基于小波变换的直扩信号检测算法研究
摘要
直接扩频序列(DSSS)信号具有伪随机编码调制和信号相关处理两大特点，使得其存在许多优点，如抗噪声、抗干扰、低功率谱密度下工作、有保密性、可多址复用和任意选址、高精度测量等，目前已经在数字通信中的诸多领域，如保密通信、多址通信、卫星导航定位中得到了广泛的应用。
目前对扩频信号的研究都是基于扩频序列已知这一前提下进行的。然而在非协作通信中，接收机并不知道DSSS中所使用的具体的扩频序列。在这种条件下怎样把信号从被噪声淹没的状态中检测出来就成了此系统必须要首先解决的一个问题。
在实际信号处理过程中，采集到的信号包含大量噪声，为了提取含噪信号中的有用信号，必须采用某种方法将噪声从信号中滤除。小波是近十几年发展起来的信号处理技术，是傅立叶分析的新发展，是一种能同时在时间域频率域内进行局部分析的信号分析技术，模极大值变换具有检测信号奇异性和突变结构的优势，因此能更准确的得到信号上特定点的奇异信息。因为信号和噪声在小波下表现出截然不同的性质，所以小波分析能用在信噪分离上。由于DSSS信号固有的强自相关性和弱互相关性，在经过模极大值变换的消噪处理后，仍然能够通过对观测数据的自相关函数进行多次累积来检测出噪声中是否存在DSSS信号。
本文详细介绍了小波变换模极大值去噪的原理，从DSSS信号的特征出发，以BPSK信号为例研究了自相关检测方法。最后对基于小波变换的直扩信号的检测系统用Matlab软件进行了仿真，验证了该方法的可行性。
The communication system of direct-sequence spread-spectrum (DSSS) has two characteristics of stochastic coding modulate and signal correlation processing, which make it has many excellence, such as restraining noise and interference, working under low density of spectrum, keeping secret, multi-address and choosing address arbitrarily .measure in high precision and so on. Now it is widely used in many areas of numeric communication, such as keeping secret communication, multi-address communication, secondary planet navigate positioning system.
Now researching on DSSS is based on knowing the PN serial .But in anti-collaboration communication, the receiving doesn't know the PN serial that DSSS uses. In this case, how to detect the message becomes the first important problem that must to be solved.
In the real signal processing, the signal we get always contains lots of noise. In order to get the useful message from the signal with noise, we must use some methods to de-noise in the message. Wavelet is a signal processing technology that develops recently, and it is the development of Fourier, which is a signal processing method that can analysis signal locally both in time-area and frequency-area. Wavelet transforms modulus maxima has predominance in detecting the singularity and break configuration of the signal, so it can get the singularity message on the given signal nicely. Signal and noise shows different properties through wavelet transform, so wavelet can be used to separate the signal and the noise. Because of the inherence characteristics such as auto-correlation and cross-correlation, by de-noising using modulus maxima, we can observe the data's function of auto-correlation which is cumulated many times to detect whether there is DSSS or not.
This thesis has introduced in detail the principles of wavelet transform modulus maxima de-noising method and studied the auto-correlation detection method of the DSSS signal based on the features of the DSSS signal, taking the BPSK signal as an example. Finally, simulation is given in this paper, using Matlab to validate the research on detecting direct spread signal based on wavelet transform method.
