基于虚拟阵列技术的DOA估计研究
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摘要
科学技术的发展日新月异,以信息技术为代表的前沿科学领域已经逐渐融入人们生活。阵列信号处理不管是在军事领域还是民用领域都有着非常重要的应用。非平稳类的宽带相干LFM信号波达方向(Direction of Arrival, DOA)估计是阵列信号处理重要的研究方向之一。同时,为了适用工程应用中在不降低系统性能的同时,提高资源利用率、降低造价成本的要求,虚拟阵列技术应运而生,并得到了快速发展。将虚拟阵列技术应用到DOA估计中,成为当前该方向研究的热点。
本文重点研究了虚拟阵列技术及其在DOA估计中的应用,同时对分数阶Fourier变换(Fractional Fourier Transform, FRFT)域的宽带相干LFM信号角度估计问题也作了研究。主要工作如下：
1.本文首先介绍了信号的基本模型,对宽带信号和窄带信号的定义做了简单的介绍,同时给出了典型的LFM信号表达式,并分析了其时域和频域的特性。接着对FRFT做了简要的介绍,然后通过仿真实验,对比了LFM信号FRFT和Wigner-Ville分布(WVD)的时频特征。
2.研究了窄带信号模型下的MUSIC算法和相干信号估计算法—FBSS算法。然后又给出了FRF域的FBSS算法,该方法可以用来估计宽带相干LFM信号,因为算法本身固有的特点,估计精度不高。针对该问题,采用矩阵数据重构的思想,通过在FRF域分别构造数据协方差矩阵行和列的Toeplitz矩阵,然后将它们求和平均,仿真结果表明,改进的方法估计精度较高,且对于多个小角度差的入射信号具有很好的分辨力。
3.针对上述方法损失阵列孔径的问题,引入了虚拟阵列技术(Virtual Array Technology, VAT),并对其中几种常见的方法分别作了阐述和研究。重点研究了虚拟阵列平移方法,该方法不损失阵列孔径,但是在低信噪比、小角度差的情况下,效果不理想。针对该问题,给出了一种前后向虚拟阵列平移方法,仿真实验表明,改进后的方法具有良好的估计效果。最后,文章将改进后的方法推广到FRF域的宽带相干LFM信号DOA估计中,从而丰富了虚拟阵列技术的应用范围。
With the rapid development of science and technology, frontier science led by information technology has been introduced into human life. Array signal processing applied very well not only in the field of military, but also in the civil side. The non-stationary class of coherent wideband signal direction of arrival (DOA) estimation is one of the major research subjects in array signal processing. At the same time, virtual array technology emerges and develops rapidly to meet the need of improving the utilization rate of resources and reducing the manufacturing cost engineering technology. Applying array technology method to DOA estimation has become a hot research field.
This paper focuses on virtual array technology as well as its application in DOA estimation, and the coherent wideband LFM angle direction finding problem in FRF domain. The main work includes the following aspects:
1. This paper first introduces the basic model of signal, involving the wideband signal and narrow-band signal. In the meantime, it explains a typical LFM signaling expression and analyzes its time domain and frequency domain properties. Then the paper briefly discusses FRFT and compares the time-frequency characteristic of FRFT and WVD in regard to LFM signals by simulation experiments.
2. Then the paper studies MUSIC algorithm and coherent signal estimation algorithm, FBSS algorithm under the narrow-band signal model. It gives the FBSS algorithm in FRF domain. This method can be used to estimate wideband coherent LFM signal, but the accuracy is not sufficient due to the inherent characteristic of this estimation method. In regard to this problem, restructuring matrix data method was introduced, this paper illustrates summation and average of covariance matrix of rows and columns of the Toeplitz matrix by constructing data in FRF domain. Simulation results show that the improved method presents a high estimation precision, and provides better resolution to incident signals for a number of small angle differences.
3. In regard to the problem of reducing the aperture of array, the paper introduces virtual array technology, and elaborates several typical methods respectively. This chapter focuses on the virtual array transformation method, also this method without reducing the aperture of array, but under low SNR and small angle difference condition, the effect is not satisfying. Corresponding to this problem, an improved forward/backward virtual array transformation method was derived, simulation results show that the improved method has good estimated performance. At last, the improved method was introduced to the wideband coherent LFM signal DOA estimation in FRF domain, so as to enrich the application fields of virtual array technology.
