扩频码的设计及其在无线通信中的应用
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摘要
在码分多址(CDMA)系统中，扩频序列的相关特性和码集合大小直接影响系统的抗干扰能力和系统容量。采用单码扩频的第三代CDMA移动通信系统，由于扩频码相关特性的不理想，使得系统的性能和容量受到多径干扰和多址接入干扰的限制。广义正交序列在其零相关区内具有理想的相关特性。因此，采用广义正交序列作为扩频码，可以有效消除多径干扰和多址接入干扰。
本文主要工作可以分为以下几个部分。
给出了序列相关特性的定义，包括(偶)周期自／互相关函数、奇周期自／互相关函数、非周期相关函数和频域相关函数。分析比较了各种现有扩频序列的相关特性，给出它们在扩频系统中的应用方式。对码集合的参数进行比较，指出存在的局限性。总体上讨论了码集合的参数与系统抗干扰能力的关系，得出系统的抗干扰能力和码集合大小之间的相互制约关系。
构造了一种基于m序列的新型二进制广义正交码，称为m-ZCZ码；给出了它的相关特性。除了具有现有广义正交码的相关特性外，m-ZCZ码的零相关区长度突破取值上的限制。因此，可以根据特定的信道条件灵活设计扩频码，从而增加码的个数，提高系统容量。讨论了m-ZCZ码在CDMA系统中的应用，给出了采用m-ZCZ码扩频的CDMA系统性能的理论分析。分析了MC-CDMA系统中多址干扰对系统性能的影响，指出现有文献中用于MC-CDMA系统的扩频码的局限性。分析了为使系统保持无多址干扰，扩频码的频域相关性所需满足的条件。在此基础上，设计了一种多相无多址干扰序列，证明了其理想的频域相关特性。最后，与现有扩频方案进行了性能的比较，给出仿真结果。
指出了序列设计及其应用中仍存在的问题和有待拓展的问题，指明了未来研究的方向。
In Code Division Multiple Access (CDMA) systems, the correlation properties of the spreading sequences play an important role and directly influence the system interference-resist ability, and the size of code set influences the system capacity. In the 3~(rd) generation mobile communication systems employing single codes as spreading codes, the system capacity is reduced by multipath interference (MI) and multiple access interference (MAI) due to the non-ideal correlation properties of the codes. Generalized Orthogonal (GO) sequences possesse ideal correlation properties in their zero correlation zone (ZCZ). Therefore, the systems employing GO sequences as spreading codes can eliminate MI and MAI effectually.
The main contents of this work are listed as follows:
The correlation functions definitions of spreading sequences are presented, including the (even) periodic correlation function, odd periodic correlation function, aperiodic correlation function and spectral correlation function. The correlation properties of several existion spreading sequences are discussed and their applications in spreading spectrum systems are analyzed. The parameters of the code set are investigated, and their limitations are point out. Then the relationship between the code set size and anti-interference ability of the system has been discussed, and their mutual restriction relation are obtained.
Based on the knowledge of m-sequences, a novel binary generalized orthogonal code, called m-ZCZ code, is constructed, and its correlation properties is presented. Besides having the same characteristics as conventional GO sequences, the value of ZCZ length breaks through the restriction, and can be flexibly chosen to match the practical channel in a high degree. So that the number of codes is increased and the system capacity is improved. Then, the applications of m-ZCZ code in CDMA systems are discussed, and the theory analysis of system BER performance is presented.
The MC-CDMA systems' performance impacted by MAI is analyzed, and the limitations of spreading codes employed in MC-CDMA systems in some literatures are pointed out. The criteria of spreading codes design to achieve an MAI-free system are analyzed. According to the criteria, a multiphase MAI-free spreading code, called GW code, is proposed, and its ideal spectral correlation properties are proved. Then, the performances of the system employing GW codes and the systems employing conventional spreading codes are compared, and the simulation results of BER are given. It is shown that the system performance is improved by using GW codes.