目前对扩频信号的研究都是基于扩频序列已知这一前提下进行的。然而在非协作通信中，接收机并不知道DSSS中所使用的具体的扩频序列。在这种条件下怎样把信号从被噪声淹没的状态中检测出来就成了此系统必须要首先解决的一个问题。
在实际信号处理过程中，采集到的信号包含大量噪声，为了提取含噪信号中的有用信号，必须采用某种方法将噪声从信号中滤除。小波是近十几年发展起来的信号处理技术，是傅立叶分析的新发展，是一种能同时在时间域频率域内进行局部分析的信号分析技术，模极大值变换具有检测信号奇异性和突变结构的优势，因此能更准确的得到信号上特定点的奇异信息。因为信号和噪声在小波下表现出截然不同的性质，所以小波分析能用在信噪分离上。由于DSSS信号固有的强自相关性和弱互相关性，在经过模极大值变换的消噪处理后，仍然能够通过对观测数据的自相关函数进行多次累积来检测出噪声中是否存在DSSS信号。
本文详细介绍了小波变换模极大值去噪的原理，从DSSS信号的特征出发，以BPSK信号为例研究了自相关检测方法。最后对基于小波变换的直扩信号的检测系统用Matlab软件进行了仿真，验证了该方法的可行性。
The communication system of direct-sequence spread-spectrum (DSSS) has two characteristics of stochastic coding modulate and signal correlation processing, which make it has many excellence, such as restraining noise and interference, working under low density of spectrum, keeping secret, multi-address and choosing address arbitrarily .measure in high precision and so on. Now it is widely used in many areas of numeric communication, such as keeping secret communication, multi-address communication, secondary planet navigate positioning system.
Now researching on DSSS is based on knowing the PN serial .But in anti-collaboration communication, the receiving doesn't know the PN serial that DSSS uses. In this case, how to detect the message becomes the first important problem that must to be solved.
In the real signal processing, the signal we get always contains lots of noise. In order to get the useful message from the signal with noise, we must use some methods to de-noise in the message. Wavelet is a signal processing technology that develops recently, and it is the development of Fourier, which is a signal processing method that can analysis signal locally both in time-area and frequency-area. Wavelet transforms modulus maxima has predominance in detecting the singularity and break configuration of the signal, so it can get the singularity message on the given signal nicely. Signal and noise shows different properties through wavelet transform, so wavelet can be used to separate the signal and the noise. Because of the inherence characteristics such as auto-correlation and cross-correlation, by de-noising using modulus maxima, we can observe the data's function of auto-correlation which is cumulated many times to detect whether there is DSSS or not.
This thesis has introduced in detail the principles of wavelet transform modulus maxima de-noising method and studied the auto-correlation detection method of the DSSS signal based on the features of the DSSS signal, taking the BPSK signal as an example. Finally, simulation is given in this paper, using Matlab to validate the research on detecting direct spread signal based on wavelet transform method.
引文
[1] Urkowitz H. Energy Detection of Unknown Deterministic Signal. Proc. IEEE, 1967, 55(4): 523～531
[2] Polydoros A, Weber C. Detection performance Considerations for Direct-Sequence and Time-Hopping LPI Waveforms. IEEE journal on Selected Areas in Communications. 1985, 3(5): 727-744
