产生混沌扩频序列及其在扩频通信中的应用
摘要
扩频通信采用伪随机编码调制，使用比信息数据大得多的带
宽。接收端使用同步的伪随机序列进行相关解调恢复出原始信息数
据。因此扩频通信能在低功率谱密度下工作，具有抗干扰、抗多径
衰落、多址能力强、频谱利用率高等特点。在民用移动通信、军事
通信等领域都得到了广泛的应用。伪随机码性能对扩频通信至关重
要。研究表明，传统的伪随机码扩频序列存在复杂度低，保密性差
等缺点，并且相关特性较好的伪随机序列数目极其有限。
混沌是在非线性系统中出现的确定性的、类随机的过程。混沌
系统最基本的特征是对初始条件极端敏感性，由此可以提供数量众
多、相关特性优良的扩频序列。
本文研究了分别采用蔡氏电路、逻辑映射和时空混沌耦合映象
格子这三种混沌系统来产生混沌扩频序列的方法，分析了产生出来
的序列的特性，主要包括自相关和互相关特性等。经过分析发现采
用混沌系统产生的混沌序列特性良好，可用来代替传统的扩频序列
以提高扩频通信系统性能，比如系统容量等。为了验证混沌扩频序
列的可行性，特此讨论了把混沌扩频序列应用于扩频通信中，特别
广西大学硕土研究生学位论文 中文摘要
分析了它在AWGN信道条件下的误码性能，得出了相应的误码性
能公式，构造蒙特卡罗仿真檬型，把理论计算结果与实际仿真结果
进行了比较，发现二者吻合得很好，从而证明了混饨序列作为扩频
序列的可行性。最后结合移动卫星通信系统模型，把混饨扩频序列
实际应用于移动卫星扩频通信系统中，相应分析了它的误码性能。
Spread spectrum communication uses much larger bandwidth
than required by spreading original information using pseudo noise
(PN) sequences. A spread spectrum receiver then uses the
synchronized replica of the pseudo noise sequences to recover the
original information. Due to this pseudo noise property of the
spreading sequences, spread spectrum communication can work at
low power spectral density and has many good characters such as
anti-noise, anti-interference, anti-multipath effect, multiple access,
efficient frequency usage. It has been applied widely in civil mobile
communication and military communication. It is well-known
that the spreading sequences generation is first step for achieving
spread spectrum communication, and the auto-correlation
property and cross-correlation property of the spreading sequences
are very importance for spread spectrum communication.
Research has showed that conventional PN has low complication
and low security, et al. In addition, PN sequences with good
correlation property are not many enough.
Chaos is produced by deterministic nonlinear systems, its
phenomena is pseudo random. Because chaotic systems exhibit
sensitivity to initiaI conditions, they can generate many enough PN
sequences with good correlation property
In this article, the methods of generating cbaotic spread
spectrum sequences by using chua's circuit, logistics-map, and
coupled map Iattice are studied. The characters of these 8equences
are also anaIyzed such as auto-correlation property and
cross-correIation property We find a fact that chaotic spread
spectrum sequences have well enough auto-correlation property
and cross-correIation property chaotic sequences can repIace
conventional PN sequences in spread spectrum communication and
improve communication system property such as capacity In order
to exam the feasibiIity of chaotic sequences applying for real spread
spectrum teIecommunications, we anaIyze the EBR in AWGN
channel in theoretics and give BER formula. The feasibiIity of
chaotic sequences are able to be used in spread spectrum
communication systems is proved by theoretic calculation and
Monte CarIo method simulation. In the last chapter of tbe article,
BER that chaotic spread spectrum sequences apply in mobile
satellite spread spectrum communication system is studied.
