稳定分布噪声下基于FLOS的波束形成技术的研究
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摘要
阵列信号处理是信号处理的一个重要分支,被广泛而迅速地应用在通信、雷达、声纳、地震勘探、射电天文等领域。传统的阵列信号处理的研究主要集中在基于高斯型噪声的环境下。但是,诸如海洋环境噪声、大气噪声、语音信号和生物医学信号及多种人为噪声等这些在自然界中更普遍存在的是非高斯型脉冲噪声。因此,近年来这类噪声引起了国内外研究工作者的广泛重视,并从理论上对此进行了深入的研究和发展。目前,作为阵列信号处理的主要内容之一的波束形成技术多依赖于高斯噪声环境,在应对脉冲噪声环境时原有方法往往产生退化,这阻碍了该技术的现实应用和发展。因此,非高斯脉冲噪声下的波束形成技术的研究尤显其重要意义。
本课题主要研究了在α稳定分布脉冲噪声下利用分数低阶统计量及神经网络的方法进行阵列信号处理(主要是波束形成)的问题。在非高斯分布中,α稳定分布是非常重要的一类模型,用来描述重拖尾特征的非高斯脉冲信号和噪声。特别是,α稳定分布包括了高斯分布的情况(当α=2时),可以说α稳定分布是广义上的高斯分布。
首先,本文对课题所应用到的知识点做了概要的介绍,其中包括α稳定分布模型,FLOS基本理论,神经网络常用方法以及波束形成技术。
其次,介绍了基于上述理论,本文研究工作的理论、模型及模拟结果分析。在阵列信号处理中,基于分数低阶统计量(FLOS)的方法包含了期望信号的波达方向(DOA)信息,因此非常适用于处理脉冲噪声下的波束形成问题。值得注意的是,基于FLOS的方法在处理α稳定分布信号和噪声时表现出良好的韧性。为了减少阵列处理的计算复杂度,把阵列信号处理看作一个从输入空间到输出空间的非线性映射,并利用RBF网络来逼近这一映射。为了克服脉冲噪声带来的负面影响,对RBF网络的输入向量采用了分数低阶预处理。文中模拟部分给出了RBF网络与各种经典算法的详细的性能对比、改变各参数情况下网络输出的分析及有无FLOS预处理的RBF网络输出的误差分析,模拟表明经过FLOS预处理的RBF网络能够在脉冲噪声条件下较好地逼近这一非线性映射。
最后,本文对上述工作做以小结,并展望了未来进一步的研究工作。
Array signal processing is one of the most important branches of signal processing, applied rapidly in the areas of communication, radar, sonar, earthquake, reconnoiter, chronometer and etc., traditional methods of which focused on the study in Gauss noise condition. In these years, there have been researching deeply especially abroad in the field whereas non-Gauss noise exists widely among the nature. The main task of my study is to provide a kind of robust methods for beamforming technology with FLOS-based RBF networks under alpha stable noise condition. Beamforming technology plays a main role of array signal processing that is used to process array signals with vectors so as to intensify the desired ones and restrain the interfacial. Alpha stable distribution, the most important model of non-Gauss distribution, is offered to describe such a character of thick tails. It is remarkable that alpha stable distribution includes the situation of Gauss when α=2. So alpha stable distribution is also called generalized Gauss distribution. Beamforming technology includes such methods as characteristic-based methods, high-order cumulant methods, subspace-based methods (MUSIC and ESPRIT) and etc. It works out worse results when second order statistics meets non-Gauss noise and high-order cumulant algorithm brings enormous computation and slower convergence speed. Therefore, people take fractional lower order statistics (FLOS) algorithm that represents better robustness in the processing of alpha stable distributed noise into account. In order to reduce the computation complexity, it makes beamforming process as a nonlinear mapping from input space to output space that approached by RBF network. Avoiding impulsive noise affection, here it takes advantage of FLOS preprocessing before RBF network. In this paper, it compares RBF network to other classical algorithms in details and the simulation represents that RBF network with FLOS preprocessing under the environment of impulsive noise can approach this nonlinear mapping nearly.
