混合混沌扩频序列的生成与性能分析
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摘要
码分多址(Code Division Multiple Access)是一种崭新而成熟的无线通信技术,在现代通信系统中有着广泛的应用。设计出数量足够多的、具有优良相关特性的扩频码是CDMA的技术基础,以满足多用户的需求。现有普遍应用在CDMA系统中的地址码是由最大长度线性移位寄存器生成的m序列以及Gold序列,虽然易于实现但是它们有长度和数量受限的缺陷。
混沌现象的发现和混沌理论的成熟为扩频序列的研究提供了新思路。混沌现象是一种在非线性系统中出现的确定类随机过程,这种现象具有非周期、不收敛和对初值具有高度敏感性的特点。利用混沌映射可以产生数量众多具有优良相关特性的伪随机序列。
本文主要围绕着数字混沌扩频序列展开研究。以Logistic和Chebyshev映射序列为代表,对序列的平衡性、相关性及旁瓣峰值和均方值进行了仿真分析。在上述研究的基础上,编制优选算法对混沌序列进行优选,并将优选序列应用到CDMA的系统模型中,最后给出了该模型在加性高斯噪声(Additive White Gaussian Noise,AWGN)信道模型下的单用户和多用户的误码率性能。仿真结果表明,上述混沌序列适合作为CDMA通信系统中的地址码。
在对混沌序列性能分析的基础上,针对传统单峰映射生成扩频序列复杂度低,抗截获性能差的缺陷,本文提出了一种利用串联结构的混合映射模型产生混沌扩频序列的方法,并对序列的相关性、平衡性以及游程性进行了仿真分析。在序列的优选上,给出了一种根据初值区域来产生源序列作为搜索目标的方法,然后将优选序列应用于CDMA系统中仿真。结果表明,由这种混合映射模型产生的混沌扩频序列具有优良的性能和较高的保密性。
Code Division Multiple Access is one kind of new and mature wireless communication technique, which has a great deal of applications in modern communication system. Designing a sufficient number of spread spectrum codes, which have excellent characteristics, are the basis of CDMA technology in order to meet the needs of many users. Commonly used in CDMA systems address code is generated by the maximum length of a linear shift register sequences such as m and Gold sequences, though easily to implement they have a length and quantity limited number of defects.
The discovery of chaotic phenomenon and the maturity of chaotic theory offer the broad way of PN sequence. The chaos phenomenon is one kind of convinced and random course that appears in nonlinear system, which has the characteristic of a non-periodic, non-convergence and highly sensitive to initial values. Making use of chaotic mapping can generate enough PN sequence with good correlation property.
This paper mainly centers on research of the chaotic digital spread-spectrum sequence. With Logistic and Chebyshev sequence represented, the balance, relevance and side-lobe peak and mean square value and other properties of performance of chaotic sequences are analyzed and simulated. On the basis of study, the optimization algorithm was complied to prepare for optimizing the chaotic sequence, and the optimal sequences are applied to CDMA system model, finally gives the BER performance in single user and multi-user circumstances under Additive White Gaussian Noise channel. The simulation results show that these chaotic sequences are suitable as address code in the CDMA communication system.
Based on the analysis of the performance of chaotic sequence, aiming at overcoming the shortcoming that the spreading spectrums sequences generated by traditional single chaotic map has low complexity and poor performance against by intercepted, a method for generating chaotic spread-spectrum sequences based on the series hybrid mapping model was proposed, then do the simulation analysis about the performance of sequence such as correlation, balance, run-length and so on. In the sequence optimization process, this paper offers a method according to the initial value area to produce source sequence as a search target. Then make the simulation in the circumstances that optimal sequences are applied to CDMA system. The results of simulation show that the chaotic spread-spectrum sequences generated by the proposed method have good performance and more secure for communication.