[3] D. E. Reed, M. A. Wickert. Minimization of Detection of Symbol-rate-Spectral lines by Delay and Multiply Receivers. IEEE Trans. on Connunications. 1988, 36(1): 118-120
[4] French C A, Gardner W. A. Spread-spectrum despreading without the code. IEEE Transactions on Communications. 1986, 34(4): 404-407
[5] Wickert. M A, Turcotte R L. Rate2Line Detection Using Higher-Order Spectra. Proc. Milcom'92. 1992, 10: 1221～1225
[6] Hill D A, Bodie J B. Carrier detection of PSK signals. IEEE Trans on Communications. 2001, 49(3)
[7] Gardner. W A measurement of Spectral Correlation. IEEE Trans. on ASSP.1986, 34(5): 1111-1123
[8] Gardner W A, Spooner C M. Signal Interception: Performance Advantages of Cyclic-Feature Detectors. IEEE trans, on Communications. 1992, 40 (1): 149-159
[9] 余敬东，郭伟，李牧．直接序列扩频通信的循环谱检测和参数估计技术．电子科技大学学报．1996，25(9)：439-443
[10] 罗来源，肖先赐．扩频信号分路相关检测器的性能分析．电子科学学刊．1998，20(4)：474-479
[11] 张建立．直扩信号的检测．无线电工程．1994，24(2)：19-21
[12] 何哲平，肖先赐．BPSK信号检测的小波相关法．信号处理．1999，15(4)： 81-84
[13] 游凌．DS直扩信号参数隐周期特征分析法．信号处理．2000，16(4)：8-14
[14] 孟建，胡来招．直扩信号检测的相关积累技术．电子对抗技术．2001，16(2)1-4
[15] 黄春琳，姜文利，周一宇．低截获概率雷达信号的循环谱相关函数检测方法分析[J]．国防科技大学学报．2001，23(4)：102-106
[16] 冯富强，陈鹏举，等．低信噪比条件下DS信号的检测和参数估计[J]．通信学报．2002，23(9)：64-67
[17] 丁国栋，向新，张敬利，等．高斯白噪背景下的直扩信号检测．空军工程大学学报．2003，4(2)：59-61
[18] 牟青，魏平．DS／SS信号检测与估计的性能．航天电子对抗．2004(2)：50-53
[19] 袁亮，刘基南，温志津．一种低信噪比直扩信号的检测．现代电子技术．2005，(5)：50-51
[20] Gilles Burel, Celine Bounder. Blind Estimation of the Pseudo—Random Sequence of a Direct Sequence Spread Spectrum Signal. IEEE—MILCOM [c]. 2000
[21] JANSEN M, BULTHEEL A. Multiple wavelet threshold estimation noise. IEEE Transactions on Image Processing. 1999, 8(7): 947-953
[22] Rioul O, and Vellerli M. Wavelets and Signal Processing. IEEE Signal Processing Magzine. 1991, 8(4): 14-38
[23] Donoho D L, De-noising by soft-threshold. IEEE Transaction on information theory. 1995, 41(3): 613-627
[24] Donoho D L. Adapting to unknown smoothness wavelet shrinkage. Amer Statistic Assoc. 1995, 90(432): 231-245
[25] ]Pan Q, zhang L, Dai G et al. Two denoising method by wavelet transform. IEEE Transaction on Signal Processing. 1999(47): 456-589
[26] Nath S K. wavelet based suppression and denoising of tomography data. Optics Communication. 1999, (167): 37-46
[27] KARIM G O, DAVID J A, Noise reduction in mulitchannel neural recording using a new array wavelet denoising algorithm. Neurocomputing. 2001, 38(4): 1687-1693
[28] THOMAS T L, ANTONY C S. Detection of transients in I/f noise with the undecimated discrete wavelet transform. IEEE Transaction on Signal Processing. 2000, 48(5): 1458-1462
[29] Stephane Mallat. A Theroy for Multiresolution Signal Decomposition the Wavelet Representation. IEEE Trans. Pattern Anal. Mach. Intell. 1998, 11(7): 674-693
[30] Pan Q, zhang L, Dal Get al. Two denoising method by wavelet transform. IEEE Transaction on Signal Processing. 1999, 47, 456-589
[31] Nath S K. wavelet based suppression and denoising oftomography data. Optics Communication. 1999, (167): 37-46
[32] 查光明，熊贤祚．扩频通信．西安：西安电子科技大学出版社，1990．
[33] CHIU H. An improved sequential estimation scheme for PN acquisition. IEEE Trans. 1988, 36(10): 1182-1184
