时空混沌伪随机序列及其应用研究
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摘要
伪随机序列是一种具有类似白噪声性质的序列,主要应用于密码学和扩频通信领域。时空混沌系统在时间和空间上均表现出混沌行为,混沌的伪随机性、非周期性、长期不可预测性使时空混沌系统在通信领域,尤其是伪随机序列生成方面有着很好的应用前景。本论文在时空混沌伪随机序列的生成以及应用方面开展了以下工作:
(1)在对常见伪随机序列和一维混沌伪随机序列概述的基础上,基于时空混沌单向耦合映象格子系统的不变分布和方向相提出了两种生成时空混沌伪随机序列的新方法:①时空混沌单向耦合映象格子系统具有不变分布特性,不变分布只与系统的参数有关,对于参数确定的系统,其分布不随系统运动而改变,根据不变分布可以确定一个判决基准来生成伪随机序列,判决基准也可以当作系统的常数。②基于时空混沌方向相来生成伪随机序列,当系统处于完全发展湍流模式时,通过比较单向耦合映象格子中格点相邻时间的两个状态值来生成伪随机位序列。运用蒙特卡洛方法,计算了上述方法生成的伪随机序列的相关性、平衡性、游程特性等,并与传统的二值化方法生成的伪随机序列进行比较,结果表明基于方向相生成的序列优势不明显,基于不变分布生成的序列优势明显,这两种方法均比传统方法生成的速度快,效率高。
(2)基于MATLAB平台,用上述方法生成的伪随机序列作扩频码,构造了一个多径、多址高斯白噪声信道的CDMA扩频通信系统。在不同扩频因子,不同信噪比、不同用户数下,仿真系统的抗白噪声、抗多址干扰和抗多径干扰的能力,结果表明,当扩频因子比较大时,应用方向相生成序列的系统的误码率与应用m序列的系统差不多,应用不变分布生成序列的系统的误码率比用传统的m序列的系统要低。在实际的CDMA通信系统中,扩频因子都是比较大的。
本论文论述的生成伪随机序列的方法,以及这些序列在CDMA通信中的应用,具有一定理论意义与工程应用价值。
A pseudorandom sequence is a code sequence of 1’s and 0’s(-1’s) whose correlation has properties similar to those of white noise. It is mainly used in cryptography and spread spectrum communication field. Spatiotemporal chaotic systems show chaotic behavior both in time and space domain. In communication field, especially in the generation of pseudorandom sequences, they have a very good prospect because of the pseudo-randomness, aperiodic, long-term unpredictability properties of the chaotic systems. The generation methods of spatiotemporal chaotic pseudorandom sequences and the application of the sequences are discussed in this paper, the main works are as following:
(1) The pseudorandom sequences and one-dimensional chaotic pseudorandom sequences are summarized. On this basis, two novel methods to generate pseudorandom sequences are proposed:①Spatiotemporal chaos one-way coupled map lattices model has the invariant distribution property, the distribution of the system only related to the parameters of the system. A threshold value can be determined in accordance with the distribution, and the sequence can be generated. The threshold value also can be as a constant of the system.②Generating pseudorandom sequences based on the direction phase of chaotic systems. The sequences are gained by comparing the two consecutive state values of a single lattice in the OCML, when the system is in the state of fully developed turbulent mode. And using the Monte Carlo method to calculate the correlation, balanced and run-length qualities of the pseudorandom sequences which are generated above, compared these with the sequences generated by the traditional methods. The results show that the sequences generated by direction phase method have not an advantage over the traditional one, but the sequences generated based on the invariant distribution gain an advantage over, and these methods can generate more sequences than the traditional methods and have high efficiency.
(2) On the MATLAB platforms, pseudorandom sequences generated by the above methods be used as spread spectrum codes, the Code Division Multiple Access (CDMA) spread spectrum communication system with multiple path、multiple access and add white Gaussian noise(AWGN) channel is constructed. With different spreading factor, different signal to noise ratio(SNR), different number of users, the anti-white noise interference, anti-Multiple Access Interference(MAI) and anti-Multiple Path Interference(MPI) capacity are simulated. The results show that the bit error rate(BER) of the system applying the sequences generated by direction phase is a little higher than that of m-sequences, the BER of the system which applies the sequences based on the invariant distribution is lower than that of m sequence, when the spreading factor relatively large. In practical CDMA communication system, spreading factor is relatively large.
The formation methods of pseudorandom sequences and their application in CDMA communications discussed in this paper, make theoretical sense to some extent, and possess practical application value.