混沌现象的发现和混沌理论的成熟为扩频序列的研究提供了新思路。混沌现象是一种在非线性系统中出现的确定类随机过程,这种现象具有非周期、不收敛和对初值具有高度敏感性的特点。利用混沌映射可以产生数量众多具有优良相关特性的伪随机序列。
本文主要围绕着数字混沌扩频序列展开研究。以Logistic和Chebyshev映射序列为代表,对序列的平衡性、相关性及旁瓣峰值和均方值进行了仿真分析。在上述研究的基础上,编制优选算法对混沌序列进行优选,并将优选序列应用到CDMA的系统模型中,最后给出了该模型在加性高斯噪声(Additive White Gaussian Noise,AWGN)信道模型下的单用户和多用户的误码率性能。仿真结果表明,上述混沌序列适合作为CDMA通信系统中的地址码。
在对混沌序列性能分析的基础上,针对传统单峰映射生成扩频序列复杂度低,抗截获性能差的缺陷,本文提出了一种利用串联结构的混合映射模型产生混沌扩频序列的方法,并对序列的相关性、平衡性以及游程性进行了仿真分析。在序列的优选上,给出了一种根据初值区域来产生源序列作为搜索目标的方法,然后将优选序列应用于CDMA系统中仿真。结果表明,由这种混合映射模型产生的混沌扩频序列具有优良的性能和较高的保密性。
Code Division Multiple Access is one kind of new and mature wireless communication technique, which has a great deal of applications in modern communication system. Designing a sufficient number of spread spectrum codes, which have excellent characteristics, are the basis of CDMA technology in order to meet the needs of many users. Commonly used in CDMA systems address code is generated by the maximum length of a linear shift register sequences such as m and Gold sequences, though easily to implement they have a length and quantity limited number of defects.
The discovery of chaotic phenomenon and the maturity of chaotic theory offer the broad way of PN sequence. The chaos phenomenon is one kind of convinced and random course that appears in nonlinear system, which has the characteristic of a non-periodic, non-convergence and highly sensitive to initial values. Making use of chaotic mapping can generate enough PN sequence with good correlation property.
This paper mainly centers on research of the chaotic digital spread-spectrum sequence. With Logistic and Chebyshev sequence represented, the balance, relevance and side-lobe peak and mean square value and other properties of performance of chaotic sequences are analyzed and simulated. On the basis of study, the optimization algorithm was complied to prepare for optimizing the chaotic sequence, and the optimal sequences are applied to CDMA system model, finally gives the BER performance in single user and multi-user circumstances under Additive White Gaussian Noise channel. The simulation results show that these chaotic sequences are suitable as address code in the CDMA communication system.
Based on the analysis of the performance of chaotic sequence, aiming at overcoming the shortcoming that the spreading spectrums sequences generated by traditional single chaotic map has low complexity and poor performance against by intercepted, a method for generating chaotic spread-spectrum sequences based on the series hybrid mapping model was proposed, then do the simulation analysis about the performance of sequence such as correlation, balance, run-length and so on. In the sequence optimization process, this paper offers a method according to the initial value area to produce source sequence as a search target. Then make the simulation in the circumstances that optimal sequences are applied to CDMA system. The results of simulation show that the chaotic spread-spectrum sequences generated by the proposed method have good performance and more secure for communication.
引文