In the end, several existing problems in the research of sequence design and their applilcations are pointed out and they outline the direction of future work.
本文主要工作可以分为以下几个部分。
给出了序列相关特性的定义，包括(偶)周期自／互相关函数、奇周期自／互相关函数、非周期相关函数和频域相关函数。分析比较了各种现有扩频序列的相关特性，给出它们在扩频系统中的应用方式。对码集合的参数进行比较，指出存在的局限性。总体上讨论了码集合的参数与系统抗干扰能力的关系，得出系统的抗干扰能力和码集合大小之间的相互制约关系。
构造了一种基于m序列的新型二进制广义正交码，称为m-ZCZ码；给出了它的相关特性。除了具有现有广义正交码的相关特性外，m-ZCZ码的零相关区长度突破取值上的限制。因此，可以根据特定的信道条件灵活设计扩频码，从而增加码的个数，提高系统容量。讨论了m-ZCZ码在CDMA系统中的应用，给出了采用m-ZCZ码扩频的CDMA系统性能的理论分析。分析了MC-CDMA系统中多址干扰对系统性能的影响，指出现有文献中用于MC-CDMA系统的扩频码的局限性。分析了为使系统保持无多址干扰，扩频码的频域相关性所需满足的条件。在此基础上，设计了一种多相无多址干扰序列，证明了其理想的频域相关特性。最后，与现有扩频方案进行了性能的比较，给出仿真结果。
指出了序列设计及其应用中仍存在的问题和有待拓展的问题，指明了未来研究的方向。
In Code Division Multiple Access (CDMA) systems, the correlation properties of the spreading sequences play an important role and directly influence the system interference-resist ability, and the size of code set influences the system capacity. In the 3~(rd) generation mobile communication systems employing single codes as spreading codes, the system capacity is reduced by multipath interference (MI) and multiple access interference (MAI) due to the non-ideal correlation properties of the codes. Generalized Orthogonal (GO) sequences possesse ideal correlation properties in their zero correlation zone (ZCZ). Therefore, the systems employing GO sequences as spreading codes can eliminate MI and MAI effectually.
The main contents of this work are listed as follows:
The correlation functions definitions of spreading sequences are presented, including the (even) periodic correlation function, odd periodic correlation function, aperiodic correlation function and spectral correlation function. The correlation properties of several existion spreading sequences are discussed and their applications in spreading spectrum systems are analyzed. The parameters of the code set are investigated, and their limitations are point out. Then the relationship between the code set size and anti-interference ability of the system has been discussed, and their mutual restriction relation are obtained.
Based on the knowledge of m-sequences, a novel binary generalized orthogonal code, called m-ZCZ code, is constructed, and its correlation properties is presented. Besides having the same characteristics as conventional GO sequences, the value of ZCZ length breaks through the restriction, and can be flexibly chosen to match the practical channel in a high degree. So that the number of codes is increased and the system capacity is improved. Then, the applications of m-ZCZ code in CDMA systems are discussed, and the theory analysis of system BER performance is presented.
The MC-CDMA systems' performance impacted by MAI is analyzed, and the limitations of spreading codes employed in MC-CDMA systems in some literatures are pointed out. The criteria of spreading codes design to achieve an MAI-free system are analyzed. According to the criteria, a multiphase MAI-free spreading code, called GW code, is proposed, and its ideal spectral correlation properties are proved. Then, the performances of the system employing GW codes and the systems employing conventional spreading codes are compared, and the simulation results of BER are given. It is shown that the system performance is improved by using GW codes.
In the end, several existing problems in the research of sequence design and their applilcations are pointed out and they outline the direction of future work.
引文
[1] A．J．Viterbi著，李世鹤，鲍刚等译，CDMA扩频通信原理，北京：人民邮电出版社，1997．
[2] 扩频通信技术，http://www.wx800.com/msg/2004/06/18/a851.php,6/2004.