本课题主要研究了在α稳定分布脉冲噪声下利用分数低阶统计量及神经网络的方法进行阵列信号处理(主要是波束形成)的问题。在非高斯分布中,α稳定分布是非常重要的一类模型,用来描述重拖尾特征的非高斯脉冲信号和噪声。特别是,α稳定分布包括了高斯分布的情况(当α=2时),可以说α稳定分布是广义上的高斯分布。
首先,本文对课题所应用到的知识点做了概要的介绍,其中包括α稳定分布模型,FLOS基本理论,神经网络常用方法以及波束形成技术。
其次,介绍了基于上述理论,本文研究工作的理论、模型及模拟结果分析。在阵列信号处理中,基于分数低阶统计量(FLOS)的方法包含了期望信号的波达方向(DOA)信息,因此非常适用于处理脉冲噪声下的波束形成问题。值得注意的是,基于FLOS的方法在处理α稳定分布信号和噪声时表现出良好的韧性。为了减少阵列处理的计算复杂度,把阵列信号处理看作一个从输入空间到输出空间的非线性映射,并利用RBF网络来逼近这一映射。为了克服脉冲噪声带来的负面影响,对RBF网络的输入向量采用了分数低阶预处理。文中模拟部分给出了RBF网络与各种经典算法的详细的性能对比、改变各参数情况下网络输出的分析及有无FLOS预处理的RBF网络输出的误差分析,模拟表明经过FLOS预处理的RBF网络能够在脉冲噪声条件下较好地逼近这一非线性映射。
最后,本文对上述工作做以小结,并展望了未来进一步的研究工作。
Array signal processing is one of the most important branches of signal processing, applied rapidly in the areas of communication, radar, sonar, earthquake, reconnoiter, chronometer and etc., traditional methods of which focused on the study in Gauss noise condition. In these years, there have been researching deeply especially abroad in the field whereas non-Gauss noise exists widely among the nature. The main task of my study is to provide a kind of robust methods for beamforming technology with FLOS-based RBF networks under alpha stable noise condition. Beamforming technology plays a main role of array signal processing that is used to process array signals with vectors so as to intensify the desired ones and restrain the interfacial. Alpha stable distribution, the most important model of non-Gauss distribution, is offered to describe such a character of thick tails. It is remarkable that alpha stable distribution includes the situation of Gauss when α=2. So alpha stable distribution is also called generalized Gauss distribution. Beamforming technology includes such methods as characteristic-based methods, high-order cumulant methods, subspace-based methods (MUSIC and ESPRIT) and etc. It works out worse results when second order statistics meets non-Gauss noise and high-order cumulant algorithm brings enormous computation and slower convergence speed. Therefore, people take fractional lower order statistics (FLOS) algorithm that represents better robustness in the processing of alpha stable distributed noise into account. In order to reduce the computation complexity, it makes beamforming process as a nonlinear mapping from input space to output space that approached by RBF network. Avoiding impulsive noise affection, here it takes advantage of FLOS preprocessing before RBF network. In this paper, it compares RBF network to other classical algorithms in details and the simulation represents that RBF network with FLOS preprocessing under the environment of impulsive noise can approach this nonlinear mapping nearly.
引文
[1] 张贤达,保铮,通信信号处理,国防工业出版社,2000:310一331,
[2] C. L. Nildas and M. shao. Signal processing with alpha-Stable sistributions and applications. New York: John Wiley & Sons Inc., 1995
[3] D. G. Manolakis, V. K. Ingle, Stephen M. Kogon 著,《统计与自适应信号处理》,周正等译,电子工作出版社, 2003: 618-620, 636-638, 709-710
[4] M. Shao and C. L. Nikias. Signal processing with fractional lower order moments: stable processes and their applications. Proceedings of IEEE, 1993, 81 (7): 986-1010
[5] Ercan Engin K. PHD thesis, Signal processing in α-stable noise environments: a least ι_ρ-norm approach, Signal Processing and Communications Laboratory. Department of Engineering, University of Cambridge, 1998, 22:1-186
[6] 王宏禹,邱天爽,自适应噪声抵销与时间延迟估计,大连:大连理工大学出版社,1999:361-378
[7] X. Ma and C. L. Nikias. Joint estimation of rime delay and frequency delay in impulsive noise using fractional lower order statistics. IEEE Transactions on Signal Processing, 1996, 44(11): 2669-2687
[8] W. Stuck. Minimum error dispersion liner filtering of scalar symmetric stable processes. IEEE Trans. Automat. Contr., 1978, AC-23 (3): 507-509