[1]Husin Maimun Huja, Sabri Mohamad Faizrizwan Mohd, Marzuki Ade Syaheda Wani Lias Kasumawati Rahmat Mohd Fua'ad. Pseudo random binary sequence on second order system [C], ICCAE 2010:398-401
[2]Scheers Bart, Nir Vincent Le. Pseudo-random binary sequence selection for delay and add direct sequence spread spectrum modulation scheme. IEEE Communications Letters [J],2010, 14(11):1002-1004
[3]Sun Fuyan, Liu Shutang. Cryptographic pseudo-random sequence from the spatial chaotic map. Chaos, Solitons and Fractals,2009,41(5):2216-2219
[4]郝柏林.分岔、混沌、奇怪吸引子及其它.物理学进展.1995,3：374-415
[5]唐巍,李殿璞,陈学允.混沌理论及其应用研究[J].电力系统自动化,2000,24(10)：67-70
[6]Chen Yong, Zhao Hangsheng, Liang Tao. Design and performance analysis of chaotic spreading code and chaotic DSSS system [J], Journal of Information and Computational Science,2008,5(3):1077-1084
[7]杜月林,陆婷.混沌扩频序列在CDMA通信系统中的应用[J].国外电子测量技术,2006,25(7)：69-73
[8]雷利华,马冠一,蔡晓静,施浒立.基于Chebyshev映射的混沌序列研究[J].计算机工程.2009,35(24)4-6
[9]Yu Jue, Gan Lu, Li Liping. Design of a real sequence chaotic direct sequence spread spectrum communication system with realizable occupied bandwidth[C], ICCCAS,2009: 282-286
[10]郝柏林.一个统一混沌系统及其研究.北京：中国科学院研究生院(数学与系统科学研究院)博士学位论文,2002
[11]Hao BL. Chaos. Singapore:World Scientific,1984
[12]Lorenz E N.The Essence of Chaos. USA:University of Washington Press,1993
[13]于万波.混沌的计算实验与分析.北京：科学出版社,2008：12-43
[14]刘宗华.混沌动力学基础及其应用[M].北京：高等教育出版社.2006,11：4-8
[15]Chua L.O. Special issue on chaos. IEEE Trans. Circuits Syst-Ⅰ.1993,40 (10):927-936
[16]Pecora LM, Carroll TL. Synchronization in chaotic systems. Phys. Rev. Lett.1990,64 (8):821-824
[17]李春福.关于混沌信号的产生、处理及其在通信系统中应用的若干研究.电子科技大学博士学位论文.2001年
[18]尉志青.基于matlab对混沌掩盖通信的仿真研究[J].科技信息.2009,8(455)：526-527
[19]卢俊国,魏荣,王执铨.基于受激蔡氏电路混沌系统的混沌键控及最佳解调[J].电子学报.2002,7(30)：1003-1005
[20]赵华,吴勇,殷奎喜.通用差分混沌键控通信系统及其性能分析[J].通信技术.2009,2(42)：79-81
[21]李一兵,楼喆,李彬.一种新的复合混沌扩频序列[J].哈尔滨工程大学学报.2001,3(22)：76-78
[22]王宏霞,虞厥邦,Logistic-Map混沌扩频序列的有限精度实现新方法[J].系统工程与电子技术,2002,24(2)
[23]安澄全,周廷显,一类由混沌映射产生扩频序列的方法[J].遥测遥控.2002,3(8)
[24]任阳.混沌序列在扩频通信中的应用：[硕士学位论文].北京：北京化工大学,2009
[25]Kohda T, Tsuneda A. Psuedonoise Sequence by Chaotic Nonlinear Maps and Their Correlation Properties. IEICE Trans. On Commun.1993,76 (8):855-862
[26]赵春明,龙肖虎,程时昕.混沌序列的数字发生及其在通信中的应用[J].东南大学学报.1995,25(4)：137-141
[27]王亥,胡建栋.数字混沌扩频通信系统.北京邮电大学学报.1998,21(4)：7-11
[28]赵艳红,张春,吴楚.扩频通信中数字混沌序列的产生[J].信息工程大学学报.2000,1(3)：40-43
[29]龚剑扬,司锡才,蒯冲,等.基于串联结构的混沌序列[J].哈尔滨工程大学学报,2003,24(4)：436-439
[30]张剑,臧国珍,李广侠,一种混沌量化的混沌扩频序列[J].系统仿真学报.2009,21(14)：4450-4456
[31]T.Y. Li, J.A.Yorke, Period Three Implies Chaos,1995(5):3670-3678
[32]Guckenheimer J, Holmes P. Nonlinear Oscillation. Dynamical Systems and Bifurcations of Vector fields[M]. New York:Springer-Verlag.1984,453.
[33]刘秉正.非线性动力学与混沌基础[M].长春,东北师范大学出版社,1994.
[34]王亥,胡健栋Logistic-Map昆沌扩频序列.电子学报,1997,25(1)：19-23
[35]聂明新,卢凌,DS-CDMA系统的最佳混沌序列研究.武汉理工大学学报(交通科学与工程版),2001,25(3)：247-250
[36]Murali K, Lakshmanan M. Transmission of signals by synchronization in a chaotic Vander Pol-buffing oscillator. In:Phys Rev E.,1993,48(4):1624-1626
[37]J. Atmos. Lorenz E N. Deterministic nonperiodic flow. Sci.1963(20):130-141
[38]FUKUMASAH, KOHNO R, IMAI H. Design of pesudonoise sequence with good odd and even correlation properties for DS-CDMA[J]. IEEE JSAC,1994,12(5):828-835.