宽。接收端使用同步的伪随机序列进行相关解调恢复出原始信息数
据。因此扩频通信能在低功率谱密度下工作，具有抗干扰、抗多径
衰落、多址能力强、频谱利用率高等特点。在民用移动通信、军事
通信等领域都得到了广泛的应用。伪随机码性能对扩频通信至关重
要。研究表明，传统的伪随机码扩频序列存在复杂度低，保密性差
等缺点，并且相关特性较好的伪随机序列数目极其有限。
混沌是在非线性系统中出现的确定性的、类随机的过程。混沌
系统最基本的特征是对初始条件极端敏感性，由此可以提供数量众
多、相关特性优良的扩频序列。
本文研究了分别采用蔡氏电路、逻辑映射和时空混沌耦合映象
格子这三种混沌系统来产生混沌扩频序列的方法，分析了产生出来
的序列的特性，主要包括自相关和互相关特性等。经过分析发现采
用混沌系统产生的混沌序列特性良好，可用来代替传统的扩频序列
以提高扩频通信系统性能，比如系统容量等。为了验证混沌扩频序
列的可行性，特此讨论了把混沌扩频序列应用于扩频通信中，特别
广西大学硕土研究生学位论文 中文摘要
分析了它在AWGN信道条件下的误码性能，得出了相应的误码性
能公式，构造蒙特卡罗仿真檬型，把理论计算结果与实际仿真结果
进行了比较，发现二者吻合得很好，从而证明了混饨序列作为扩频
序列的可行性。最后结合移动卫星通信系统模型，把混饨扩频序列
实际应用于移动卫星扩频通信系统中，相应分析了它的误码性能。
Spread spectrum communication uses much larger bandwidth
than required by spreading original information using pseudo noise
(PN) sequences. A spread spectrum receiver then uses the
synchronized replica of the pseudo noise sequences to recover the
original information. Due to this pseudo noise property of the
spreading sequences, spread spectrum communication can work at
low power spectral density and has many good characters such as
anti-noise, anti-interference, anti-multipath effect, multiple access,
efficient frequency usage. It has been applied widely in civil mobile
communication and military communication. It is well-known
that the spreading sequences generation is first step for achieving
spread spectrum communication, and the auto-correlation
property and cross-correlation property of the spreading sequences
are very importance for spread spectrum communication.
Research has showed that conventional PN has low complication
and low security, et al. In addition, PN sequences with good
correlation property are not many enough.
Chaos is produced by deterministic nonlinear systems, its
phenomena is pseudo random. Because chaotic systems exhibit
sensitivity to initiaI conditions, they can generate many enough PN
sequences with good correlation property
In this article, the methods of generating cbaotic spread
spectrum sequences by using chua's circuit, logistics-map, and
coupled map Iattice are studied. The characters of these 8equences
are also anaIyzed such as auto-correlation property and
cross-correIation property We find a fact that chaotic spread
spectrum sequences have well enough auto-correlation property
and cross-correIation property chaotic sequences can repIace
conventional PN sequences in spread spectrum communication and
improve communication system property such as capacity In order
to exam the feasibiIity of chaotic sequences applying for real spread
spectrum teIecommunications, we anaIyze the EBR in AWGN
channel in theoretics and give BER formula. The feasibiIity of
chaotic sequences are able to be used in spread spectrum
communication systems is proved by theoretic calculation and
Monte CarIo method simulation. In the last chapter of tbe article,
BER that chaotic spread spectrum sequences apply in mobile
satellite spread spectrum communication system is studied.
