基于高阶累积量的低信噪比复杂信号识别研究
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摘要
雷达技术的迅猛发展对雷达侦察系统提出了严峻的挑战。一方面,国内外军用雷达采用的信号形式日益复杂;另一方面,各种电子对抗设备数目急剧增加,电磁信号日趋密集,使雷达侦察系统处于高度密集的信号环境中。因此,信号提取和识别的能力已成为衡量电子对抗技术先进程度的重要标志之一,同时它也是现代雷达技术中急需解决且难度较大的课题之一。本文对低信噪比情况下基于高阶累积量的复杂信号识别研究正是在这一基础上提出来的。
本文通过对分数阶Fourier变换和高阶累积量的理论分析研究,把高阶累积量能有效抑制各种高斯噪声的性质和线性调频(LFM)信号在分数阶域的能量聚集性相结合,提出了一种新的时频分析方法——线性调频信号基于高阶累积量的分数阶域的峰度检测。
通过仿真,不仅验证了该方法的有效性,还把该方法与原有传统的时频分析方法进行了比较。结果表明,在低信噪比情况下,无论是针对单分量LFM信号还是多分量LFM信号,该方法都可以比传统方法更有效地抑制各种高斯噪声,摆脱交叉项的影响,识别有用信号。因此峰度检测算法可用于低信噪比,多分量LFM信号的复杂情况下,并能有效地抑制各种高斯噪声,更有利于复杂信号的识别。
当然,分数阶Fourier域和高阶累积量的研究应用都有待进一步开展。不仅可以应用峰度检测、分数阶Fourier变换对LFM信号的重要特征参数进行估计,还可以将高阶循环累积量的优良性质应用到检测与识别领域。
Rapid development of radar technology has put forward an austere challenge to radar reconnaissance system. On the one hand, the forms of both domestic and foreign radar signal become more and more complex. On the other hand, the number of different kinds of electronic reconnaissance equipment increases rapidly, and the electromagnetism signals become more and more dense, so radar reconnaissance system is operating under a highly dense signal environment. Therefore, the ability of distinguishing and identifying the signals has not only become one of the important criterions to estimate the advanced degree of electronic reconnaissance technology, but also become one of the urgent and difficult tasks of modern radar technology. Research on complex signal identification under low signal/noise rate based on high-order cumulant is put forward based on this idea.
By carefully analyzing and studying the theory of fractional Fourier transform and high-order cumulant, high-order cumulant has been combined with fractional Fourier transform, because high-order cumulant can effectively inhibit different kinds of Gaussian noise, and the energy of linear-frequency modulate signal congregates in fractional Fourier domain. Therefore, a novel time-frequency analyze method has been put forward in the thesis, that is, the algorithm of LFM signal kurtosis detection based on high-order cumulant in fractional Fourier domain.
The results of the simulations have not only proved the validity of the method, but also compared this method with existed traditional time-frequency analysis methods. It has proved that under the circumstance of low signal/noise rate, for either single LFM signal or multi-LFM signal, compared with traditional methods, this method can more effectively inhibit different kinds of Gaussian noise, avoid the influence of cross term and identify useful signal. So the kurtosis detection algorithm can be used in complex circumstance of multi-LFM signal with low signal/noise rate. It can inhibit different kinds of Gaussian noise more effectively and be more suitable for the identification of complex signal.
However, the research and application of both fractional Fourier domain and
high-order cumulant should be studied further. In the future work, the kurtosis detection and fractional Fourier transform can be used to estimate important characteristic parameters of LFM signal, and some fine characteristics of high-order cyclic cumulant can also be used in the field of signal detection and identification.
本文通过对分数阶Fourier变换和高阶累积量的理论分析研究,把高阶累积量能有效抑制各种高斯噪声的性质和线性调频(LFM)信号在分数阶域的能量聚集性相结合,提出了一种新的时频分析方法——线性调频信号基于高阶累积量的分数阶域的峰度检测。
通过仿真,不仅验证了该方法的有效性,还把该方法与原有传统的时频分析方法进行了比较。结果表明,在低信噪比情况下,无论是针对单分量LFM信号还是多分量LFM信号,该方法都可以比传统方法更有效地抑制各种高斯噪声,摆脱交叉项的影响,识别有用信号。因此峰度检测算法可用于低信噪比,多分量LFM信号的复杂情况下,并能有效地抑制各种高斯噪声,更有利于复杂信号的识别。
当然,分数阶Fourier域和高阶累积量的研究应用都有待进一步开展。不仅可以应用峰度检测、分数阶Fourier变换对LFM信号的重要特征参数进行估计,还可以将高阶循环累积量的优良性质应用到检测与识别领域。
Rapid development of radar technology has put forward an austere challenge to radar reconnaissance system. On the one hand, the forms of both domestic and foreign radar signal become more and more complex. On the other hand, the number of different kinds of electronic reconnaissance equipment increases rapidly, and the electromagnetism signals become more and more dense, so radar reconnaissance system is operating under a highly dense signal environment. Therefore, the ability of distinguishing and identifying the signals has not only become one of the important criterions to estimate the advanced degree of electronic reconnaissance technology, but also become one of the urgent and difficult tasks of modern radar technology. Research on complex signal identification under low signal/noise rate based on high-order cumulant is put forward based on this idea.