[3] M. Zeng, A. Annamalai, and V. K. Bhargava, "Recent advances in cellular wireless communications," IEEE Communications Magazine, vol. 36, no. 9, pp. 128-138, September 1999.
[4] R. L. Pickholtz, L. B. Milstein and D. L. Schiling, "Spread spectrum for mobile communications," IEEE Trans. Veh. Technol., vol. 40, no. 2, pp. 313-322, May 1991.
[5] S. W Golomb, "Sequences with randomness properties," Terminal Progress Report under Contract, 639498, Glenn L. Martin Co., Baltimore, 1955.
[6] N. Zierler, "Several binary sequence generators," Technical report 95, MIT Lincoln Lab., 1955.
[7] L. R. Welch, "Lower bounds on the maximum cross correlation of signals," IEEE Transactions on Information Theory, vol. IT-20, no. 3, pp. 397-399, May 1974.
[8] V. M. Sidelnikov, "On mutual correlation of sequences," Soviet math. Dokl., vol. 12, pp. 197-201, 1971.
[9] D. V. Sarwate, "Bounds on crosscorrelation and autocorrelation of sequences," IEEE Trans. Inform. Theory, vol. IT-25, pp. 720-724, Nov. 1979.
[10] X. Tang, P. Z Fan, and S. Matsufuji, "Lower bounds on the correlation of spreading sequence set with low or zero corelation zone," Electronics Letters, vol. 36, no. 6, pp. 551-552, March 2000.
[11] X. H. Chen, T. Lang, and J. Oksman, "Searching for quasi-optimal subfamilies of m-sequences for CDMA systems," IEEE 7th Int. Syrup. Pers., Indoor, Mobile Radio Commun. Proc., vol. 1, pp. 113-117, Oct. 15-18, 1996.
[12] R. Gold, "Optimal binary sequences for spread spectrum multiplexing," IEEE Trans. Inform. Theory, vol. 13, pp. 619-621, 1967.
[13] R. Gold, "Maximal recursive sequences with 3-valued recursive crosscorrelation functions," IEEE Trans. Inf. Theory, vol. IT-14, no. 1, pp. 154-156, Jan. 1968.
[14] J. Lahtonen, "On the odd and the aperiodic correlation properties of the Kasami sequences," IEEE Trans. Inf. Theory, vol. 41, no. 5, pp. 1506-1508, Sep. 1995.
[15] RayoGuang Cheng, Phone Lin, "OVSF code channel assignment for IMT-2000," IEEE 51st Vehicular Technology Conf. Proceedings, 2000 (VTC 2000), Tokyo, vol. 3, pp. 2188-2192, 2000.
[16] F. Adachi, M. Sawahashi, K. OKawa, "Tree-structured generation of orthogonai spreading codes with different lengths for the forward link of DS-CDMA mobile radio," IEEE Electronics Letters, vol. 33, no. 1, pp. 27-28, 1997.
[17] P. Z. Fan and L. Hao, "Generalized orthogonal Sequences and their applications in synchronous CDMA systems," IEICE Trans. Fund., vol. E83-A, no. 11: 1-16, Nov. 2000.
[18] D. B. Li, A method for spread spectrum multiple access coding with zero correlation window [P]. PCT/CN00/000028, 2000.
[19] P. Z. Fan, N. Suehiro, N. Kuroyanagi, and XM. Deng, "A class of binary sequenes with zero correlation zone," IEE Electronics Letters, vol. 35, no. 10, pp. 777-779, 1999.
[20] WG-1, CWTS, LAS-CDMA presented at 3Gpp-2 RAN WG-1, Seoul, Korea, 10 April, 2000.
[21] Hsiao-Hwa Chen, Hsin-Wei Chiu, "Generation of perfect orthogonal complementary codes for their applications in interference-free CDMA systems," The 15th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC2004), vol. 1, pp. 734-738, 5-8 Sept. 2004.
[22] R. L. Frank and S. A. Zadoff, "Phase shift codes with good periodic correlation properties," IRE Trans. Inform. Theoty, vol. IT-8, pp. 381-382, Oct. 1962.