[34] ]LAURENCE B M. Interference techniques in spread spectrum communications. Processing of the IEEE. 1988, 76(6): 102-111
[35] Tazebay Mehmet V, Aksansu Ali N, Adaptive Sub band Transforms in Time-Frequency Exciters for DSSS Commtmication System. IEEE Trans. on Signal Processing, 1995: 276-282
[36] Branislav and M Popovic. Spreading Sequences for Multicarrier CDMA Systems. IEEE Transactions on communications. 1999, 147(6)
[37] Gardner W A, Signal intercepition: a unifying theoretical framework for feature detection. IEEE Trans Commun. 1988, 36(8): 897～906
[38] Gardner W A, Spooner C M. Detection and source location of weak cyclostationary signlas: simplifications of the maxmium likeihood receiver. IEEE Yrans Commun. 1993, 41(6): 905～916
[39] I. Daubechies. The Wavelet transform: Time-Frequency Localization and Signal Analysis, IEEE Trans. On Information Theory. 1990, 36(5): 961-1005
[40] JANSEN M, BULTHEEL A. Multiple wavelet threshold estimation noise. IEEE Transactions on Image Processing. 1999, 8(7): 947-953
[41] Donoho D L. Adapting to unknown smoothness wavelet shrinkage. Amer Statistic Assoc. 1995, 90(432): 231-245
[42] Stephane Mallat. A Theroy for Multiresolution Signal Decomposition the Wavelet Representation. IEEE Trans. Pattern Anal.Mach. Intell. 1998, 11(7): 674-693
[43] 胡昌华．基于MATLAB的系统分析与设计——小波分析．西安：西安电子科技大学出版社，1999
[44] Mallat S. and zhong S. Characterization of signals from multiscale edges. IEEE Trans. On PAMI. 1992, 14(7): 710-732
[45] 张晓春．小波变换在奇异信号检测中的应用．传感器技术．2002，21(3)：33-35
[46] 冉启文．小波分析方法及其应用．哈尔滨：哈尔滨工业大学出版社，1995
[47] Madhow U, HonigM L. MMSE Interference Suppression of Direct Spread-Spectrum CDMA. IEEE Trans on Comm. 1994, 3178-3188
[48] Vikram Frishnamurthy. George Yin. Sumetpal Singh. Adaptive Step-size Algorithms for Blind Interference Suppression in DS/CDMA System. IEEE Trans. on Signal Processing. 2001, 49(1): 190-201
[49] S. G. Mallat, Characterization of signals From Multiscales Edges, NYU, Computer Science Tech, Report, 1991
[50] R. Hummel, R. Moniot. Reconstruction from Zero-Crossing in Scale Space. IEEE Trans. Acoustic Speech Signal Processing. 37(12), 1989
[51] A. Yuille, T. Poggio. Scale Theorems for Zero Crossing. IEEE Trans. Patt. Anal. Machine Intell. PAMI-8(1)1986
[52] Y. Meyer, Un Contre-example a la Conjecture de Marr et al. Celle de S. Mallat. Preprint, 1991
[53] S. Mallat,Zero_Crossing of a Wavelet Transform. IEEE Trans. Infor. Theory. 1991, 37(7)
[54] MALLAT S G. Characterization of signals From Multiscales Edges. IEEE Trans Patt Anal Machine Intell. 1992, 14 (7): 326-351
[55] I. Daubechies. Orthonormal Bases of Commpactly Supported Wavelets Common. Pure and Appti. Math. XLT, 1998
[56] Donoho D L. De-noising by soft-threshold. IEEE Transaction on information theory. 1995, 41(3): 613-627
[57] 程正兴．小波分析算法与应用．西安：西安交通大学出版社，1997
[58] 徐佩霞，孙功宪．小波分析与应用实例．北京：中国科学技术大学出版社，1997
[2] Polydoros A, Weber C. Detection performance Considerations for Direct-Sequence and Time-Hopping LPI Waveforms. IEEE journal on Selected Areas in Communications. 1985, 3(5): 727-744