引文
[1] . Ojanera.T,and R.Prasad,"Overview of Air Interface Multiple Access for IMT-2000/UMTS",IEEE Communication Magazine September 1998．
[2] . L.O.Chua,"Chua's circuit:An overview ten years later",J.of circuit,systems and compter,4,117(1994)
[3] . GKolambab, M.P.Kennedy, L.O.Chua, "The role of synchronization in digital communications using-chaos-Part I: Fundamentals of digital communications " , IEEE Trans. On CAS-I, 44, 927(1997) ;
[4] . GMazzini, GSetfi, R.Rovatfi " Chaotic complex spreading sequences for asynchronous DS-CDMA-Part I: System modeling and results " IEEE Trans. On CAS-I, 44, 937(1997) ;
[5] . K.Kelber, T.Falk, M.Gotz, et al , "Discrete-time chaotic coder for information encryption-Part Ⅱ : Continuous and discrete value realization " , in Proc. Workshop Nonliner Dynamics Electronic System, Seville, 1996, P.27-32:
[6] . GH.Baterni , C.D.Megillem , " A chaotic direct-sequence spread spectrum communications system" , IEEE Trans. , Commun.42, 1524(1994) ;
[7] . C.L.Koh, T.Ushio, "Digital communication method based on M-synchronized chaotic system " , IEEE, Trans. On CAS-I, 44, 383(1997) ;
[8] . F.Dachselt, K.Kelber, W.Schwarz, "Discrete time chaotic encryption system-Part Ⅲ : Cryptographical analysis ", IEEE Trans. On CAS-I, 45, 982(1998) ;
[9] . RRovatfi, GSetfi, GMazzini, " Chaotic complex spreading sequences for asynchronous DS-CDMA-Part Ⅱ: Some theoretical performance bounds " IEEE Trans. On CAS-I, 45, 469(1998) ;
[10] . M.Gotz, K.Kelber, W.Schwarz, "Discrete-time chaotic encryption system-Part I: statistical design approach" , IEEE Trans. On CAS-I, 44, 963(1997) ;
[11] . Deraney RL. An Introduction to Chaotic Dynomical System,California Addision Wsabley Publishing Company Inc,1989
[12] . R. S. Shaw, Strange attractor, chaotic behavior, an in formation
flow, Z. Naturforsch, 36a(1981)80
[13]、L. O. Chua, M. Komuro, T. Matsumoto, "The double scroll family, Part Ⅰ and Ⅱ", IEEE Trans. Circuits syst. Vol. 33, NO.11, 1986, 1073-1118.
[14]、L.O.Chua and M.Hasler, Special issue on Chua in nonlinear electronic circuits,part A and part B, IEEE Trans. On CAS-Ⅰ, vol.40, No. 10 and No. 11, 1993; part C, IEEE,Trans, On CAS-Ⅱ, vol.40, No.10, 1993;
[15]、Kennedy. M.P, Ogorzalek. M.J, Special Issue on Chaos Synchronization and Control:theory and application, IEEE Transactions on Circuits and Systems,1997,44(10):853-1039.
[16]、王亥、胡健栋，改进型Logistic-map混沌扩频序列，通信学报，1997，18(8)：71～74
[17]、Heidari-Bateri G,M cGillem C D.A chaotic direct-sequence spread spectrum communication system IEEE Trans on Communications,1994,42(2/3/4): 1524-2527
[18]、尤肖虎，赵春明，陈时昕，混沌信号与多址和保密通信 第四界全国青年通信学术会议论文集
[19]、王亥、胡健栋，Logistic-map混沌扩频序列，电子学报，1997，Vol．25，NO．1，19～23
[20]、L. M. Pecora and T. L. Carroll. Synchronization in chaotic systems. Phys. Rev. Lett., 1990, 64(8): 821～824
[21]、Pursley M B. Performance Evaluation for Pase-Code Spread-Spectrum Multiple-Access Communication-Part Ⅱ: Code Sequence Analysis. IEEE Transactions on Communications, 1977, COM-25(8):800～803
[22]、Richard D J v Nee, Prasad R. Spread-Spectrum Path Diversity in a Shadowed Rician Fading Land-Mobile Satellite Channel. IEEE Transaction on Vehicular Technology,1993,42(2),131～136
[23]、Kavehrad M, Mclane P J. Performance of Low-Complexity Channel Coding and Diversity for Spread Spectrum in Indoor,Wireless Communication. AT&T Technial Journal ,1985,64(8):1927～1965.