[9] S.Haykin著,神经网络原理,叶世伟 史忠植译,原书第2版,机械工业出版社,2004:1,24-29,81-82,102-103,109-120,175,112-121,160-165,183-184,209-210,229,247,321-328
[10] S. E Applebaum. Adaptive arrays. IEEE Trans. Antenna and Propagation, 1976,24:585-598
[11] B. Windrow, R E. Mantey, L. J. Griffiths, B. B. Goode. Adaptive antenna systems. Proc. IEEE, 1967,55:2143-2159
[12] J. Capon. High-resolution frequency wave number spectrum analysis. Proc.IEEE, 1969, 57:1408-1418
[13] E. Serpedin, G. B. Giannakis. Blind channel identifications and equalizations with modulation-induced cyclostationarity. IEEE Trans. Signal Processing, 1998, 46: 1930-1944
[14] R. Roy, A. Paulraj, T. Kailath. ESPRIT---A subspace rotation approach to estimation of parameter of cisoids in noise. IEEE Trans. Acoust., Speech, Signal Processing, 1986, 34:1340-1342
[15] W. F. Gabriel. Adaptive arrays---An introduction. Proc. IEEE, 1976, 64:239-272
[16] J. A. Anderson. "General introduction," Neurocomputing: Foundations of Research (J.A.Anderson and E.Rosenfield), eds, Cambridge, MA: MIT Press, 1988: xiii-xxi
[17] S. Grossberg. Content-addressable memory storage by neural networks: A general model and global Liapunov method. In Computational Neuroscience, E.L. Schwartz, ed., Cambridge, MA: MIT Press, 1990:56-65
[18] S. J. Russell, P. Novig. Artificial Intelligence: A Modem Approach. Upper Saddle River, NJ: Prentice-Hall, 1995
[19] W. Rall. Some historical notes, in Computational Neuroscience. E.L., Schwartz, ed., Cambridge: MIT Press, 1990:3-8
[20] J.G. Taylor. Neuroal computation: The historical background, in E.Fiesler and R.Beale, eds, Handbook of neural Computation, New York: Oxford University Press, 1997
[21] 邱天爽,张旭秀,李小兵,孙永梅,统计信号处理——非高斯信号处理及其应用,电子工业出 版社,2004:26-35,139-140,151,159-162,187-193
[2
[22] 张金凤,邱天爽,分数低阶稳定分布下DLMP算法的收敛特性分析,电子学报,2005,33(1):74-77
[23] S. Haykin, Neural Networks, second edition, 清华大学出版社, 2002
[24] X. Kong and T. Qiu. Injury detection and signal discrimination of EEG by higher order crossings. IEEE EMBS'98, Hong Kong, China, 1998, (10): 2016-2019
[25] T. Qiu and X. Kong. Latency change detection in evoked potentials by direct least mean p norm adaptive time delay estimation. IEEE EMBS'98, Hong Kong, China, 1998, (10): 2054-2057
[26] T. Qiu and X. Kong. Estimation of latency changes of evoked potentials with adaptive phase spectral time delay estimation. IEEE EMBS'97, Chicago, USA, 1997, (11): 1522-1525
[27] O L. Frost. An algorithm for linear constrained adaptive array processing. Proc. IEEE, 1972, 60(8):926-935
[28] P. Petrus. Novel adaptive array algorithms and their impact on cellular system capacity, PhD Thesis, The virginia polytechnic institute and state university, 1997
[29] R. Gooch, J. Lundell. The CM array: An adaptive beamformer for constant modulus signal. IEEE Proc. ICASSP, Japan, 1986:2523-2526
[30] 何振亚,自适应信号处理,北京:科学出版社,2002
[31] 张贤达,现代信号处理(第二版),北京:清华大学出版社,2002
[32] P. Tsakalides and C. L. Nikias, The robust covariation-based MUSIC (ROC-MUSIC) algorithm for bearing estimation in impulsive noise environments, IEEE Transactions on signal processing, 1996, 44(7):1623-1633
[33] S. Haykin, Adaptive filter theory, 电子工业出版社, Forth edition, 2002
[34] R. Roy and T. Kailath. ESPRIT-A subspace rotation approach to estimation of parameters of cisoids in noise. IEEE Trans. on Acoust, Speech, signal, 1986, 34:1340-1342,
[35] L. Tsung-Hsien, J.M. Mendel. A subspace-based direction finding algorithm using fractional lower order statistics. IEEE Transactions on signal processing, 2001, 49(8): 1605-1613
[36] M. Rupi, E Tsakaiides, E. Del Re and C.L. Nikias. Robust spatial filtering of coherent sources for wireless communications. Elsevier Signal Processing, 2000, 80:381-396