[3] D. E. Reed, M. A. Wickert. Minimization of Detection of Symbol-rate-Spectral lines by Delay and Multiply Receivers. IEEE Trans. on Connunications. 1988, 36(1): 118-120
[4] French C A, Gardner W. A. Spread-spectrum despreading without the code. IEEE Transactions on Communications. 1986, 34(4): 404-407
[5] Wickert. M A, Turcotte R L. Rate2Line Detection Using Higher-Order Spectra. Proc. Milcom'92. 1992, 10: 1221～1225
[6] Hill D A, Bodie J B. Carrier detection of PSK signals. IEEE Trans on Communications. 2001, 49(3)
[7] Gardner. W A measurement of Spectral Correlation. IEEE Trans. on ASSP.1986, 34(5): 1111-1123
[8] Gardner W A, Spooner C M. Signal Interception: Performance Advantages of Cyclic-Feature Detectors. IEEE trans, on Communications. 1992, 40 (1): 149-159
[9] 余敬东，郭伟，李牧．直接序列扩频通信的循环谱检测和参数估计技术．电子科技大学学报．1996，25(9)：439-443
[10] 罗来源，肖先赐．扩频信号分路相关检测器的性能分析．电子科学学刊．1998，20(4)：474-479
[11] 张建立．直扩信号的检测．无线电工程．1994，24(2)：19-21
[12] 何哲平，肖先赐．BPSK信号检测的小波相关法．信号处理．1999，15(4)： 81-84
[13] 游凌．DS直扩信号参数隐周期特征分析法．信号处理．2000，16(4)：8-14
[14] 孟建，胡来招．直扩信号检测的相关积累技术．电子对抗技术．2001，16(2)1-4
[15] 黄春琳，姜文利，周一宇．低截获概率雷达信号的循环谱相关函数检测方法分析[J]．国防科技大学学报．2001，23(4)：102-106
[16] 冯富强，陈鹏举，等．低信噪比条件下DS信号的检测和参数估计[J]．通信学报．2002，23(9)：64-67
[17] 丁国栋，向新，张敬利，等．高斯白噪背景下的直扩信号检测．空军工程大学学报．2003，4(2)：59-61
[18] 牟青，魏平．DS／SS信号检测与估计的性能．航天电子对抗．2004(2)：50-53
[19] 袁亮，刘基南，温志津．一种低信噪比直扩信号的检测．现代电子技术．2005，(5)：50-51
[20] Gilles Burel, Celine Bounder. Blind Estimation of the Pseudo—Random Sequence of a Direct Sequence Spread Spectrum Signal. IEEE—MILCOM [c]. 2000
[21] JANSEN M, BULTHEEL A. Multiple wavelet threshold estimation noise. IEEE Transactions on Image Processing. 1999, 8(7): 947-953
[22] Rioul O, and Vellerli M. Wavelets and Signal Processing. IEEE Signal Processing Magzine. 1991, 8(4): 14-38
[23] Donoho D L, De-noising by soft-threshold. IEEE Transaction on information theory. 1995, 41(3): 613-627
[24] Donoho D L. Adapting to unknown smoothness wavelet shrinkage. Amer Statistic Assoc. 1995, 90(432): 231-245
[25] ]Pan Q, zhang L, Dai G et al. Two denoising method by wavelet transform. IEEE Transaction on Signal Processing. 1999(47): 456-589
[26] Nath S K. wavelet based suppression and denoising of tomography data. Optics Communication. 1999, (167): 37-46
[27] KARIM G O, DAVID J A, Noise reduction in mulitchannel neural recording using a new array wavelet denoising algorithm. Neurocomputing. 2001, 38(4): 1687-1693
[28] THOMAS T L, ANTONY C S. Detection of transients in I/f noise with the undecimated discrete wavelet transform. IEEE Transaction on Signal Processing. 2000, 48(5): 1458-1462
[29] Stephane Mallat. A Theroy for Multiresolution Signal Decomposition the Wavelet Representation. IEEE Trans. Pattern Anal. Mach. Intell. 1998, 11(7): 674-693
[30] Pan Q, zhang L, Dal Get al. Two denoising method by wavelet transform. IEEE Transaction on Signal Processing. 1999, 47, 456-589
[31] Nath S K. wavelet based suppression and denoising oftomography data. Optics Communication. 1999, (167): 37-46