[24]、I. Waller and R. Kapral, Spatial and temporal structure in system of couple nonlinear oscillators, Phys. Rev. 30A(1984)2047
[25] . K. Kaneko, Turbulence in coupled map lattices, Physica, 18D(1986) 475
[26] . LOO C. Measurements and models of a mobile satellite channel and their applications to MSK signals. IEEE Transactions Vehicular Technology,1987,VT-36(3) ,114-112
[27] . J. M. H. Elmirghani, &E. A. Cryan, New chaotic based communication technoque with mutiuser provision , electon . Lett. , Vol. 38 , No. 15 ,1994
[28] . Frey . D, R. Chaotic , Digital encoding : An approach to secure communication, IEEE Trans CAS, 1993, CAS-40(10) :660-666
[29] .M. T. Thompson, H. B. Stewart, Nonlinear Dynamics and chaos , Geometrical Methods for Engineering and Scientists, New York, John Wiley&Sons Ltd., 1986
[30] . K. Kaneko, Period-doubling of kink-antikink patterns, quasiperiodicity in antiferro-like structrues and spatial intermittency in couple logistic lattice:towards a prelude of a "field theory of chaos" , Pro. Theor. Phys., 72(1984) 480
[31] . K. Kaneko, Ph. D. Thesis, Coolapse of Tori and Genesis of Chaos in Dissipative System, 1983(enlarged vision is published by World Sci. Pub., 1986)
[32] . J. P. Crutchfield and K. Kaneko, " Phenomenology of Spatiotemporal Chaos" , in Directions in Chaos vol. 1(ed. B.-L. Hao World Sci. Pub., 1987) 272．
[33] . R. Kaparal, Pattern formation in two dimensional arrays of coupled, dicrete-time oscillators, Phys. Rev., 31A(1985) 3868
[34] . F. Kaspar and H. G. Schuster, Scaling at the onset of spatial discorder in couple ppecewise linear mapping,Phys.Lett., 113A(1986) 451
[35] . I. Waller and R. Kapral, Spatial and temporal structure in system of couple nonlinear oscillators, Phys. Rev. 30A(1984) 2047
[36] . International Journal of Bifurcations and Chaos vol.2 NO. 3(1992)
[37] . Theory and applications of cellular automata, ed. S Wolfram, World Sci.Pub. 1986
[38] . H. Chate and P. Manneville,Transition to turbulence via spatiotemporal intermittency, Phys. Rev. Lett., 58(1987) 112
[39] . K. Kaneko, Turbulence in coupled map lattices, Physica, 18D(1986) 475
[40] . Corazza G. E, et al. A Statistical model for land mobile satellite channels and its application to nongeosateionary orbit systems. IEEE Trans Veh Technol, 1994,43(3)
[41] . Van Nee R, et al. Spread Spectrum Path Diversity in a Shadowed Rician Fading Land Mobile Satellite Channel. IEEE Trans Veh Technol 1993,42(2) :131-136
[42] . Ginvanni E C, Francesco V. A Statistical Model for Mobile Satellite Channels and Its Application to Nongeostationary Orbit Systems. IEEE Trans on Communication, 1994,43(3) :738-742
[43] . Corazza G E, Jahn A Lutz E, Vatalaro F, Channel Characterization for Mobile Satellite Communications. In:Proceedings of the First European Workshop on Mobile/Personal Satcoms(EMPS 94) , London:Springer-Verlag London Limited, 1995
[44] . LOO C.A statistical model for a land mobile satellite link. IEEE Trans on VT ,1985,VT-34(3) : 122-127 4 chapter uses
[45] . LOO C. Digital transmission through a mobile satellite channel. IEEE Trans on Communications, 1990,38(5) :693-697
[47] . Richard D J v Nee , Rogier N V W, Ramjee P. Slotted ALOHA and Code Division Multiple Access Techniques for Land Mobile Satellite Personal Communications. IEEE Journal on Areas In Communications,1995, Vol-13(2) :382-388