[23] D. C. Chu, "Polyphase codes with good periodic correlation properties," IEEE Trans. Inform. Theory, vol. IT-18, pp. 531-532, July 1972.
[24] B. M. Popovic, "Generalized chirp-like polyphase sequences with optimum correlation properties," IEEE Transactions on Information Theory, vol. 38, no. 4, pp. 1406-1409, July 1992.
[25] N. Suehiro and M. Hatori, "Modulatable orthogonal sequences and their application to SSMA systems," IEEE Trans. Inform. Theory, vol. 34, pp. 93-100, Jan. 1988.
[26] R. Frank, "Polyphase complementary codes," IEEE Trans. on information theory, vol. 26, no. 6, pp. 641-647, 1980.
[27] B. M. Popovic, "Complementary sets of chirp-like polyphase sequences," Elecronics Letters, vol. 27, no. 3, pp. 254-255, 1991.
[28] S. Hara, R. Prasad, "Overview of multicarrier CDMA," IEEE Communications magazine, vol. 35, no. 12, pp. 126-133, Dec. 1997.
[29] S. Hara, R Prasad, "Design and performance of multicarrier CDMA system in frequency-selective Rayleigh fading channels," IEEE Transactions on Vehicular Technology, vol. 48, no. 5, pp. 1584-1595, 1999.
[30] Q. Shi, M. Latva-aho, "Performance analysis of MC-CDMA in Rayleigh fading channels with correlated envelopes and phases", IEE Proceedings Communications, vol. 150, no. 3, pp. 214-220, 2003.
[31] 杨大成等著，移动传播环境：理论基础·分析方法和建模技术，北京：机械工业出版社，2003．
[32] 吴志忠，移动通信—无线电波传播，北京：人民邮电出版社，2002．
[33] M. Pursley, "Performance evaluation for phase-coded spread-spectrum multiple-access communication-part Ⅰ: system analysis," IEEE Trans. on communications, vol. 25, no. 8, pp. 795-799, 1977.
[34] J．S．Lee，L．E．Miller等著，许希斌，周世东等译，CDMA系统工程手册，北京：人民邮电出版社，2001．
[35] A. I. Giortzis, L. F. Turner, "Application of mathematical programming to the fixed channel assignment problem in mobile radio networks," IEE Proc. Commun., vol. 144, no. 4, pp. 257-264, 1997.
[36] C. C. Tseng and C. L. Liu, "Complementary Sets of Sequences," IEEE Trans. Inform. Theory, vol. IT-18, pp. 644-652, 1972.
[37] N. Suehiro, "Complete Complementary code composed of N-multiple-shift orthogonal sequences," IECE Trans., vol. J65-A, pp. 1247-1253, Dec. 1982.
[38] 中国发明专利申请“超级互补码的产生方法、系统及利用超级互补码的通信系统”。发明人：陈晓华、黄爱苹。公开号：CN1625090，公开日：2005．06．08．
[39] J. Li, A. P. Huang, H. H. Chen, "Intergroup complementary codes for interference-resist CDMA wireless communications," IEEE trans, on wireless communications, submitted, 2007.
[40] D. A. Huffman, "The generation of impulse-equivalent pulse trains," IRE Trans. on, vol. 8, no. 9, pp. 10-16, 1962.
[41] D. Sarwate, "Bounds on crosscorrelation and autocorrelation of sequences," IEEE Trans. on information Theroy, vol. 25, no. 6, pp. 720-724, 1979.
[42] Hsiao-Hwa Chen, Hsin-Wei Chiu, M. Guizani, "Orthogonal complementary codes for interference-free CDMA technologies," IEEE Wireless Communications, vol. 13, Issue 1, pp. 68-79, Feb. 2006.
[43] X. H. Tang, P. Z. Fan, and S. Matsufuji, "Lower bounds on the maximum correlation of sequence set with low or zero correlation zone," IEE Electro. Lett., vol. 36, pp. 551-552, Mar. 2000.