[37] P. Tsakalides and C. L. Nikias. Robust adaptive beamforming in alpha-stable noise environments. IEEE Intemational Conference on. ICASSP-96. Conference Proceedings, 1996, (5): 2884-2887
[38] A.H.El Zooghbv, C.G. Christodoulou, and M. Georgiopoulos. Neural network-based adaptive beamforming for one-and two-dimensional arrays. IEEE Transactions on Antenna propagation, 1998, 46(12):1891-1893
[39] A.H.El Zooghby, C.G. Christodoulou and M. Georgiopoulos. A neural network-based smart antenna for multiple source tracking. IEEE Transactions on antenna and propagation, 2000, 48(5): 768-776
[40] A.H.El Zooghby, C.G. Christodoulou and M. Georgiopoulos. Performance of Radiai-basis function networks for direction of arrival estimation with antenna arrays. IEEE Transactions antennas and propagation, 1997, 45(11): 1611-1617
[41] P.R. Chang and W.H. Yang. A neural network approach to MVDR beamforming problem. IEEE Transactions on antenna propagation, 1992, 40(3): 313-322
[42] Berger and B. Mandelbrot. A new model for error clustering in telephone circiuts. IBM J. Res. and Develop., 1963, 7: 224-236
[43] P. Levy. Calcul des Probabilites. Paris: Gauthier-Villars, 1925
[44] W. Stuck and B. Kleiner. A statistical analysis of telephone noise. Bell Syst. Tech. J., 1974, 53 (7): 1263-1320
[2] C. L. Nildas and M. shao. Signal processing with alpha-Stable sistributions and applications. New York: John Wiley & Sons Inc., 1995
[3] D. G. Manolakis, V. K. Ingle, Stephen M. Kogon 著,《统计与自适应信号处理》,周正等译,电子工作出版社, 2003: 618-620, 636-638, 709-710
[4] M. Shao and C. L. Nikias. Signal processing with fractional lower order moments: stable processes and their applications. Proceedings of IEEE, 1993, 81 (7): 986-1010
[5] Ercan Engin K. PHD thesis, Signal processing in α-stable noise environments: a least ι_ρ-norm approach, Signal Processing and Communications Laboratory. Department of Engineering, University of Cambridge, 1998, 22:1-186
[6] 王宏禹,邱天爽,自适应噪声抵销与时间延迟估计,大连:大连理工大学出版社,1999:361-378
[7] X. Ma and C. L. Nikias. Joint estimation of rime delay and frequency delay in impulsive noise using fractional lower order statistics. IEEE Transactions on Signal Processing, 1996, 44(11): 2669-2687
[8] W. Stuck. Minimum error dispersion liner filtering of scalar symmetric stable processes. IEEE Trans. Automat. Contr., 1978, AC-23 (3): 507-509
[9] S.Haykin著,神经网络原理,叶世伟 史忠植译,原书第2版,机械工业出版社,2004:1,24-29,81-82,102-103,109-120,175,112-121,160-165,183-184,209-210,229,247,321-328
[10] S. E Applebaum. Adaptive arrays. IEEE Trans. Antenna and Propagation, 1976,24:585-598
[11] B. Windrow, R E. Mantey, L. J. Griffiths, B. B. Goode. Adaptive antenna systems. Proc. IEEE, 1967,55:2143-2159
[12] J. Capon. High-resolution frequency wave number spectrum analysis. Proc.IEEE, 1969, 57:1408-1418
[13] E. Serpedin, G. B. Giannakis. Blind channel identifications and equalizations with modulation-induced cyclostationarity. IEEE Trans. Signal Processing, 1998, 46: 1930-1944
[14] R. Roy, A. Paulraj, T. Kailath. ESPRIT---A subspace rotation approach to estimation of parameter of cisoids in noise. IEEE Trans. Acoust., Speech, Signal Processing, 1986, 34:1340-1342
[15] W. F. Gabriel. Adaptive arrays---An introduction. Proc. IEEE, 1976, 64:239-272
[16] J. A. Anderson. "General introduction," Neurocomputing: Foundations of Research (J.A.Anderson and E.Rosenfield), eds, Cambridge, MA: MIT Press, 1988: xiii-xxi
[17] S. Grossberg. Content-addressable memory storage by neural networks: A general model and global Liapunov method. In Computational Neuroscience, E.L. Schwartz, ed., Cambridge, MA: MIT Press, 1990:56-65