(1)在对常见伪随机序列和一维混沌伪随机序列概述的基础上,基于时空混沌单向耦合映象格子系统的不变分布和方向相提出了两种生成时空混沌伪随机序列的新方法:①时空混沌单向耦合映象格子系统具有不变分布特性,不变分布只与系统的参数有关,对于参数确定的系统,其分布不随系统运动而改变,根据不变分布可以确定一个判决基准来生成伪随机序列,判决基准也可以当作系统的常数。②基于时空混沌方向相来生成伪随机序列,当系统处于完全发展湍流模式时,通过比较单向耦合映象格子中格点相邻时间的两个状态值来生成伪随机位序列。运用蒙特卡洛方法,计算了上述方法生成的伪随机序列的相关性、平衡性、游程特性等,并与传统的二值化方法生成的伪随机序列进行比较,结果表明基于方向相生成的序列优势不明显,基于不变分布生成的序列优势明显,这两种方法均比传统方法生成的速度快,效率高。
(2)基于MATLAB平台,用上述方法生成的伪随机序列作扩频码,构造了一个多径、多址高斯白噪声信道的CDMA扩频通信系统。在不同扩频因子,不同信噪比、不同用户数下,仿真系统的抗白噪声、抗多址干扰和抗多径干扰的能力,结果表明,当扩频因子比较大时,应用方向相生成序列的系统的误码率与应用m序列的系统差不多,应用不变分布生成序列的系统的误码率比用传统的m序列的系统要低。在实际的CDMA通信系统中,扩频因子都是比较大的。
本论文论述的生成伪随机序列的方法,以及这些序列在CDMA通信中的应用,具有一定理论意义与工程应用价值。
A pseudorandom sequence is a code sequence of 1’s and 0’s(-1’s) whose correlation has properties similar to those of white noise. It is mainly used in cryptography and spread spectrum communication field. Spatiotemporal chaotic systems show chaotic behavior both in time and space domain. In communication field, especially in the generation of pseudorandom sequences, they have a very good prospect because of the pseudo-randomness, aperiodic, long-term unpredictability properties of the chaotic systems. The generation methods of spatiotemporal chaotic pseudorandom sequences and the application of the sequences are discussed in this paper, the main works are as following:
(1) The pseudorandom sequences and one-dimensional chaotic pseudorandom sequences are summarized. On this basis, two novel methods to generate pseudorandom sequences are proposed:①Spatiotemporal chaos one-way coupled map lattices model has the invariant distribution property, the distribution of the system only related to the parameters of the system. A threshold value can be determined in accordance with the distribution, and the sequence can be generated. The threshold value also can be as a constant of the system.②Generating pseudorandom sequences based on the direction phase of chaotic systems. The sequences are gained by comparing the two consecutive state values of a single lattice in the OCML, when the system is in the state of fully developed turbulent mode. And using the Monte Carlo method to calculate the correlation, balanced and run-length qualities of the pseudorandom sequences which are generated above, compared these with the sequences generated by the traditional methods. The results show that the sequences generated by direction phase method have not an advantage over the traditional one, but the sequences generated based on the invariant distribution gain an advantage over, and these methods can generate more sequences than the traditional methods and have high efficiency.
(2) On the MATLAB platforms, pseudorandom sequences generated by the above methods be used as spread spectrum codes, the Code Division Multiple Access (CDMA) spread spectrum communication system with multiple path、multiple access and add white Gaussian noise(AWGN) channel is constructed. With different spreading factor, different signal to noise ratio(SNR), different number of users, the anti-white noise interference, anti-Multiple Access Interference(MAI) and anti-Multiple Path Interference(MPI) capacity are simulated. The results show that the bit error rate(BER) of the system applying the sequences generated by direction phase is a little higher than that of m-sequences, the BER of the system which applies the sequences based on the invariant distribution is lower than that of m sequence, when the spreading factor relatively large. In practical CDMA communication system, spreading factor is relatively large.
The formation methods of pseudorandom sequences and their application in CDMA communications discussed in this paper, make theoretical sense to some extent, and possess practical application value.
引文
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[4] Abel A , Schwarz W. Chaos communication-Principles, Schemes and System Analysis [J]. Proceedings of the IEEE, 2002, 90(5):691-710.
[5] Pecora L M, Carroll T L. Synchronization in chaotic system [J]. Phys Rev Lett, 1990, 64(8):821-824
[6] Kocarev L. Chua L O. Experimental demonstration of secure communication via chaotic synchronization [J]. Int J Bifurc Chaos, 1992, 2(3):709-713.
[7] Cuomo K M, Oppenheim A V , Strogatz S H. Synchronization of Lorenz-based chaotic circuits with applications to communications [J]. IEEE Trans on Circ SystⅡ, 1993, 40(10):626-633.
[8] Yang T, Chua L O. Secure Communication via Chaotic Parameter Modulation [J]. IEEE Trans Circuits Syst I , 1996, 43(9):817-819.
[9] Dedieu H , Kennedy M P. Chaos shift keying: modulation and demodulation of a chaoticcarrieer using self synchronizing Chua’s circuits [J]. Circuits and SystemsⅡ: Analog and Digital Signal Processing.IEEE.1993 40(10):634-642
[10] Halle K S, Chua L O. Spread spectrum communication through modulation chaos [J]. Int J Bifurc Chaos, 1993, 3(2):469-477.
[11] Kark K H. Meaning of maximum and mean square cross-correlation as a performance measure for CDMA families and their influence on system capacity [J]. IEICE Trans. Comm., 1993, E76-B(8):848-854.
[12] Heidari-Bateni G, McGillem C D. A chaotic direct-sequence spread-spectrum communication system [J]. IEEE Trans on Comm, 42(234) :1524-1527.