[44] S. Matsufuji, "Non-binary sequence sets with zero correlation zone for AS-CDMA systems," in Proc. 1st Int. Workshop on Sequence Design and Applications for CDMA systems (IWSDA2001), Chengdu, China, pp. 89-98, Sept. 2001.
[45] B. M. Popovic, "Spreading sequences for multi-carrier CDMA systems," IEEE Trans. on communications, vol. 47, no. 6, pp. 918-926, 1999.
[46] S. -H. Tsai, Y. -P. Lin and C. -C. J. Kuo, "MAI-Free MC-CDMA systems based on Hadamard-Walsh codes," IEEE Trans. on signal processing, vol. 54, no. 8, pp. 3166-3179, 2006.
[47] B. Natarajan, CR. Nassar and S. Shattil, "High-performance MC-CDMA via carrier intefferometry codes," IEEE Trans. on Vehicular Technology, vol. 50, no. 6, pp 1344-1352, 2001.
[48] Q. Shi and M. Latva-aho, "Simple sprea_ding code allocation scheme for downlink MCCDMA," Electron. Lett., vol. 38, pp. 807-809, Jul. 2002.
[49] D. Mottier, D. Castelain," A spreading sequence allocation procedure for MC-CDMA transmission systems," IEEE 52nd Vehicular Technology Conf. 2000 (VTC 2000), vol. 3, pp. 1270-1275, 2000.
[50] R. M. Gray, "On the asymptotic eigenvalue distribution of Toeplitz matrices," IEEE Trans. Inf. Theory, vol. IT-18, pp. 725-730, Nov. 1972.
[51] J. Brewer, "Kronecker products and matrix calculus in system theory," IEEE Trans. on Circuits and Systems, vol. 25, no. 9, pp. 772-781, 1978.
[52] Hsiao-Hwa Chen, J. F. Yeh & N. Suehiro, "A multicarrier CDMA architecture based on orthogonal complementary codes for new generations of wideband wireless communications," IEEE Communications Magazines, vol. 39, no. 10, pp. 126-135, October 2001.
[53] J. G. Proakis, Digital communications, 4th ed, New York, McGral-Hill, 2003.
[2] 扩频通信技术，http://www.wx800.com/msg/2004/06/18/a851.php,6/2004.
[3] M. Zeng, A. Annamalai, and V. K. Bhargava, "Recent advances in cellular wireless communications," IEEE Communications Magazine, vol. 36, no. 9, pp. 128-138, September 1999.
[4] R. L. Pickholtz, L. B. Milstein and D. L. Schiling, "Spread spectrum for mobile communications," IEEE Trans. Veh. Technol., vol. 40, no. 2, pp. 313-322, May 1991.
[5] S. W Golomb, "Sequences with randomness properties," Terminal Progress Report under Contract, 639498, Glenn L. Martin Co., Baltimore, 1955.
[6] N. Zierler, "Several binary sequence generators," Technical report 95, MIT Lincoln Lab., 1955.
[7] L. R. Welch, "Lower bounds on the maximum cross correlation of signals," IEEE Transactions on Information Theory, vol. IT-20, no. 3, pp. 397-399, May 1974.
[8] V. M. Sidelnikov, "On mutual correlation of sequences," Soviet math. Dokl., vol. 12, pp. 197-201, 1971.
[9] D. V. Sarwate, "Bounds on crosscorrelation and autocorrelation of sequences," IEEE Trans. Inform. Theory, vol. IT-25, pp. 720-724, Nov. 1979.
[10] X. Tang, P. Z Fan, and S. Matsufuji, "Lower bounds on the correlation of spreading sequence set with low or zero corelation zone," Electronics Letters, vol. 36, no. 6, pp. 551-552, March 2000.
