基于分数阶Fourier变换的LFM信号的DOA估计分析
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摘要
波达方向(DOA)估计是阵列信号处理领域的一个重要研究方向,应用非常广泛,非平稳宽带线性调频(LFM)信号的DOA估计是波达方向(DOA)估计一个新的研究热点。作为一种新的时频分析工具,分数阶Fourier变换可以理解为一种线性的时频处理方法,用来处理LFM类信号时具有一些其他的分析工具所没有的优点。结合阵列信号处理技术,本文把FRFT应用到对LFM信号的DOA估计领域,并对其进行了相应地探讨。
1、论文首先对分数阶Fourier变换的定义进行了详细地介绍,分析了一些基本的性,并给出一种离散算法,在此基础上分析了高斯白噪声在分数阶Fourier变换域的性质。
2、分析了DOA估计技术的一些经典算法,在建立信号的接收模型,针对窄带不相干平稳信号源,对延迟-相加法和Capon最小方差法进行简单的描述,并做了简单的对比,Capon最小方差法的分辨能力要比对延迟-相加法有所改善;接着对多重信号分类算法(MUSIC)算法和信号子空间特征矢量生成广义特征值(GEESE)算法进行了详细地分析。针对对窄带不相干平稳正弦信号源,这两种方法可以有效的对信号进行DOA估计,与延迟-相加法和Capon最小方差法相比,这两种算法的估计性能要优越的多,并分析了阵元数目对估计分辨能力的影响。
3、从LFM信号的时频特性出发,对其在分数阶Fourier域的特性进行了分析。利用LFM信号在特定的FRFT域呈现能量聚集的特性,在相应的分数阶Fourier域,根据天线阵列各阵元接收信号之间的相位差关系,构造出信号在分数阶Fourier域的时不变方向向量。然后分别采用MUSIC算法和GEESE算法对宽带LFM信号进行DOA估计。从而实现LFM信号的DOA估计,从算法原理、实现过程等方面,分析了该算法,并进行了仿真分析。
Direction of Arrival (DOA) estimation has been a significant research area in array Signal processing. The DOA estimation of the non-stationary Linear Frequency Modulation (LFM) signal has been becoming a new hot topic and it has been received growing attention in recent years. With good cross-terms reduction and high time-frequency resolution, the Fractional Fourier Transform (FRFT) has been considered a linear and full time domain analysis tool for non-stationary signal processing. For a newly developed time-frequency analysis tool,it has been widely used in the multi-component LFM signal processing for its perfect property. Combining the FRFT with array Signal processing,the DOA estimation of LFM signal is discussed based on the FRFT in this thesis.
1、We presented the definition of FRFT and some basic characteristics, and analysis a discrete algorithm. Then the energy distribution of Gaussian white noise in the FRFT domain also is discussed.
2、Analyze some classic algorithm for the DOA estimation. We establish signal reception model firstly, then the Delayed-add and Minimum Variance Distorionless Response (MVDER) estimation algorithm have been discussed for the narrowband non-coherent stationary signal source, compare this two algorithm we can get that the resolving power of the MVDER algorithm’s is better than the Delayed-add algorithm. Further more, anther two methods for DOA estimation are discussed: Multiple Signal Classification (MUSIC) algorithm and Generalized Eigenvalues utilizing Signal subspace Eigenveetors (GEESE) algorithm. In the same condition, the resolving power of MUSIC and GEESE algorithms are better than Delayed-add and MVDER algorithm. But all these algorithms can not estimate the DOA when signal is non-stationary LFM signal. We also discussed the influence for MUSIC algorithm performance when the number of array is different. Simulation results proved that
3、According to the time-frequency properties of LFM signal, we have analyzed some properties of LFM signal in the FRFT domain, consider the LFM signal in certain fractional Fourier domain can take on energy concentration property, and the phase relationship between the received signal of received array element, the time-invariant direction matrix in that FRFT domain is derived,then the signal direction can be estimated by the MUSIC and GEESE algorithm, GEESE algorithm has a low complexity. The simulation results show that the algorithm can effectively estimate the signal direction even in a low Signal to Noise Ratio (SNR).
