SVM在阵列天线领域的应用研究
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摘要
本文主要包含三方面的内容：阵列天线、支持向量机以及两者结合应用研究。
支持向量机是由Vapnik等人提出的小样本统计理论——统计学习理论发展而来的一种新的通用学习算法，特别在高维空间中表示复杂函数，避免了常规算法“维数灾难”等麻烦问题，可直接用阵列原始数据作为特征向量而不影响系统性能。本文主要将SVM这一新的机器学习方法应用到阵列天线领域，并用该算法实现对目标信源的测定。
为了利用支持向量机的函数拟合来预测信源位置，我们将支持向量机理论和阵列天线模型结合在一起，根据两者的不同特点构造了一个训练数据结构；并设计了通过改变不同参数对训练机器进行优化的新的系统模型。这样不仅发挥了SVM技术的优越性，而且还推广了该技术应用领域。本文仿真采用6元直线等距阵列天线对于平面波入射的处理情形。把阵列天线采集的训练样本的协方差矩阵进行适当变换之后送入SVM训练器进行学习，然后根据这个学习机对未知样本进行SVM的函数拟合，得到信源方向。训练中需要采用不同的参数，以求得最佳学习机。这种算法处理速度很快，能实时跟踪目标运动，且在环境不是很恶劣的情况下精度较高，能有效的减少运算量。同时我们还将SVM与MUSIC算法进行了比较，可以看出，在预测精度和跟踪速度方面，SVM算法的优点得到了很好的体现。
This thesis includes three aspects of contents: Antenna array, SVM and their combination.
SVM is a kind of universal learning algorithm, which developed from Statistical Learning Theory, that is, small sample learning theory proposed by Vapnik. It can represent complicated functions especially in high dimensions, which can avoid the trouble of the dimension tragedy that happened in general algorithm. It also will not affect the system performance by using original data of the array for the eigenvector directly. We apply SVM, the new machine-learning algorithm, to the domain of the antenna array, in order to realize the source location in this thesis mainly.
In order to predict source location by using the SVM regression, we combine the SVM theory & the antenna array module, construct a training data structure; design a new system module which optimize the train machine by altering different parameter. It does not only exert the superiority of the SVM technology, but also extend its application domain. We use six linear equally spaced antenna arrays to simulate SVM algorithm for treating with the incident plane wave. The covariance of the training samples which are sampled from the antenna arrays is delivered into SVM training machine after transformed suitably, then we use SVM regression on the unknown samples according as the trained machine for getting the source location. We should adopt different parameter to get the optimal learning machine. This algorithm processes rapidly, and can track the movement of the source. It also has high precision where the SNR is not so bad, and can reduce the compute quantum efficiently. The SVM has high precision of the forecast & tracldng speed compared with the MUSIC algorithm.
支持向量机是由Vapnik等人提出的小样本统计理论——统计学习理论发展而来的一种新的通用学习算法，特别在高维空间中表示复杂函数，避免了常规算法“维数灾难”等麻烦问题，可直接用阵列原始数据作为特征向量而不影响系统性能。本文主要将SVM这一新的机器学习方法应用到阵列天线领域，并用该算法实现对目标信源的测定。
为了利用支持向量机的函数拟合来预测信源位置，我们将支持向量机理论和阵列天线模型结合在一起，根据两者的不同特点构造了一个训练数据结构；并设计了通过改变不同参数对训练机器进行优化的新的系统模型。这样不仅发挥了SVM技术的优越性，而且还推广了该技术应用领域。本文仿真采用6元直线等距阵列天线对于平面波入射的处理情形。把阵列天线采集的训练样本的协方差矩阵进行适当变换之后送入SVM训练器进行学习，然后根据这个学习机对未知样本进行SVM的函数拟合，得到信源方向。训练中需要采用不同的参数，以求得最佳学习机。这种算法处理速度很快，能实时跟踪目标运动，且在环境不是很恶劣的情况下精度较高，能有效的减少运算量。同时我们还将SVM与MUSIC算法进行了比较，可以看出，在预测精度和跟踪速度方面，SVM算法的优点得到了很好的体现。
This thesis includes three aspects of contents: Antenna array, SVM and their combination.
SVM is a kind of universal learning algorithm, which developed from Statistical Learning Theory, that is, small sample learning theory proposed by Vapnik. It can represent complicated functions especially in high dimensions, which can avoid the trouble of the dimension tragedy that happened in general algorithm. It also will not affect the system performance by using original data of the array for the eigenvector directly. We apply SVM, the new machine-learning algorithm, to the domain of the antenna array, in order to realize the source location in this thesis mainly.