By carefully analyzing and studying the theory of fractional Fourier transform and high-order cumulant, high-order cumulant has been combined with fractional Fourier transform, because high-order cumulant can effectively inhibit different kinds of Gaussian noise, and the energy of linear-frequency modulate signal congregates in fractional Fourier domain. Therefore, a novel time-frequency analyze method has been put forward in the thesis, that is, the algorithm of LFM signal kurtosis detection based on high-order cumulant in fractional Fourier domain.
The results of the simulations have not only proved the validity of the method, but also compared this method with existed traditional time-frequency analysis methods. It has proved that under the circumstance of low signal/noise rate, for either single LFM signal or multi-LFM signal, compared with traditional methods, this method can more effectively inhibit different kinds of Gaussian noise, avoid the influence of cross term and identify useful signal. So the kurtosis detection algorithm can be used in complex circumstance of multi-LFM signal with low signal/noise rate. It can inhibit different kinds of Gaussian noise more effectively and be more suitable for the identification of complex signal.
However, the research and application of both fractional Fourier domain and
high-order cumulant should be studied further. In the future work, the kurtosis detection and fractional Fourier transform can be used to estimate important characteristic parameters of LFM signal, and some fine characteristics of high-order cyclic cumulant can also be used in the field of signal detection and identification.
引文
[1] 骆云飞. 雷达信号的提取与分析综述. 见:袁秀华等. 雷达与电子对抗分册论文集. 扬州. 2002. 扬州:中国造船工程学会电子技术学术委员会,2002. 145～149
[2] 赵国庆. 雷达对抗原理. 第1版. 西安:西安电子科技大学出版社,1999. 1～8
[3] 张义军. 基于高阶统计量的舰船辐射噪声特征提取及分类识别研究:[硕士学位论文]。西安:西安工业大学图书馆,2001.
[4] 徐春光. 非平稳信号的时频分析与处理方法研究:[博士学位论文]。西安:西安电子科技大学图书馆,1999.
[5] L.科恩. 时-频分析:理论与应用. 第1版. 白居宪. 西安:西安交通大学出版社,1998. 1～21,94～111
[6] L. Cohen. Time-frequency distributions – a review. Proc. IEEE, 1989, 77: 941~981
[7] S. Stankovic, L. J. Stankovic, Z. Uskokovic. On the local frequency, group shift, and cross-terms in some multidimensional time-frequency distributions: A method for multidimensional time-frequency analysis. IEEE Trans. on Signal Processing, 1995, 43(7): 1719~1724
[8] F. Patrick, G. B. Richard, M. Olivier. Time-frequency complexity and information. ICASSP’94, 1994, 3: 329~332
[9] F. Peyrin, R. A. Prost. A unified definition for the discrete-time, discrete-frequency, and discrete-time/frequency Wigner distribution. IEEE Trans. on Acoustic, Speech and Signal Processing, 1986, 34(4): 858~867
[10] K. M. M. Prabhu, R. S. Sundaram. Some results on fixed-point error analysis of Wigner-Ville distribution. Signal Processing, 1996, 51(3): 235~240
[11] B. Boashash, P. Black. An efficient real time implementation of the Wigner-Ville distribution. IEEE Trans. on Acoustic, Speech, and Signal Processing, 1987, 35(11): 1611~1618
[12] L. B. Almeida. The Fractional Transform and Time-frequency Representation. IEEE Trans. on Signal Processing , 1994(11):3084~3091
[13] A. W. Lachmann, B. H. Soffer. Relationship between the Radon-Wigner and fractional Fourier transform. Journal of Optics Society of American, 1994, 11: 1798~1801
[14] P. Soo-Chang, Y. Min-Hung. Fractional time-frequency distributions. Proc. of 1997 Int. Sym. on Circuit and Systems, ISCAS’97, 4: 2673~2676
[15] T. Alieva, A. M. Barbe. Fractional Fourier and Radon-Wigner transform of periodic signals. Signal Processing, 1998, 69(2): 183~190
[16] 张贤达,保铮. 非平稳信号分析与处理. 第1版. 北京:国防工业出版社,1998. 7,46～58,153～178,186～221
[17] Namias V. The Fractional Order Fourier Transform and Its Application to Quantum Mechanics. J. Inst. Math. Appl., 1980(25): 241~265
[18] 张贤达. 时间序分析——高阶统计量方法. 第1版. 北京:清华大学出版社,1996. 1～20
[19] 万小磊. 常规雷达目标双谱特征分析及应用:[硕士学位论文]。西安:西安电子科技大学图书馆,1999.