[11] X. H. Chen, T. Lang, and J. Oksman, "Searching for quasi-optimal subfamilies of m-sequences for CDMA systems," IEEE 7th Int. Syrup. Pers., Indoor, Mobile Radio Commun. Proc., vol. 1, pp. 113-117, Oct. 15-18, 1996.
[12] R. Gold, "Optimal binary sequences for spread spectrum multiplexing," IEEE Trans. Inform. Theory, vol. 13, pp. 619-621, 1967.
[13] R. Gold, "Maximal recursive sequences with 3-valued recursive crosscorrelation functions," IEEE Trans. Inf. Theory, vol. IT-14, no. 1, pp. 154-156, Jan. 1968.
[14] J. Lahtonen, "On the odd and the aperiodic correlation properties of the Kasami sequences," IEEE Trans. Inf. Theory, vol. 41, no. 5, pp. 1506-1508, Sep. 1995.
[15] RayoGuang Cheng, Phone Lin, "OVSF code channel assignment for IMT-2000," IEEE 51st Vehicular Technology Conf. Proceedings, 2000 (VTC 2000), Tokyo, vol. 3, pp. 2188-2192, 2000.
[16] F. Adachi, M. Sawahashi, K. OKawa, "Tree-structured generation of orthogonai spreading codes with different lengths for the forward link of DS-CDMA mobile radio," IEEE Electronics Letters, vol. 33, no. 1, pp. 27-28, 1997.
[17] P. Z. Fan and L. Hao, "Generalized orthogonal Sequences and their applications in synchronous CDMA systems," IEICE Trans. Fund., vol. E83-A, no. 11: 1-16, Nov. 2000.
[18] D. B. Li, A method for spread spectrum multiple access coding with zero correlation window [P]. PCT/CN00/000028, 2000.
[19] P. Z. Fan, N. Suehiro, N. Kuroyanagi, and XM. Deng, "A class of binary sequenes with zero correlation zone," IEE Electronics Letters, vol. 35, no. 10, pp. 777-779, 1999.
[20] WG-1, CWTS, LAS-CDMA presented at 3Gpp-2 RAN WG-1, Seoul, Korea, 10 April, 2000.
[21] Hsiao-Hwa Chen, Hsin-Wei Chiu, "Generation of perfect orthogonal complementary codes for their applications in interference-free CDMA systems," The 15th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC2004), vol. 1, pp. 734-738, 5-8 Sept. 2004.
[22] R. L. Frank and S. A. Zadoff, "Phase shift codes with good periodic correlation properties," IRE Trans. Inform. Theoty, vol. IT-8, pp. 381-382, Oct. 1962.
[23] D. C. Chu, "Polyphase codes with good periodic correlation properties," IEEE Trans. Inform. Theory, vol. IT-18, pp. 531-532, July 1972.
[24] B. M. Popovic, "Generalized chirp-like polyphase sequences with optimum correlation properties," IEEE Transactions on Information Theory, vol. 38, no. 4, pp. 1406-1409, July 1992.
[25] N. Suehiro and M. Hatori, "Modulatable orthogonal sequences and their application to SSMA systems," IEEE Trans. Inform. Theory, vol. 34, pp. 93-100, Jan. 1988.
[26] R. Frank, "Polyphase complementary codes," IEEE Trans. on information theory, vol. 26, no. 6, pp. 641-647, 1980.
[27] B. M. Popovic, "Complementary sets of chirp-like polyphase sequences," Elecronics Letters, vol. 27, no. 3, pp. 254-255, 1991.
[28] S. Hara, R. Prasad, "Overview of multicarrier CDMA," IEEE Communications magazine, vol. 35, no. 12, pp. 126-133, Dec. 1997.
[29] S. Hara, R Prasad, "Design and performance of multicarrier CDMA system in frequency-selective Rayleigh fading channels," IEEE Transactions on Vehicular Technology, vol. 48, no. 5, pp. 1584-1595, 1999.