[32] 查光明，熊贤祚．扩频通信．西安：西安电子科技大学出版社，1990．
[33] CHIU H. An improved sequential estimation scheme for PN acquisition. IEEE Trans. 1988, 36(10): 1182-1184
[34] ]LAURENCE B M. Interference techniques in spread spectrum communications. Processing of the IEEE. 1988, 76(6): 102-111
[35] Tazebay Mehmet V, Aksansu Ali N, Adaptive Sub band Transforms in Time-Frequency Exciters for DSSS Commtmication System. IEEE Trans. on Signal Processing, 1995: 276-282
[36] Branislav and M Popovic. Spreading Sequences for Multicarrier CDMA Systems. IEEE Transactions on communications. 1999, 147(6)
[37] Gardner W A, Signal intercepition: a unifying theoretical framework for feature detection. IEEE Trans Commun. 1988, 36(8): 897～906
[38] Gardner W A, Spooner C M. Detection and source location of weak cyclostationary signlas: simplifications of the maxmium likeihood receiver. IEEE Yrans Commun. 1993, 41(6): 905～916
[39] I. Daubechies. The Wavelet transform: Time-Frequency Localization and Signal Analysis, IEEE Trans. On Information Theory. 1990, 36(5): 961-1005
[40] JANSEN M, BULTHEEL A. Multiple wavelet threshold estimation noise. IEEE Transactions on Image Processing. 1999, 8(7): 947-953
[41] Donoho D L. Adapting to unknown smoothness wavelet shrinkage. Amer Statistic Assoc. 1995, 90(432): 231-245
[42] Stephane Mallat. A Theroy for Multiresolution Signal Decomposition the Wavelet Representation. IEEE Trans. Pattern Anal.Mach. Intell. 1998, 11(7): 674-693
[43] 胡昌华．基于MATLAB的系统分析与设计——小波分析．西安：西安电子科技大学出版社，1999
[44] Mallat S. and zhong S. Characterization of signals from multiscale edges. IEEE Trans. On PAMI. 1992, 14(7): 710-732
[45] 张晓春．小波变换在奇异信号检测中的应用．传感器技术．2002，21(3)：33-35
[46] 冉启文．小波分析方法及其应用．哈尔滨：哈尔滨工业大学出版社，1995
[47] Madhow U, HonigM L. MMSE Interference Suppression of Direct Spread-Spectrum CDMA. IEEE Trans on Comm. 1994, 3178-3188
[48] Vikram Frishnamurthy. George Yin. Sumetpal Singh. Adaptive Step-size Algorithms for Blind Interference Suppression in DS/CDMA System. IEEE Trans. on Signal Processing. 2001, 49(1): 190-201
[49] S. G. Mallat, Characterization of signals From Multiscales Edges, NYU, Computer Science Tech, Report, 1991
[50] R. Hummel, R. Moniot. Reconstruction from Zero-Crossing in Scale Space. IEEE Trans. Acoustic Speech Signal Processing. 37(12), 1989
[51] A. Yuille, T. Poggio. Scale Theorems for Zero Crossing. IEEE Trans. Patt. Anal. Machine Intell. PAMI-8(1)1986
[52] Y. Meyer, Un Contre-example a la Conjecture de Marr et al. Celle de S. Mallat. Preprint, 1991
[53] S. Mallat,Zero_Crossing of a Wavelet Transform. IEEE Trans. Infor. Theory. 1991, 37(7)
[54] MALLAT S G. Characterization of signals From Multiscales Edges. IEEE Trans Patt Anal Machine Intell. 1992, 14 (7): 326-351
[55] I. Daubechies. Orthonormal Bases of Commpactly Supported Wavelets Common. Pure and Appti. Math. XLT, 1998
[56] Donoho D L. De-noising by soft-threshold. IEEE Transaction on information theory. 1995, 41(3): 613-627
[57] 程正兴．小波分析算法与应用．西安：西安交通大学出版社，1997
[58] 徐佩霞，孙功宪．小波分析与应用实例．北京：中国科学技术大学出版社，1997