[20] Anabthram, Swami, Georgios B. et al. Bibliography on Higher-Order Statistics, Signal Processing, 1997, 60: 65~126
[21] 姚天任,孙洪. 现代数字信号处理. 第1版. 武汉:华中理工大学出版社,1999. 184～205
[22] G. B. Giannakis. Cumulants: A powerful tool in signal processing. Proc. IEEE, 1987, 75(9): 1333~1334
[23] 张安清,章新华. 四阶累积量的递推估计及其应用. 信号处理,2002,18(1):88～90
[24] Mendel J M. Tutorial on higher order statistics(spectra) in signal processing and system thoery: Theoretical results and some applications. Proc of IEEE., 1991, 79(3): 278~305
[25] 张贤达,保铮. 通信信号处理. 第1版. 北京:国防工业出版社,2000. 94～
102,277～280,383~389
[26] 孙晓兵,保铮. 分数阶傅立叶变换及其应用. 电子学报,1996,24(12):60～65
[27] 赵兴浩,陶然,周思永等. 基于Radon-Ambiguity变换和分数阶傅立叶变换的chirp信号检测及多参数估计. 北京理工大学学报,2003, 23(3):371～377
[28] Ozaktas H M, Kutay M A. Digital computation of the fractional Fourier transform[J]. IEEE Trans Signal Processing, 1996, 44(9):2141~2150
[29] 齐林,陶然,周思永等. 基于分数阶Fourier变换的多分量LFM信号的检测和参数估计. 中国科学(E辑),2003,33(8):749～759
[30] O. Akay, G. F. Boudreaux-Bartels. Fractional convolution and correlation via operator methods and an application to detection of linear FM signals. IEEE Trans. Sig-Proc., 2001, 49(5): 979~993
[31] 王宏艳,吴彦鸿,叶伟等. 分数阶Fourier变换在SAR动目标检测中的应用. 装备指挥技术学院学报,2003,14(1):70～73
[32] 唐斌,肖先赐. 基于高阶统计的空间信号频率与二维到达方向估计. 信号处理,2000,16(1):74～78
[33] Nikias C L, Mendel J M. Signal processing with higher-order spectral. IEEE Signal Processing Mag., 1993, 10(3): 10~37
[34] P. O. Amblard, J. M. Brossier. Adaptive estimation of the fourth-order cumulant of a white stochastic process. Signal Processing, 1995(42): 37~43
[35] 樊养余,孙进才,李平安等. 基于高阶谱的舰船辐射噪声特征提取[J]. 声学学报,1999,24(6):611～616
[36] 唐祖强,杨知行,潘长勇. 基于LMK准则的盲自适应多用户检测器. 电子学报,2000(4):40～42
[37] Wei Yu, Huang Chang, Sun Debao. The Detection of the Linear Frequency Modulated Signal by Fractional Fourier Transform. in: Guang Fan Shi eds. Proceedings of the 2nd International Conference on Information Technology for Application. Harbin, China. 2004. Harbin: Technical Programme Committee,
2004.
[38] Comon P. MA. Identification using fourth order cumulants. Signal Processing, 1992, 26: 381~388
[39] C. B. Papadias. Globally convergent blind source separation based on a multiuser kurtosis maximization criterion. IEEE Trans. Signal Processing, 2000, 48(12): 3508~3519
[40] J. F. Cardoso. Source separation using higher order moments. Proc. ICASSP 89, Glasgow, Scotland, May, 1989(4): 2109~2112
[41] 李英祥,肖先赐. 低信噪比下线性调频信号检测与参数估计. 系统工程与电子技术,2002,24(8):43～46
[42] 陈光化,马世伟,曹家麟. 基于分数阶傅立叶变换的自适应时频表示. 系统工程与电子技术,2001,23(4):69～71
[43] 吴新余,周井泉,沈元隆. 信号与系统——时域、频域分析及MATLAB软件的应用. 第1版. 北京:电子工业出版社,1999. 1～126
[44] 张海勇. 基于局域波法的非平稳随机信号分析中若干问题的研究:[博士学位论文]。大连:大连理工大学图书馆,2001.