[30] Q. Shi, M. Latva-aho, "Performance analysis of MC-CDMA in Rayleigh fading channels with correlated envelopes and phases", IEE Proceedings Communications, vol. 150, no. 3, pp. 214-220, 2003.
[31] 杨大成等著，移动传播环境：理论基础·分析方法和建模技术，北京：机械工业出版社，2003．
[32] 吴志忠，移动通信—无线电波传播，北京：人民邮电出版社，2002．
[33] M. Pursley, "Performance evaluation for phase-coded spread-spectrum multiple-access communication-part Ⅰ: system analysis," IEEE Trans. on communications, vol. 25, no. 8, pp. 795-799, 1977.
[34] J．S．Lee，L．E．Miller等著，许希斌，周世东等译，CDMA系统工程手册，北京：人民邮电出版社，2001．
[35] A. I. Giortzis, L. F. Turner, "Application of mathematical programming to the fixed channel assignment problem in mobile radio networks," IEE Proc. Commun., vol. 144, no. 4, pp. 257-264, 1997.
[36] C. C. Tseng and C. L. Liu, "Complementary Sets of Sequences," IEEE Trans. Inform. Theory, vol. IT-18, pp. 644-652, 1972.
[37] N. Suehiro, "Complete Complementary code composed of N-multiple-shift orthogonal sequences," IECE Trans., vol. J65-A, pp. 1247-1253, Dec. 1982.
[38] 中国发明专利申请“超级互补码的产生方法、系统及利用超级互补码的通信系统”。发明人：陈晓华、黄爱苹。公开号：CN1625090，公开日：2005．06．08．
[39] J. Li, A. P. Huang, H. H. Chen, "Intergroup complementary codes for interference-resist CDMA wireless communications," IEEE trans, on wireless communications, submitted, 2007.
[40] D. A. Huffman, "The generation of impulse-equivalent pulse trains," IRE Trans. on, vol. 8, no. 9, pp. 10-16, 1962.
[41] D. Sarwate, "Bounds on crosscorrelation and autocorrelation of sequences," IEEE Trans. on information Theroy, vol. 25, no. 6, pp. 720-724, 1979.
[42] Hsiao-Hwa Chen, Hsin-Wei Chiu, M. Guizani, "Orthogonal complementary codes for interference-free CDMA technologies," IEEE Wireless Communications, vol. 13, Issue 1, pp. 68-79, Feb. 2006.
[43] X. H. Tang, P. Z. Fan, and S. Matsufuji, "Lower bounds on the maximum correlation of sequence set with low or zero correlation zone," IEE Electro. Lett., vol. 36, pp. 551-552, Mar. 2000.
[44] S. Matsufuji, "Non-binary sequence sets with zero correlation zone for AS-CDMA systems," in Proc. 1st Int. Workshop on Sequence Design and Applications for CDMA systems (IWSDA2001), Chengdu, China, pp. 89-98, Sept. 2001.
[45] B. M. Popovic, "Spreading sequences for multi-carrier CDMA systems," IEEE Trans. on communications, vol. 47, no. 6, pp. 918-926, 1999.
[46] S. -H. Tsai, Y. -P. Lin and C. -C. J. Kuo, "MAI-Free MC-CDMA systems based on Hadamard-Walsh codes," IEEE Trans. on signal processing, vol. 54, no. 8, pp. 3166-3179, 2006.
[47] B. Natarajan, CR. Nassar and S. Shattil, "High-performance MC-CDMA via carrier intefferometry codes," IEEE Trans. on Vehicular Technology, vol. 50, no. 6, pp 1344-1352, 2001.
[48] Q. Shi and M. Latva-aho, "Simple sprea_ding code allocation scheme for downlink MCCDMA," Electron. Lett., vol. 38, pp. 807-809, Jul. 2002.
[49] D. Mottier, D. Castelain," A spreading sequence allocation procedure for MC-CDMA transmission systems," IEEE 52nd Vehicular Technology Conf. 2000 (VTC 2000), vol. 3, pp. 1270-1275, 2000.
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