本文重点研究了虚拟阵列技术及其在DOA估计中的应用,同时对分数阶Fourier变换(Fractional Fourier Transform, FRFT)域的宽带相干LFM信号角度估计问题也作了研究。主要工作如下：
1.本文首先介绍了信号的基本模型,对宽带信号和窄带信号的定义做了简单的介绍,同时给出了典型的LFM信号表达式,并分析了其时域和频域的特性。接着对FRFT做了简要的介绍,然后通过仿真实验,对比了LFM信号FRFT和Wigner-Ville分布(WVD)的时频特征。
2.研究了窄带信号模型下的MUSIC算法和相干信号估计算法—FBSS算法。然后又给出了FRF域的FBSS算法,该方法可以用来估计宽带相干LFM信号,因为算法本身固有的特点,估计精度不高。针对该问题,采用矩阵数据重构的思想,通过在FRF域分别构造数据协方差矩阵行和列的Toeplitz矩阵,然后将它们求和平均,仿真结果表明,改进的方法估计精度较高,且对于多个小角度差的入射信号具有很好的分辨力。
3.针对上述方法损失阵列孔径的问题,引入了虚拟阵列技术(Virtual Array Technology, VAT),并对其中几种常见的方法分别作了阐述和研究。重点研究了虚拟阵列平移方法,该方法不损失阵列孔径,但是在低信噪比、小角度差的情况下,效果不理想。针对该问题,给出了一种前后向虚拟阵列平移方法,仿真实验表明,改进后的方法具有良好的估计效果。最后,文章将改进后的方法推广到FRF域的宽带相干LFM信号DOA估计中,从而丰富了虚拟阵列技术的应用范围。
With the rapid development of science and technology, frontier science led by information technology has been introduced into human life. Array signal processing applied very well not only in the field of military, but also in the civil side. The non-stationary class of coherent wideband signal direction of arrival (DOA) estimation is one of the major research subjects in array signal processing. At the same time, virtual array technology emerges and develops rapidly to meet the need of improving the utilization rate of resources and reducing the manufacturing cost engineering technology. Applying array technology method to DOA estimation has become a hot research field.
This paper focuses on virtual array technology as well as its application in DOA estimation, and the coherent wideband LFM angle direction finding problem in FRF domain. The main work includes the following aspects:
1. This paper first introduces the basic model of signal, involving the wideband signal and narrow-band signal. In the meantime, it explains a typical LFM signaling expression and analyzes its time domain and frequency domain properties. Then the paper briefly discusses FRFT and compares the time-frequency characteristic of FRFT and WVD in regard to LFM signals by simulation experiments.
2. Then the paper studies MUSIC algorithm and coherent signal estimation algorithm, FBSS algorithm under the narrow-band signal model. It gives the FBSS algorithm in FRF domain. This method can be used to estimate wideband coherent LFM signal, but the accuracy is not sufficient due to the inherent characteristic of this estimation method. In regard to this problem, restructuring matrix data method was introduced, this paper illustrates summation and average of covariance matrix of rows and columns of the Toeplitz matrix by constructing data in FRF domain. Simulation results show that the improved method presents a high estimation precision, and provides better resolution to incident signals for a number of small angle differences.
3. In regard to the problem of reducing the aperture of array, the paper introduces virtual array technology, and elaborates several typical methods respectively. This chapter focuses on the virtual array transformation method, also this method without reducing the aperture of array, but under low SNR and small angle difference condition, the effect is not satisfying. Corresponding to this problem, an improved forward/backward virtual array transformation method was derived, simulation results show that the improved method has good estimated performance. At last, the improved method was introduced to the wideband coherent LFM signal DOA estimation in FRF domain, so as to enrich the application fields of virtual array technology.
引文
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[2]R. O. Schmidt. Multiple emitter location and signal parameter estimation. IEEE Transaction on Antennas and Propagation,1986,34(3):276-280.