[18] S. J. Russell, P. Novig. Artificial Intelligence: A Modem Approach. Upper Saddle River, NJ: Prentice-Hall, 1995
[19] W. Rall. Some historical notes, in Computational Neuroscience. E.L., Schwartz, ed., Cambridge: MIT Press, 1990:3-8
[20] J.G. Taylor. Neuroal computation: The historical background, in E.Fiesler and R.Beale, eds, Handbook of neural Computation, New York: Oxford University Press, 1997
[21] 邱天爽,张旭秀,李小兵,孙永梅,统计信号处理——非高斯信号处理及其应用,电子工业出 版社,2004:26-35,139-140,151,159-162,187-193
[2
[22] 张金凤,邱天爽,分数低阶稳定分布下DLMP算法的收敛特性分析,电子学报,2005,33(1):74-77
[23] S. Haykin, Neural Networks, second edition, 清华大学出版社, 2002
[24] X. Kong and T. Qiu. Injury detection and signal discrimination of EEG by higher order crossings. IEEE EMBS'98, Hong Kong, China, 1998, (10): 2016-2019
[25] T. Qiu and X. Kong. Latency change detection in evoked potentials by direct least mean p norm adaptive time delay estimation. IEEE EMBS'98, Hong Kong, China, 1998, (10): 2054-2057
[26] T. Qiu and X. Kong. Estimation of latency changes of evoked potentials with adaptive phase spectral time delay estimation. IEEE EMBS'97, Chicago, USA, 1997, (11): 1522-1525
[27] O L. Frost. An algorithm for linear constrained adaptive array processing. Proc. IEEE, 1972, 60(8):926-935
[28] P. Petrus. Novel adaptive array algorithms and their impact on cellular system capacity, PhD Thesis, The virginia polytechnic institute and state university, 1997
[29] R. Gooch, J. Lundell. The CM array: An adaptive beamformer for constant modulus signal. IEEE Proc. ICASSP, Japan, 1986:2523-2526
[30] 何振亚,自适应信号处理,北京:科学出版社,2002
[31] 张贤达,现代信号处理(第二版),北京:清华大学出版社,2002
[32] P. Tsakalides and C. L. Nikias, The robust covariation-based MUSIC (ROC-MUSIC) algorithm for bearing estimation in impulsive noise environments, IEEE Transactions on signal processing, 1996, 44(7):1623-1633
[33] S. Haykin, Adaptive filter theory, 电子工业出版社, Forth edition, 2002
[34] R. Roy and T. Kailath. ESPRIT-A subspace rotation approach to estimation of parameters of cisoids in noise. IEEE Trans. on Acoust, Speech, signal, 1986, 34:1340-1342,
[35] L. Tsung-Hsien, J.M. Mendel. A subspace-based direction finding algorithm using fractional lower order statistics. IEEE Transactions on signal processing, 2001, 49(8): 1605-1613
[36] M. Rupi, E Tsakaiides, E. Del Re and C.L. Nikias. Robust spatial filtering of coherent sources for wireless communications. Elsevier Signal Processing, 2000, 80:381-396
[37] P. Tsakalides and C. L. Nikias. Robust adaptive beamforming in alpha-stable noise environments. IEEE Intemational Conference on. ICASSP-96. Conference Proceedings, 1996, (5): 2884-2887
[38] A.H.El Zooghbv, C.G. Christodoulou, and M. Georgiopoulos. Neural network-based adaptive beamforming for one-and two-dimensional arrays. IEEE Transactions on Antenna propagation, 1998, 46(12):1891-1893
[39] A.H.El Zooghby, C.G. Christodoulou and M. Georgiopoulos. A neural network-based smart antenna for multiple source tracking. IEEE Transactions on antenna and propagation, 2000, 48(5): 768-776
[40] A.H.El Zooghby, C.G. Christodoulou and M. Georgiopoulos. Performance of Radiai-basis function networks for direction of arrival estimation with antenna arrays. IEEE Transactions antennas and propagation, 1997, 45(11): 1611-1617
[41] P.R. Chang and W.H. Yang. A neural network approach to MVDR beamforming problem. IEEE Transactions on antenna propagation, 1992, 40(3): 313-322
[42] Berger and B. Mandelbrot. A new model for error clustering in telephone circiuts. IBM J. Res. and Develop., 1963, 7: 224-236
[43] P. Levy. Calcul des Probabilites. Paris: Gauthier-Villars, 1925
[44] W. Stuck and B. Kleiner. A statistical analysis of telephone noise. Bell Syst. Tech. J., 1974, 53 (7): 1263-1320