[45] 孙晓昶,皇甫堪. 基于Wigner2Hough变换的多分量LFM信号检测及离散计算方法. 电子学报,2003,31(2):241～244
[46] 丁康,陈健林,苏向荣. 平稳和非平稳振动信号的若干处理方法及发展. 振动工程学报,2003,16(1):1～10
[47] 胡娟,张军. 时频分布与雷达信号的多目标分辨. 雷达与对抗,2003(3):26～29
[48] 郭汉伟,梁甸农,董臻. 不同时频分析方法综合检测信号. 信号处理,2003,19(6):586～589
[49] 邹红星,周小波,李衍达. 时频分析:回溯与前瞻. 电子学报,2000,28(9): 78～84
[50] 于风芹,姚旭辉,曹家麟. 分数阶傅立叶变换的若干问题. 江南大学学报(自然科学版),2002,1(4):349～353
[2] 赵国庆. 雷达对抗原理. 第1版. 西安:西安电子科技大学出版社,1999. 1～8
[3] 张义军. 基于高阶统计量的舰船辐射噪声特征提取及分类识别研究:[硕士学位论文]。西安:西安工业大学图书馆,2001.
[4] 徐春光. 非平稳信号的时频分析与处理方法研究:[博士学位论文]。西安:西安电子科技大学图书馆,1999.
[5] L.科恩. 时-频分析:理论与应用. 第1版. 白居宪. 西安:西安交通大学出版社,1998. 1～21,94～111
[6] L. Cohen. Time-frequency distributions – a review. Proc. IEEE, 1989, 77: 941~981
[7] S. Stankovic, L. J. Stankovic, Z. Uskokovic. On the local frequency, group shift, and cross-terms in some multidimensional time-frequency distributions: A method for multidimensional time-frequency analysis. IEEE Trans. on Signal Processing, 1995, 43(7): 1719~1724
[8] F. Patrick, G. B. Richard, M. Olivier. Time-frequency complexity and information. ICASSP’94, 1994, 3: 329~332
[9] F. Peyrin, R. A. Prost. A unified definition for the discrete-time, discrete-frequency, and discrete-time/frequency Wigner distribution. IEEE Trans. on Acoustic, Speech and Signal Processing, 1986, 34(4): 858~867
[10] K. M. M. Prabhu, R. S. Sundaram. Some results on fixed-point error analysis of Wigner-Ville distribution. Signal Processing, 1996, 51(3): 235~240
[11] B. Boashash, P. Black. An efficient real time implementation of the Wigner-Ville distribution. IEEE Trans. on Acoustic, Speech, and Signal Processing, 1987, 35(11): 1611~1618
[12] L. B. Almeida. The Fractional Transform and Time-frequency Representation. IEEE Trans. on Signal Processing , 1994(11):3084~3091
[13] A. W. Lachmann, B. H. Soffer. Relationship between the Radon-Wigner and fractional Fourier transform. Journal of Optics Society of American, 1994, 11: 1798~1801
[14] P. Soo-Chang, Y. Min-Hung. Fractional time-frequency distributions. Proc. of 1997 Int. Sym. on Circuit and Systems, ISCAS’97, 4: 2673~2676
[15] T. Alieva, A. M. Barbe. Fractional Fourier and Radon-Wigner transform of periodic signals. Signal Processing, 1998, 69(2): 183~190
[16] 张贤达,保铮. 非平稳信号分析与处理. 第1版. 北京:国防工业出版社,1998. 7,46～58,153～178,186～221
[17] Namias V. The Fractional Order Fourier Transform and Its Application to Quantum Mechanics. J. Inst. Math. Appl., 1980(25): 241~265
[18] 张贤达. 时间序分析——高阶统计量方法. 第1版. 北京:清华大学出版社,1996. 1～20
[19] 万小磊. 常规雷达目标双谱特征分析及应用:[硕士学位论文]。西安:西安电子科技大学图书馆,1999.