[3]Richard Roy, Thomas Kailath. ESPRIT-estimation of signal parameters via rotational invariance techniques[J]. IEEE Transaction on Acoustic Speech and Signal Processing,1989,37(7):984-995
[4]J.Ville. Theorie et applications de la notion de signal analytique[M]. Cableset Transmission,1948,2A:61-74
[5]Namias V. The fractional Fourier transform and its application in quantum mechanics, J Inst April Math,1980,25:241-265
[6]S. Barbarossa, A. Scaglione, G. B. Giannakis. Product high-order ambiguity function for multicomponent polynomial-phase signal modeling[J]. IEEE Transaction on Signal Processing,1998,46(3):691-708
[7]Hing Cheung So, Hongqing Liu. Subspace-Based Algorithm for Parameter Estimation of Polynomial Phase Signals[J], IEEE Transaction on Signal Processing,2008,56(10):4977-4983
[8]H. M. Elkamchouchi. Estimating the parameters of signals modeled by the sum of three-dimensional complex exponential using matrix pencil method[J]. National Radio Science Conference,2008:1-9
[9]陈客松,何子述,韩春林.非均匀线天线阵优化布阵研究.电子学报,2006,34(12)：2263-2266
[10]刘洪盛.高分辨测向阵列几何结构研究.电子科技大学博士学位论文,2009
[11]P. Pal, P. P. Vaidyanathan. Multiple level nested array:an Effective geometry for 2qth order cumulant based array processing[J]. IEEE Transactions on Signal Processing, 2012,60(3):1253-1269.
[12]J. E. Evans, J. R. Johnson, D. F. Sun, High resolution angular spectrum estimation techniques for terrain scattering analysis and angle of arrival estimation[C]. Processing 1st ASSP Workshop Spectral Estimation, Hamilton. Ontario. Canada,1981:134-139
[13]T. J. Shan, M. Wax, T. Kailath. On spatial Smoothing for Direction-of-Arrival Estimation of Coherent Signals[J]. IEEE Transactions on Acoustic Speech and Signal Processing,1985,33(4):806-811
[14]S. U. Pillai, B. H. Kwon. Forward/Backward Spatial Smoothing Techniques for Coherent Signal Identification[J]. IEEE Transactions on Acoustic Speech and Signal Processing,1989,37(1):8-15
[15]Fang-Ming Han, Xian-Da Zhang. An ESPRIT-like algorithm for coherent DOA estimation[J]. IEEE Transactions on Antennas and wireless propagation letters,2005,4 (1):443-446
[16]Fang-Jiong Chen, Sam Kwong, Chi-Wah Kok. ESPRIT-like two-dimensional DOA estimation for coherent signals[J]. IEEE Transactions on Aerospace and Electronic Systems,2010,46(3):1477-1484
[17]Yang-ho Choi. Improved adaptive ing of Coherent Interference Without Spatial Smoothing[J]. IEEE Transactions on SP,2004,52(12):3464-3469
[18]S. S. Abeysekera, S. M. Raihan. Efficient Wideband Parameter Estimation Using Arbitrary Enveloped LFM Signals via Hermite Decompositions[J]. IEEE Journal of Oceaniac Engineering,2009,34(1):63-74
[19]Ervin Sejdica, Igor Djurovicb, Jin Jiang. Time-frequency feature representation using energy concentration:An overview of recent advances. Digital Signal Processing,2009,19(1):153-183
[20]D Kundu. Modified MUSIC algorithm for estimation DOA of signals[J]. Signal Processing,1996,48(1):85-90
[21]Ye Z, Xiang L, Xu X. DOA estimation with circular array via spatial averaging algorithm[J]. IEEE Transactions on Antennas and Wireless Propagation Letters,2007,6:74-76
f22]韩冲,廉保旺,菜会甫.估计相干与非相干信源的ESPRIT方法研究[J].计算机工程与应用,2011,47(14)：112-114
[23]张贤达.矩阵分析与应用.清华大学出版社,2004
[24]Namias V. The fractional Fourier transform and its application in quantum mechanics. J Inst Appl Math,1980,25:241-265
[25]Ervin Sejdic, Igor Djurovic, LJubisa Stankovic. Fractional Fourier transform as a signal processing tool:An overview of recent developments[J]. Signal Processing,2011,91 (6):1351-1369
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