processing, 2016, 64(4): 995–1006. doi: 10.1109/TSP.2015.2493987

    29. [29]

      FERNANDEZGRANDA C. Super-resolution of point sources via convex programming[C]. IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Cancun, Mexico, 2015: 41–44.

    30. [30]

      CANDES E J and FERNANDEZ-GRANDA C. Towards a mathematical theory of super-resolution[J]. Communications on Pure and Applied Mathematics, 2014, 67(6): 906–956. doi: 10.1002/cpa.v67.6

    31. [31]

      STURM J F. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones[J]. Optimization Methods and Software, 1999, 11(1/4): 625–653. doi: 10.1080/10556789908805766

    32. [32]

      TOH K C, TODD M J, and TUTUNCU R H. SDPT3—A Matlab software package for semidefinite programming, Version 1.3[J]. Optimization Methods and Software, 1999, 11(1/4): 545–581. doi: 10.1080/10556789908805762

    33. [33]

      STURM J F. Implementation of interior point methods for mixed semidefinite and second order cone optimization problems[J]. Optimization Methods and Software, 2002, 17(6): 1105–1154. doi: 10.1080/1055678021000045123

    34. [34]

      STOICA P and NEHORAI A. Performance study of conditional and unconditional direction-of-arrival estimation[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1990, 38(10): 1783–1795. doi: 10.1109/29.60109

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  • 图 1  RMSE仿真实验结果

    图 2  相邻源RMSE仿真实验结果

    图 3  不同贝塞尔函数阶数的本文方法仿真实验结果

    表 1  不同贝塞尔函数阶数的本文方法平均运行时间(s)

    N20406080
    运行时间0.74531.75364.03658.0497
    下载: 导出CSV
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文章相关
  • 通讯作者:  王剑书, wangjs123@mail.nwpu.edu.cn
  • 收稿日期:  2018-04-12
  • 录用日期:  2018-09-04
  • 网络出版日期:  2018-09-12
  • 刊出日期:  2019-02-01
通讯作者: 陈斌, bchen63@163.com
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