In order to predict source location by using the SVM regression, we combine the SVM theory & the antenna array module, construct a training data structure; design a new system module which optimize the train machine by altering different parameter. It does not only exert the superiority of the SVM technology, but also extend its application domain. We use six linear equally spaced antenna arrays to simulate SVM algorithm for treating with the incident plane wave. The covariance of the training samples which are sampled from the antenna arrays is delivered into SVM training machine after transformed suitably, then we use SVM regression on the unknown samples according as the trained machine for getting the source location. We should adopt different parameter to get the optimal learning machine. This algorithm processes rapidly, and can track the movement of the source. It also has high precision where the SNR is not so bad, and can reduce the compute quantum efficiently. The SVM has high precision of the forecast & tracldng speed compared with the MUSIC algorithm.
引文
[1] L. Bigler, H. P. Lin, S. S. Jeng, and G. Xu, "Experimental Direction-of-Arrival and Spatial Signature Measurements at 900 MHz for Smart Antenna Systems" 1995 IEEE 45th Vehicular Technology Conf., Chicago, IL, 1995.
[2] R. L. Johnson, "Eigenvector Matrix Partition and Radio Direction Finding Performance" IEEE Trans. On Antennas and Propagation, Vol. AP-34, No. 8, pp. 985-991, Aug 1986.
[3] R. O. Schmidt, "Multiple Emitter Location and Signal Parameter Estimation" Proc. Of RADC Spectrum Estimation Workshop, Griffiss AFB, NY, pp. 243-258, 1979.
[4] R. O. Schmidt, "Multiple Emitter Location and Signal Parameter Estimation" IEEE Trans. On Antennas and Propagation, Vol. AP-34, No. 3, Mar. 1986.
[5] A. J. Barabell, "Improving the Resolution Performance of Eigenstructure-based Direction Finding Algorithms" Proc. Of the IEEE Int'l. Conf. on Acoustics, Speech, and Signal Processing-83, pp. 336-339, 1983.
[6] R. Roy and T. Kailath, "ESPRIT-Estimation of Signal Parameters via Rotational Invariance Techniques" IEEE Trans. On Acoustics, Speech, and Signal Processing, Vol. 37, pp. 984-995, July 1986.
[7] A. Paulraj, R. Roy, and T. Kailath, "Estimation of Signal Parameters via Rotational Invariance Techniques-ESPRIT" Proc. Of 19th Asilomar Conf. on Circuits and Systems, pp. 83-89, 1985.
[8] W. A. Gardner, "Simplification of MUSIC and ESPRIT by Exploitation of Cyclostationarity" Proc. Of the IEEE, Vol. 76, pp. 845-847, July 1988.
[9] J. E. Evans, J. R. Johnson, and D. F. Sun, "High Resolution Angular Spectrum Estimation Techniques for Terrain Scattering Analysis and Angle of Arrival Estimation in ATC Navigation and Surveillance System" M. I. T. Lincoln Lab., Lexington, MA, Rep. 582, 1982.
[10] I. Parra, G. Xu, and H. Liu, "A Least Squares Projective Constant Modulus Approach" Proc. Sixth IEEE Int'l. Symposium on, Vol. 2, 1995, pp. 673-676.
[11] B. Agee, "Blind Separation and Capture of Communications Signals Using a Multi-target Constant Modulus Beamformer" 1989 IEEE Military Communications
Conf., Boston, MA, Oct. 1989.
[12] M. G. Larimore and J. R. Treichler, "Convergence Behavior of the Constant Modulus Algorithm" IEEE. Int. Conf. on Acoust., Speech, and Signal Processing, Boston, MA, 1983.
[13] Z. Rong, T. S. Rappaport, "Simulation of MultiTarget Adaptive Algorithms for Wireless CDMA Systems" Proc. IEEE Vehicular Technology Conf., Apr. 1996.
[14] W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, John Wiley & Sons, NY, 1981.
[15] M. Lu, T. Lo, and J. Litva, "A Decision-Directed Beamforming Algorithm for CDMA Systems with Noncoherent M-ary Orthogonal Modulation" Submitted to IEEE Trans. On Comm., 1998.
[16] B. Widrow, P. E. Mantey, L. J. Griffiths, and B. B. Goode, "Adaptive Antenna Systems" Proc. Of the IEEE, Vol. 55, No. 12, Dec. 1967.
[17] Bershan, "On theoptimum gain parameters in LMS adaptation" IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-35, pp. 1065-1068.
[18] Vapnik V. N., and J. Wiley, "Statiscal Learning Theory" New York, 1998.
[19] Vapnik V. N., and Chervonenkis A Ja., "On the uniform convergence of relative frequencies of events to their probabilities" Theory Probab. Apl. 16: 264-280, 1971.