[48] . Richard D J v Nee, Howard S M, Ramjee P. Direct-sequence spread spectrum in a shadowed Rician fading land mobile satellite channel. IEEE J on Selected Areas In Communications, 1993,42(2) : 181-186
[2] . L.O.Chua,"Chua's circuit:An overview ten years later",J.of circuit,systems and compter,4,117(1994)
[3] . GKolambab, M.P.Kennedy, L.O.Chua, "The role of synchronization in digital communications using-chaos-Part I: Fundamentals of digital communications " , IEEE Trans. On CAS-I, 44, 927(1997) ;
[4] . GMazzini, GSetfi, R.Rovatfi " Chaotic complex spreading sequences for asynchronous DS-CDMA-Part I: System modeling and results " IEEE Trans. On CAS-I, 44, 937(1997) ;
[5] . K.Kelber, T.Falk, M.Gotz, et al , "Discrete-time chaotic coder for information encryption-Part Ⅱ : Continuous and discrete value realization " , in Proc. Workshop Nonliner Dynamics Electronic System, Seville, 1996, P.27-32:
[6] . GH.Baterni , C.D.Megillem , " A chaotic direct-sequence spread spectrum communications system" , IEEE Trans. , Commun.42, 1524(1994) ;
[7] . C.L.Koh, T.Ushio, "Digital communication method based on M-synchronized chaotic system " , IEEE, Trans. On CAS-I, 44, 383(1997) ;
[8] . F.Dachselt, K.Kelber, W.Schwarz, "Discrete time chaotic encryption system-Part Ⅲ : Cryptographical analysis ", IEEE Trans. On CAS-I, 45, 982(1998) ;
[9] . RRovatfi, GSetfi, GMazzini, " Chaotic complex spreading sequences for asynchronous DS-CDMA-Part Ⅱ: Some theoretical performance bounds " IEEE Trans. On CAS-I, 45, 469(1998) ;
[10] . M.Gotz, K.Kelber, W.Schwarz, "Discrete-time chaotic encryption system-Part I: statistical design approach" , IEEE Trans. On CAS-I, 44, 963(1997) ;
[11] . Deraney RL. An Introduction to Chaotic Dynomical System,California Addision Wsabley Publishing Company Inc,1989
[12] . R. S. Shaw, Strange attractor, chaotic behavior, an in formation
flow, Z. Naturforsch, 36a(1981)80
[13]、L. O. Chua, M. Komuro, T. Matsumoto, "The double scroll family, Part Ⅰ and Ⅱ", IEEE Trans. Circuits syst. Vol. 33, NO.11, 1986, 1073-1118.
[14]、L.O.Chua and M.Hasler, Special issue on Chua in nonlinear electronic circuits,part A and part B, IEEE Trans. On CAS-Ⅰ, vol.40, No. 10 and No. 11, 1993; part C, IEEE,Trans, On CAS-Ⅱ, vol.40, No.10, 1993;
[15]、Kennedy. M.P, Ogorzalek. M.J, Special Issue on Chaos Synchronization and Control:theory and application, IEEE Transactions on Circuits and Systems,1997,44(10):853-1039.
[16]、王亥、胡健栋，改进型Logistic-map混沌扩频序列，通信学报，1997，18(8)：71～74
[17]、Heidari-Bateri G,M cGillem C D.A chaotic direct-sequence spread spectrum communication system IEEE Trans on Communications,1994,42(2/3/4): 1524-2527
[18]、尤肖虎，赵春明，陈时昕，混沌信号与多址和保密通信 第四界全国青年通信学术会议论文集
[19]、王亥、胡健栋，Logistic-map混沌扩频序列，电子学报，1997，Vol．25，NO．1，19～23
[20]、L. M. Pecora and T. L. Carroll. Synchronization in chaotic systems. Phys. Rev. Lett., 1990, 64(8): 821～824
[21]、Pursley M B. Performance Evaluation for Pase-Code Spread-Spectrum Multiple-Access Communication-Part Ⅱ: Code Sequence Analysis. IEEE Transactions on Communications, 1977, COM-25(8):800～803
[22]、Richard D J v Nee, Prasad R. Spread-Spectrum Path Diversity in a Shadowed Rician Fading Land-Mobile Satellite Channel. IEEE Transaction on Vehicular Technology,1993,42(2),131～136
[23]、Kavehrad M, Mclane P J. Performance of Low-Complexity Channel Coding and Diversity for Spread Spectrum in Indoor,Wireless Communication. AT&T Technial Journal ,1985,64(8):1927～1965.