1、论文首先对分数阶Fourier变换的定义进行了详细地介绍,分析了一些基本的性,并给出一种离散算法,在此基础上分析了高斯白噪声在分数阶Fourier变换域的性质。
2、分析了DOA估计技术的一些经典算法,在建立信号的接收模型,针对窄带不相干平稳信号源,对延迟-相加法和Capon最小方差法进行简单的描述,并做了简单的对比,Capon最小方差法的分辨能力要比对延迟-相加法有所改善;接着对多重信号分类算法(MUSIC)算法和信号子空间特征矢量生成广义特征值(GEESE)算法进行了详细地分析。针对对窄带不相干平稳正弦信号源,这两种方法可以有效的对信号进行DOA估计,与延迟-相加法和Capon最小方差法相比,这两种算法的估计性能要优越的多,并分析了阵元数目对估计分辨能力的影响。
3、从LFM信号的时频特性出发,对其在分数阶Fourier域的特性进行了分析。利用LFM信号在特定的FRFT域呈现能量聚集的特性,在相应的分数阶Fourier域,根据天线阵列各阵元接收信号之间的相位差关系,构造出信号在分数阶Fourier域的时不变方向向量。然后分别采用MUSIC算法和GEESE算法对宽带LFM信号进行DOA估计。从而实现LFM信号的DOA估计,从算法原理、实现过程等方面,分析了该算法,并进行了仿真分析。
Direction of Arrival (DOA) estimation has been a significant research area in array Signal processing. The DOA estimation of the non-stationary Linear Frequency Modulation (LFM) signal has been becoming a new hot topic and it has been received growing attention in recent years. With good cross-terms reduction and high time-frequency resolution, the Fractional Fourier Transform (FRFT) has been considered a linear and full time domain analysis tool for non-stationary signal processing. For a newly developed time-frequency analysis tool,it has been widely used in the multi-component LFM signal processing for its perfect property. Combining the FRFT with array Signal processing,the DOA estimation of LFM signal is discussed based on the FRFT in this thesis.
1、We presented the definition of FRFT and some basic characteristics, and analysis a discrete algorithm. Then the energy distribution of Gaussian white noise in the FRFT domain also is discussed.
2、Analyze some classic algorithm for the DOA estimation. We establish signal reception model firstly, then the Delayed-add and Minimum Variance Distorionless Response (MVDER) estimation algorithm have been discussed for the narrowband non-coherent stationary signal source, compare this two algorithm we can get that the resolving power of the MVDER algorithm’s is better than the Delayed-add algorithm. Further more, anther two methods for DOA estimation are discussed: Multiple Signal Classification (MUSIC) algorithm and Generalized Eigenvalues utilizing Signal subspace Eigenveetors (GEESE) algorithm. In the same condition, the resolving power of MUSIC and GEESE algorithms are better than Delayed-add and MVDER algorithm. But all these algorithms can not estimate the DOA when signal is non-stationary LFM signal. We also discussed the influence for MUSIC algorithm performance when the number of array is different. Simulation results proved that
3、According to the time-frequency properties of LFM signal, we have analyzed some properties of LFM signal in the FRFT domain, consider the LFM signal in certain fractional Fourier domain can take on energy concentration property, and the phase relationship between the received signal of received array element, the time-invariant direction matrix in that FRFT domain is derived,then the signal direction can be estimated by the MUSIC and GEESE algorithm, GEESE algorithm has a low complexity. The simulation results show that the algorithm can effectively estimate the signal direction even in a low Signal to Noise Ratio (SNR).
引文
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[2] Capon J,High-resolution frequency-wave number spectrum analysis [J],Proc. of IEEE,1969,Vol.57(8):1408-1418
[3] Schmidt R O, Multiple emitter location and signal parameter estimation[J],IEEE Trans. April 1986,Vol.34(3):276-280
[4] R.Roy.A. Paulraj and T. Kailath, ESPRIT-a Subspace Rotation approach to Estimation of Parameters of Cissoids in Noise [A]. IEEE Trans on ASSP[C],October 1986,vol.34:1340-1342
[5] T.J.Shan,T.Kailath and M.Wax,Spatial Smoothing Approach for Location Estimate of Coherent Sources[A],IEEE.TraPs.ASSP,June 1985,vol.33(3):527-536
[6] Benjanmin Friedlander and Anthony J.Weiss, Direction finding using spatial Smoothing with interpolated arrays [J], IEEE Trans. On aerospace and electronic Systems,1992,vol.28:574-587