[39]朱近康.扩展频谱通信及其应用[M].合肥：中国科学技术大学出版社,1993,4：13-24
[40]田日才.扩频通信.清华大学出版社.2007
[41]胡健栋,郑朝辉,龙必起等.码分多址与个人通信.人民邮电出版社.1996
[42]Gold R. Maximal Recusive Sequence with 3-Valued Recusive Cross-Correlation Function IEEE.1968,14(10)
[43]Mazzini, G.., Setti, G.., Rovatti, R, Chaotic complex spreading sequences for asynchronous DS-CDMA. Ⅰ. System modeling and results; Circuits and Systems Ⅰ: Fundamental Theory and Applications, IEEE Transactions on Volume 44, Issue 10, Oct.1997 Page(s):937-947
[44]G. Heidari-Bateni, "Chaotic signals for digital communication", Ph. D. Dissertation, School of Electrical Engineering, Purdue University, W. Lafayette, IN, Dec.1992
[45]张琪,郑君里,孙守宇.混沌序列在准同步码分多址系统中的应用[J].清华大学学报(自然科学版),2003,43(4)：453-456
[46]李长庚,周家令,孙克辉,盛利元.四种数字混沌序列的平衡性分析[J].计算机应用,2008,28(1)：68-70
[47]Karkkainen K H. Meaning of Maximun and Mean-Square Cross-Correlation as a Performance as a Performance Measure for CDMA Code Families and Their Influence on System Capacity [J]. IEICE Trans. on Commun.1993, E76-B(8):848-854
[48]Sandoval-Morantes D, Munoz-Rodriguez D. Chaotic Sequences for Multiple Access [J]. Electronics Letters,1998,34(3):235-237
[49]米良,朱中梁.混沌直扩序列的优选及与传统序列的性能比较[J].系统工程与电子技术.2002,24(8)：117-120
[50]余振标,冯久超.一种混沌扩频序列的产生方法及其优选算法[J].物理学报.2008,57(3)：1409-1415
[51]刘庆玲.基于混沌理论的扩频码通信系统的研究：[硕士学位论文].哈尔滨工程大学,2005
[52]WaiM.Tam etc. Performance Analysis of Mutiple Access Chaotic Sequence Spread spectrum Communication Systems Employing Parallel Interference Cancellation[J]. IEEETrans,2003:208-211
[53]周家令.多用户混沌扩频通信系统的研究：[硕士学位论文].中南大学,2006
[2]Scheers Bart, Nir Vincent Le. Pseudo-random binary sequence selection for delay and add direct sequence spread spectrum modulation scheme. IEEE Communications Letters [J],2010, 14(11):1002-1004
[3]Sun Fuyan, Liu Shutang. Cryptographic pseudo-random sequence from the spatial chaotic map. Chaos, Solitons and Fractals,2009,41(5):2216-2219
[4]郝柏林.分岔、混沌、奇怪吸引子及其它.物理学进展.1995,3：374-415
[5]唐巍,李殿璞,陈学允.混沌理论及其应用研究[J].电力系统自动化,2000,24(10)：67-70
[6]Chen Yong, Zhao Hangsheng, Liang Tao. Design and performance analysis of chaotic spreading code and chaotic DSSS system [J], Journal of Information and Computational Science,2008,5(3):1077-1084
[7]杜月林,陆婷.混沌扩频序列在CDMA通信系统中的应用[J].国外电子测量技术,2006,25(7)：69-73
[8]雷利华,马冠一,蔡晓静,施浒立.基于Chebyshev映射的混沌序列研究[J].计算机工程.2009,35(24)4-6
[9]Yu Jue, Gan Lu, Li Liping. Design of a real sequence chaotic direct sequence spread spectrum communication system with realizable occupied bandwidth[C], ICCCAS,2009: 282-286
[10]郝柏林.一个统一混沌系统及其研究.北京：中国科学院研究生院(数学与系统科学研究院)博士学位论文,2002
[11]Hao BL. Chaos. Singapore:World Scientific,1984
[12]Lorenz E N.The Essence of Chaos. USA:University of Washington Press,1993
[13]于万波.混沌的计算实验与分析.北京：科学出版社,2008：12-43
[14]刘宗华.混沌动力学基础及其应用[M].北京：高等教育出版社.2006,11：4-8
[15]Chua L.O. Special issue on chaos. IEEE Trans. Circuits Syst-Ⅰ.1993,40 (10):927-936
[16]Pecora LM, Carroll TL. Synchronization in chaotic systems. Phys. Rev. Lett.1990,64 (8):821-824
[17]李春福.关于混沌信号的产生、处理及其在通信系统中应用的若干研究.电子科技大学博士学位论文.2001年
[18]尉志青.基于matlab对混沌掩盖通信的仿真研究[J].科技信息.2009,8(455)：526-527
[19]卢俊国,魏荣,王执铨.基于受激蔡氏电路混沌系统的混沌键控及最佳解调[J].电子学报.2002,7(30)：1003-1005
[20]赵华,吴勇,殷奎喜.通用差分混沌键控通信系统及其性能分析[J].通信技术.2009,2(42)：79-81
[21]李一兵,楼喆,李彬.一种新的复合混沌扩频序列[J].哈尔滨工程大学学报.2001,3(22)：76-78
[22]王宏霞,虞厥邦,Logistic-Map混沌扩频序列的有限精度实现新方法[J].系统工程与电子技术,2002,24(2)
[23]安澄全,周廷显,一类由混沌映射产生扩频序列的方法[J].遥测遥控.2002,3(8)
[24]任阳.混沌序列在扩频通信中的应用：[硕士学位论文].北京：北京化工大学,2009
[25]Kohda T, Tsuneda A. Psuedonoise Sequence by Chaotic Nonlinear Maps and Their Correlation Properties. IEICE Trans. On Commun.1993,76 (8):855-862
[26]赵春明,龙肖虎,程时昕.混沌序列的数字发生及其在通信中的应用[J].东南大学学报.1995,25(4)：137-141
[27]王亥,胡建栋.数字混沌扩频通信系统.北京邮电大学学报.1998,21(4)：7-11
[28]赵艳红,张春,吴楚.扩频通信中数字混沌序列的产生[J].信息工程大学学报.2000,1(3)：40-43
[29]龚剑扬,司锡才,蒯冲,等.基于串联结构的混沌序列[J].哈尔滨工程大学学报,2003,24(4)：436-439
[30]张剑,臧国珍,李广侠,一种混沌量化的混沌扩频序列[J].系统仿真学报.2009,21(14)：4450-4456
[31]T.Y. Li, J.A.Yorke, Period Three Implies Chaos,1995(5):3670-3678
[32]Guckenheimer J, Holmes P. Nonlinear Oscillation. Dynamical Systems and Bifurcations of Vector fields[M]. New York:Springer-Verlag.1984,453.