[20] Anabthram, Swami, Georgios B. et al. Bibliography on Higher-Order Statistics, Signal Processing, 1997, 60: 65~126
[21] 姚天任,孙洪. 现代数字信号处理. 第1版. 武汉:华中理工大学出版社,1999. 184～205
[22] G. B. Giannakis. Cumulants: A powerful tool in signal processing. Proc. IEEE, 1987, 75(9): 1333~1334
[23] 张安清,章新华. 四阶累积量的递推估计及其应用. 信号处理,2002,18(1):88～90
[24] Mendel J M. Tutorial on higher order statistics(spectra) in signal processing and system thoery: Theoretical results and some applications. Proc of IEEE., 1991, 79(3): 278~305
[25] 张贤达,保铮. 通信信号处理. 第1版. 北京:国防工业出版社,2000. 94～
102,277～280,383~389
[26] 孙晓兵,保铮. 分数阶傅立叶变换及其应用. 电子学报,1996,24(12):60～65
[27] 赵兴浩,陶然,周思永等. 基于Radon-Ambiguity变换和分数阶傅立叶变换的chirp信号检测及多参数估计. 北京理工大学学报,2003, 23(3):371～377
[28] Ozaktas H M, Kutay M A. Digital computation of the fractional Fourier transform[J]. IEEE Trans Signal Processing, 1996, 44(9):2141~2150
[29] 齐林,陶然,周思永等. 基于分数阶Fourier变换的多分量LFM信号的检测和参数估计. 中国科学(E辑),2003,33(8):749～759
[30] O. Akay, G. F. Boudreaux-Bartels. Fractional convolution and correlation via operator methods and an application to detection of linear FM signals. IEEE Trans. Sig-Proc., 2001, 49(5): 979~993
[31] 王宏艳,吴彦鸿,叶伟等. 分数阶Fourier变换在SAR动目标检测中的应用. 装备指挥技术学院学报,2003,14(1):70～73
[32] 唐斌,肖先赐. 基于高阶统计的空间信号频率与二维到达方向估计. 信号处理,2000,16(1):74～78
[33] Nikias C L, Mendel J M. Signal processing with higher-order spectral. IEEE Signal Processing Mag., 1993, 10(3): 10~37
[34] P. O. Amblard, J. M. Brossier. Adaptive estimation of the fourth-order cumulant of a white stochastic process. Signal Processing, 1995(42): 37~43
[35] 樊养余,孙进才,李平安等. 基于高阶谱的舰船辐射噪声特征提取[J]. 声学学报,1999,24(6):611～616
[36] 唐祖强,杨知行,潘长勇. 基于LMK准则的盲自适应多用户检测器. 电子学报,2000(4):40～42
[37] Wei Yu, Huang Chang, Sun Debao. The Detection of the Linear Frequency Modulated Signal by Fractional Fourier Transform. in: Guang Fan Shi eds. Proceedings of the 2nd International Conference on Information Technology for Application. Harbin, China. 2004. Harbin: Technical Programme Committee,
2004.
[38] Comon P. MA. Identification using fourth order cumulants. Signal Processing, 1992, 26: 381~388
[39] C. B. Papadias. Globally convergent blind source separation based on a multiuser kurtosis maximization criterion. IEEE Trans. Signal Processing, 2000, 48(12): 3508~3519
[40] J. F. Cardoso. Source separation using higher order moments. Proc. ICASSP 89, Glasgow, Scotland, May, 1989(4): 2109~2112
[41] 李英祥,肖先赐. 低信噪比下线性调频信号检测与参数估计. 系统工程与电子技术,2002,24(8):43～46
[42] 陈光化,马世伟,曹家麟. 基于分数阶傅立叶变换的自适应时频表示. 系统工程与电子技术,2001,23(4):69～71
[43] 吴新余,周井泉,沈元隆. 信号与系统——时域、频域分析及MATLAB软件的应用. 第1版. 北京:电子工业出版社,1999. 1～126
[44] 张海勇. 基于局域波法的非平稳随机信号分析中若干问题的研究:[博士学位论文]。大连:大连理工大学图书馆,2001.
[45] 孙晓昶,皇甫堪. 基于Wigner2Hough变换的多分量LFM信号检测及离散计算方法. 电子学报,2003,31(2):241～244
[46] 丁康,陈健林,苏向荣. 平稳和非平稳振动信号的若干处理方法及发展. 振动工程学报,2003,16(1):1～10
[47] 胡娟,张军. 时频分布与雷达信号的多目标分辨. 雷达与对抗,2003(3):26～29
[48] 郭汉伟,梁甸农,董臻. 不同时频分析方法综合检测信号. 信号处理,2003,19(6):586～589
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