[24]、I. Waller and R. Kapral, Spatial and temporal structure in system of couple nonlinear oscillators, Phys. Rev. 30A(1984)2047
[25] . K. Kaneko, Turbulence in coupled map lattices, Physica, 18D(1986) 475
[26] . LOO C. Measurements and models of a mobile satellite channel and their applications to MSK signals. IEEE Transactions Vehicular Technology,1987,VT-36(3) ,114-112
[27] . J. M. H. Elmirghani, &E. A. Cryan, New chaotic based communication technoque with mutiuser provision , electon . Lett. , Vol. 38 , No. 15 ,1994
[28] . Frey . D, R. Chaotic , Digital encoding : An approach to secure communication, IEEE Trans CAS, 1993, CAS-40(10) :660-666
[29] .M. T. Thompson, H. B. Stewart, Nonlinear Dynamics and chaos , Geometrical Methods for Engineering and Scientists, New York, John Wiley&Sons Ltd., 1986
[30] . K. Kaneko, Period-doubling of kink-antikink patterns, quasiperiodicity in antiferro-like structrues and spatial intermittency in couple logistic lattice:towards a prelude of a "field theory of chaos" , Pro. Theor. Phys., 72(1984) 480
[31] . K. Kaneko, Ph. D. Thesis, Coolapse of Tori and Genesis of Chaos in Dissipative System, 1983(enlarged vision is published by World Sci. Pub., 1986)
[32] . J. P. Crutchfield and K. Kaneko, " Phenomenology of Spatiotemporal Chaos" , in Directions in Chaos vol. 1(ed. B.-L. Hao World Sci. Pub., 1987) 272．
[33] . R. Kaparal, Pattern formation in two dimensional arrays of coupled, dicrete-time oscillators, Phys. Rev., 31A(1985) 3868
[34] . F. Kaspar and H. G. Schuster, Scaling at the onset of spatial discorder in couple ppecewise linear mapping,Phys.Lett., 113A(1986) 451
[35] . I. Waller and R. Kapral, Spatial and temporal structure in system of couple nonlinear oscillators, Phys. Rev. 30A(1984) 2047
[36] . International Journal of Bifurcations and Chaos vol.2 NO. 3(1992)
[37] . Theory and applications of cellular automata, ed. S Wolfram, World Sci.Pub. 1986
[38] . H. Chate and P. Manneville,Transition to turbulence via spatiotemporal intermittency, Phys. Rev. Lett., 58(1987) 112
[39] . K. Kaneko, Turbulence in coupled map lattices, Physica, 18D(1986) 475
[40] . Corazza G. E, et al. A Statistical model for land mobile satellite channels and its application to nongeosateionary orbit systems. IEEE Trans Veh Technol, 1994,43(3)
[41] . Van Nee R, et al. Spread Spectrum Path Diversity in a Shadowed Rician Fading Land Mobile Satellite Channel. IEEE Trans Veh Technol 1993,42(2) :131-136
[42] . Ginvanni E C, Francesco V. A Statistical Model for Mobile Satellite Channels and Its Application to Nongeostationary Orbit Systems. IEEE Trans on Communication, 1994,43(3) :738-742
[43] . Corazza G E, Jahn A Lutz E, Vatalaro F, Channel Characterization for Mobile Satellite Communications. In:Proceedings of the First European Workshop on Mobile/Personal Satcoms(EMPS 94) , London:Springer-Verlag London Limited, 1995
[44] . LOO C.A statistical model for a land mobile satellite link. IEEE Trans on VT ,1985,VT-34(3) : 122-127 4 chapter uses
[45] . LOO C. Digital transmission through a mobile satellite channel. IEEE Trans on Communications, 1990,38(5) :693-697
[47] . Richard D J v Nee , Rogier N V W, Ramjee P. Slotted ALOHA and Code Division Multiple Access Techniques for Land Mobile Satellite Personal Communications. IEEE Journal on Areas In Communications,1995, Vol-13(2) :382-388
[48] . Richard D J v Nee, Howard S M, Ramjee P. Direct-sequence spread spectrum in a shadowed Rician fading land mobile satellite channel. IEEE J on Selected Areas In Communications, 1993,42(2) : 181-186