[33]刘秉正.非线性动力学与混沌基础[M].长春,东北师范大学出版社,1994.
[34]王亥,胡健栋Logistic-Map昆沌扩频序列.电子学报,1997,25(1)：19-23
[35]聂明新,卢凌,DS-CDMA系统的最佳混沌序列研究.武汉理工大学学报(交通科学与工程版),2001,25(3)：247-250
[36]Murali K, Lakshmanan M. Transmission of signals by synchronization in a chaotic Vander Pol-buffing oscillator. In:Phys Rev E.,1993,48(4):1624-1626
[37]J. Atmos. Lorenz E N. Deterministic nonperiodic flow. Sci.1963(20):130-141
[38]FUKUMASAH, KOHNO R, IMAI H. Design of pesudonoise sequence with good odd and even correlation properties for DS-CDMA[J]. IEEE JSAC,1994,12(5):828-835.
[39]朱近康.扩展频谱通信及其应用[M].合肥：中国科学技术大学出版社,1993,4：13-24
[40]田日才.扩频通信.清华大学出版社.2007
[41]胡健栋,郑朝辉,龙必起等.码分多址与个人通信.人民邮电出版社.1996
[42]Gold R. Maximal Recusive Sequence with 3-Valued Recusive Cross-Correlation Function IEEE.1968,14(10)
[43]Mazzini, G.., Setti, G.., Rovatti, R, Chaotic complex spreading sequences for asynchronous DS-CDMA. Ⅰ. System modeling and results; Circuits and Systems Ⅰ: Fundamental Theory and Applications, IEEE Transactions on Volume 44, Issue 10, Oct.1997 Page(s):937-947
[44]G. Heidari-Bateni, "Chaotic signals for digital communication", Ph. D. Dissertation, School of Electrical Engineering, Purdue University, W. Lafayette, IN, Dec.1992
[45]张琪,郑君里,孙守宇.混沌序列在准同步码分多址系统中的应用[J].清华大学学报(自然科学版),2003,43(4)：453-456
[46]李长庚,周家令,孙克辉,盛利元.四种数字混沌序列的平衡性分析[J].计算机应用,2008,28(1)：68-70
[47]Karkkainen K H. Meaning of Maximun and Mean-Square Cross-Correlation as a Performance as a Performance Measure for CDMA Code Families and Their Influence on System Capacity [J]. IEICE Trans. on Commun.1993, E76-B(8):848-854
[48]Sandoval-Morantes D, Munoz-Rodriguez D. Chaotic Sequences for Multiple Access [J]. Electronics Letters,1998,34(3):235-237
[49]米良,朱中梁.混沌直扩序列的优选及与传统序列的性能比较[J].系统工程与电子技术.2002,24(8)：117-120
[50]余振标,冯久超.一种混沌扩频序列的产生方法及其优选算法[J].物理学报.2008,57(3)：1409-1415
[51]刘庆玲.基于混沌理论的扩频码通信系统的研究：[硕士学位论文].哈尔滨工程大学,2005
[52]WaiM.Tam etc. Performance Analysis of Mutiple Access Chaotic Sequence Spread spectrum Communication Systems Employing Parallel Interference Cancellation[J]. IEEETrans,2003:208-211
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