[20] Vapnik V. N., and Chervonenkis A Ja., "Necessary and sufficient conditions for consistency of the method of empirical risk minimization" Classification, and Forecasting, 2, Nauka, Moscow, 207-249, 1989.
[21] Bottou L., and Vapnik V. N., "Local learning algorithms" Neural Computation, 4(6): 888-901.
[22] Akaike H., "Statistical predictor identification" Annals of the Institute of Statistical Mathematical, 202-217, 1970.
[23] T. B. Sorensen et, al., "Testbed for Evaluation of Adaptive Transmit and Receive Antennas" Proc. 4th ACTS Mobile Communications Summit, vol. 2, 1999.
[24] CHRYSSOMALLIS M. Smart Antennas [J], IEEE Antennas and Propagation Magazine, 2000, 42(3): 129～135.
[25] MUAMMARR, GUPTASC. Co-channel Interferernce in High-Capacity Mobile Radio
Systems [J]. IEEE Transactions on Communications, 1982, 30(8): 1973～1978.
[26] Rong Xiao, Jicheng Wang, Fayan Zhang, "An approach to incremental SVM learning algorithm" Tools with Artificial Intelligence, 2000. ICTAI 2000. Proceedings. 12th IEEE International Conference on, 13-15 Nov. 2000 p268-273
[27] Kuh, A., "Analysis of detectors for support vector machines and least square support vector machines" Neural Networks, 2002. IJCNN '02. Proceedings of the 2002 International Joint Conference on, Volume: 2, 12-17 May 2002 p1075-1079
[28] Anguita, D., Boni, A., "Improved neural network for SVM learning" Neural Networks, IEEE Transactions on, Volume: 13, Issue: 5, Sep 2002 p1243-1244
[29] Weiyu Zhu, Song Wang, Ruei-Sung Lin, Levinson, S., "Tracking of object with SVM regression" Computer Vision and Pattern Recognition, 2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on, Volume: 2, 8-14 Dec. 2001 pll-240-ll-245 vol. 2
[30] Zhang Li, Zhou Weida, Jiao Licheng, "Radar target recognition based on support vector machine" Signal Processing Proceedings, 2000. WCCC-ICSP 2000. 5th International Conference on, Volume: 3, 21-25 Aug. 2000 p1453-1456 vol. 3
[31] Chih-Chung Chang and Chih-Jen Lin, LIBSVM: a library for support vector machines, 2001. Software available at http://www.csie.ntu.edu.tw/～cjlin/libsvm.
[32] 张贤达，现代信号处理，清华大学出版社，1995。
[33] 边肇祺，张学工，模式识别，清华大学出版社，2000。
[34] Vapnik V. N., The nature of statistical learning theory, 2000．
[35] 沈凤麟，叶中付，钱玉美，信号统计分析与处理，中国科学技术大学出版社，2001。
[2] R. L. Johnson, "Eigenvector Matrix Partition and Radio Direction Finding Performance" IEEE Trans. On Antennas and Propagation, Vol. AP-34, No. 8, pp. 985-991, Aug 1986.
[3] R. O. Schmidt, "Multiple Emitter Location and Signal Parameter Estimation" Proc. Of RADC Spectrum Estimation Workshop, Griffiss AFB, NY, pp. 243-258, 1979.
[4] R. O. Schmidt, "Multiple Emitter Location and Signal Parameter Estimation" IEEE Trans. On Antennas and Propagation, Vol. AP-34, No. 3, Mar. 1986.
[5] A. J. Barabell, "Improving the Resolution Performance of Eigenstructure-based Direction Finding Algorithms" Proc. Of the IEEE Int'l. Conf. on Acoustics, Speech, and Signal Processing-83, pp. 336-339, 1983.
[6] R. Roy and T. Kailath, "ESPRIT-Estimation of Signal Parameters via Rotational Invariance Techniques" IEEE Trans. On Acoustics, Speech, and Signal Processing, Vol. 37, pp. 984-995, July 1986.
[7] A. Paulraj, R. Roy, and T. Kailath, "Estimation of Signal Parameters via Rotational Invariance Techniques-ESPRIT" Proc. Of 19th Asilomar Conf. on Circuits and Systems, pp. 83-89, 1985.
[8] W. A. Gardner, "Simplification of MUSIC and ESPRIT by Exploitation of Cyclostationarity" Proc. Of the IEEE, Vol. 76, pp. 845-847, July 1988.
[9] J. E. Evans, J. R. Johnson, and D. F. Sun, "High Resolution Angular Spectrum Estimation Techniques for Terrain Scattering Analysis and Angle of Arrival Estimation in ATC Navigation and Surveillance System" M. I. T. Lincoln Lab., Lexington, MA, Rep. 582, 1982.