[7] Williams.T.R and Prasal.S, An Improved Spatial Smoothing Technique for Bearing Estimation in a Multi-path Environment[A],IEEE Trans.ASSP,1988,vol,36(4):425-431
[8] Pillai.U.S and Kwon.H.B, Forward/backward Spatial Smoothing Techniques For Coherent signal Identification[A],IEEE Trans. ASSP,1989,vol.37(1):8-15
[9] Delis.A, Enhanced Forward/backward Spatial filtering method for DOA Estimation of narrowband coherent sources[A],IEEE Proceeding:RSN,1996,vol.143(1):1350-2395
[10] Moghaddanjoo A and Chang T C, Analysis of the Spatial Filter Approach to the De-correlation of Coherent Sources[J].IEEE Trans. on SP,1992,vol.40 (3):692一694
[11] Moghaddanjoo.A. Application Spatial Filters to DOA Estimation of Coherent Sources[J].IEEE Trans. on SP,1991,vol.39(1):219一221
[12]刘德树,尹成友等,前/后向预测构造投影矩阵对相关源实现超分辨处理[J].电子工程学院学报,1994年第13卷第2期,页码:1-11
[13] H.Wang, Coherent Signal-Subspace Processing for the Detection and Estimation of Angles of Multiple Wide-Band Sources[J].IEEE Trans.ASSP,Ang,1985,vol.33(4):823-831
[14] A.Doron and J.Weiss. On Focusing Matrices for Wide-band Array Processing[J],IEEE Trans.on SP,Jun,1992,vol.42(6):1295-1302
[15] A.Hassanien, A.B.Gershman and M.G.Ainln, Time-frequency ESPRIT for direction-of-arrival estimation of chirp signals[J],Proc. Sensor Array and Multi-channel Signal Processing Workshop,2002,337-341
[16] Y.Zhang,W.Mu and M.Amin, Time-frequency maximum likelihood method for direction finding[J], Joumal of Franklin Institute,2000,vol.337(4):483-497
[17] L.Jin,Q.In and W.Wang, Time-frequency signal subspace fitting method for direction-of-arrival estimation [J], Proc. The 2000 IEEE International Symposium on Circuits and Systems,Geneva,2000, 375-378
[18] Yimin Zhang, Weifeng Mu and M.G.Amin. Subspace analysis of spatial Time-Frequency distributions matrices[J].IEEE Transaction on Signal Processing,2001,vol.49(4):747-758
[19]张艳红,齐林,穆晓敏.陶然.基于分数阶傅里叶变换的WLFM信号DOA估计[J].信号处理,2005,第21卷第4A期
[20]陶然,周云松.基于分数阶傅里叶变换的宽带LFM信号波达方向估计新算法[J],北京理工大学学报. 2005,25(10):895-899
[21]黄克骥,田达,陈天麟.基于时域汇聚和补偿估计WLFM信号的DOA的FRFT-MUSIC算法[J].信号处理,2003,Vol.19:No.1
[22] Xiaoxiang Luo,Haitao Qu, Junsheng Yu, Shaohua Liu. DOA Estimation of Multi-component LFM Signals Based on the FRFT[A].ICSP.08 proceedings[C]
[23]屈海涛,齐林,穆晓敏.基于FRFT的均匀圆阵DOA估计[J].计算机工程,2008,Vol.34:No12
[24] Wiener N, Hermitian polynomials and Fourier analysis [J]. Journal of Mathematics Physics MIT, 1929, 18: 70-73.
[25] E. U. Condon, Immersion of Fourier transform in a continuous group of functional transformations [J]. Proc. National Academy of Sciences, 1937, 23: 158-164.
[26] V. Bargmann. On a Hilbert space of analytic functions and an associated integral transform, Part 1 [J]. Communications on Pure and Applied Mathematics. 1961, 14: 187-214.
[27] V. Namias. The fractional order Fourier transform and its application to quantum mechanics [J]. Journal of the Institute of Mathematical Applications, 1980, 25: 241-265.
[28] McBride A. C, H. Kerr F. On Namias’s fractional Fourier transforms [J]. IMA Journal of Applied Mathematics, 1987, 39: 159-175.
[29] D. Mendlovic, H. M. Ozatkas, and A. W. Lohmann. Self Fourier functions and fractional Fourier transforms [J]. Optics Communications, 1994, 105: 36-38.
[30] I. S. Yetik, M. A. Kutay, H. M. Ozaktas. Continuous and discrete fractional Fourier domain decomposition [C]. ICASSP’00, Proceedings, IEEE, 2000: 93-96.
[31] Ozaktas H M, Arikan O, Kutay MA, et al. Digital computation of the fractional Fourier transform [J].IEEE Trans Signal Processing, 1996,44(9):2141-2150
[32]王永良,陈辉,彭应宁,万群,空间谱估计理论与算法[M],北京:清华大学出版社,2005
[33]张贤达,现代信号处理(第二版) [M],北京:清华大学出版社,2002
[34] Wigner E P. On the quantum correction for thermodynamic equilibrium. Phys.Rev.,1932 40:749-759
[35] Ville J. Theories et applications de la notion de signal analytique[M]. Cableset Transmission, 1948, 2A:61-74
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