[13] Kennedy M P, Kolumban G, Kis G, et al. Performance Evaluation of FM-DCSK Modulation in Multipath Environments [J]. IEEE Trans Circ SystⅠ,2000, 47(12):1702-1711.
[14] Kennedy M P. Rovatti R, Setti E G. Chaotic Electronics in Telecommunications[M]. Boca Raton, Florida: CRC Press LLC,2000.
[15] Ciftci M, Williams D B. An optimal estimation algorithm for multiuser chaotic communication systems [C]. ISCAS IEEE International Symposium on Circuits and Systems , 2002, 1:397-400.
[16] Fan P, Darnell M. Sequence Design for Communications Applications [M]. John Wiley, Research Studies Press, Taunton, 1996.
[17] Helleseth T, Kumar P V. Sequences with low correlation [A].in Handbook of Coding Theory [M].The Netherlands: Elsevier, 1998: 1765-1854.
[18]肖国镇,梁传甲,王育民.伪随机序列及其应用[M].北京:国防工业出版社,1985.
[19] Golomb S W. Shift Register Sequences [M]. San Francisco, CA: Holdcn-Day, 1967. Rewised edition: Laguna Hills, CA: Acgcan Park, 1982.
[20] Berlekamp E R. Algebraic Coding Theory [M]. McGraw-Hill, New York, 1968.
[21] Massey J L. Shift register synthesis and BCH decoding [J]. IEEE Transactions on Information Theory, 1969, 15 (1):122-127.
[22]胡健东.码分多址与个人通信[M].北京:人民邮电出版社,1996.
[23]闫统江.伪随机序列的构造及其性质研究[D]西安:西安电子科技大学, 2001:1.
[24] Kumar P V. Frequency-hopping code sequence designs having large linear span [J]. IEEE Transactions on Information Theory, 1988, 34(1):146-151.
[25] No J S, Golomb S W, Gong G, et al. Binary pseudorandom sequences of period 2 n ?1 with ideal autocorrelation [J]. IEEE Transactions on Information Theory, 1998, 44(2): 814-817.
[26] Matolak D W, Manchiraju D. Evaluation of pseudorandom sequences for third generation spread spectrum [C]. Proceedings of the 35th IEEE Southeastern Symposium on System Theory. Morgantown, 2003: 288-290.
[27] Mei W H, Yang Y X. Families of FH sequences based on pseudorandom sequences over GF(p) [C]. International Conference on Communication Technology WCC-ICCT 2000, 1(1): 536-538.
[28] Ding C, Helleseth T, Lam K Y. Several classes of binary sequences with three-level auto-correlation [J]. IEEE Transactions on Information Theory, 1999, 45(7):2606-2612.
[29]丁存生,肖国镇.流密码学及其应用[M].北京:国防工业出版社,1994.
[30] Schneider B., Applied Cryptography: Protocols, algorithm and source code [M]. Wily, New York, 1996.
[31] Heidari-Bateni G, McGillem C D, Chaotic Sequences for Spread Spectrum: An Alternative to PN-Sequences [J]. IEEE ICWC’92, 1992.
[32] Mazzini G, Setti G, Rovatti R. Chaotic complex spreading sequences for asynchronous DS-CDMA-PartⅠ: system modeling and results [J], IEEE Trans Circuits SystⅠ. 1997, 44(10): 937-947.
[33] Perez G, Cerdeira H A, Extracting messages masked by chaos [J]. Phys Rev Lett, 1995, 74(11):1970-1973.
[34] Yang T, Lin B Y, Chun M Y. Application of neural networks to unmasking chaotic secure communication [J]. Physic D, 1998, 124(13):248-257.
[35] Kohda T, Tsuneda A. Pseudonoise sequences by chaotic nonlinear maps and their correlation properties [J]. IEICE Trans Commun, 1993,E76-B(8):855-862 .
[36] Kohda T, Tsuneda A. Chaotic bit sequence for stream cipher cryptography and their correlation functions [J]. Chaotic Circuits for Communication in: Proceeding of SPIE, 1995, 26(12):86-97.
[37] Wang Xingang,Zhang Meng,Gang Xiaofeng, et al. Spread-spectrum communication using binary spatiotemporal chaotic codes [J]. Phys Lett A,2005, 334(1):30-36.
[38] Bernstein G M, Lieberman M A. Secure random number generation using chaotic circuits [J]. IEEE Transactions on Circuits and Systems, Sept. 1990, 37( 9):1157 -1164.
[39] Kohda T, Tsuneda A. Stream cipher systems based on chaotic binary sequences [C]. January 1996,In: Proc SCIS96-11C.
[40] Zhou H, A design methodology of chaotic stream ciphers and the realization problems in finite precision [D]. Department of Electronic Engineering, Fudan University, 1996.
[41] Kohda T,Tsuneda A. Statistics of chaotic binary sequences [J]. IEEE Transactions on Information Theory, Jan. 1997, 43( 1) :104– 112.
[42]田日才.扩频通信[M].北京:清华大学出版社,2007:42
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