[10] I. Parra, G. Xu, and H. Liu, "A Least Squares Projective Constant Modulus Approach" Proc. Sixth IEEE Int'l. Symposium on, Vol. 2, 1995, pp. 673-676.
[11] B. Agee, "Blind Separation and Capture of Communications Signals Using a Multi-target Constant Modulus Beamformer" 1989 IEEE Military Communications
Conf., Boston, MA, Oct. 1989.
[12] M. G. Larimore and J. R. Treichler, "Convergence Behavior of the Constant Modulus Algorithm" IEEE. Int. Conf. on Acoust., Speech, and Signal Processing, Boston, MA, 1983.
[13] Z. Rong, T. S. Rappaport, "Simulation of MultiTarget Adaptive Algorithms for Wireless CDMA Systems" Proc. IEEE Vehicular Technology Conf., Apr. 1996.
[14] W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, John Wiley & Sons, NY, 1981.
[15] M. Lu, T. Lo, and J. Litva, "A Decision-Directed Beamforming Algorithm for CDMA Systems with Noncoherent M-ary Orthogonal Modulation" Submitted to IEEE Trans. On Comm., 1998.
[16] B. Widrow, P. E. Mantey, L. J. Griffiths, and B. B. Goode, "Adaptive Antenna Systems" Proc. Of the IEEE, Vol. 55, No. 12, Dec. 1967.
[17] Bershan, "On theoptimum gain parameters in LMS adaptation" IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-35, pp. 1065-1068.
[18] Vapnik V. N., and J. Wiley, "Statiscal Learning Theory" New York, 1998.
[19] Vapnik V. N., and Chervonenkis A Ja., "On the uniform convergence of relative frequencies of events to their probabilities" Theory Probab. Apl. 16: 264-280, 1971.
[20] Vapnik V. N., and Chervonenkis A Ja., "Necessary and sufficient conditions for consistency of the method of empirical risk minimization" Classification, and Forecasting, 2, Nauka, Moscow, 207-249, 1989.
[21] Bottou L., and Vapnik V. N., "Local learning algorithms" Neural Computation, 4(6): 888-901.
[22] Akaike H., "Statistical predictor identification" Annals of the Institute of Statistical Mathematical, 202-217, 1970.
[23] T. B. Sorensen et, al., "Testbed for Evaluation of Adaptive Transmit and Receive Antennas" Proc. 4th ACTS Mobile Communications Summit, vol. 2, 1999.
[24] CHRYSSOMALLIS M. Smart Antennas [J], IEEE Antennas and Propagation Magazine, 2000, 42(3): 129～135.
[25] MUAMMARR, GUPTASC. Co-channel Interferernce in High-Capacity Mobile Radio
Systems [J]. IEEE Transactions on Communications, 1982, 30(8): 1973～1978.
[26] Rong Xiao, Jicheng Wang, Fayan Zhang, "An approach to incremental SVM learning algorithm" Tools with Artificial Intelligence, 2000. ICTAI 2000. Proceedings. 12th IEEE International Conference on, 13-15 Nov. 2000 p268-273
[27] Kuh, A., "Analysis of detectors for support vector machines and least square support vector machines" Neural Networks, 2002. IJCNN '02. Proceedings of the 2002 International Joint Conference on, Volume: 2, 12-17 May 2002 p1075-1079
[28] Anguita, D., Boni, A., "Improved neural network for SVM learning" Neural Networks, IEEE Transactions on, Volume: 13, Issue: 5, Sep 2002 p1243-1244
[29] Weiyu Zhu, Song Wang, Ruei-Sung Lin, Levinson, S., "Tracking of object with SVM regression" Computer Vision and Pattern Recognition, 2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on, Volume: 2, 8-14 Dec. 2001 pll-240-ll-245 vol. 2
[30] Zhang Li, Zhou Weida, Jiao Licheng, "Radar target recognition based on support vector machine" Signal Processing Proceedings, 2000. WCCC-ICSP 2000. 5th International Conference on, Volume: 3, 21-25 Aug. 2000 p1453-1456 vol. 3
[31] Chih-Chung Chang and Chih-Jen Lin, LIBSVM: a library for support vector machines, 2001. Software available at http://www.csie.ntu.edu.tw/～cjlin/libsvm.
[32] 张贤达，现代信号处理，清华大学出版社，1995。
[33] 边肇祺，张学工，模式识别，清华大学出版社，2000。
[34] Vapnik V. N., The nature of statistical learning theory, 2000．
[35] 沈凤麟，叶中付，钱玉美，信号统计分析与处理，中国科学技术大学出版社，2001。