ZCZ序列偶集构造方法研究
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摘要
近似同步码分多址(AS-CDMA)系统,其同步误差可根据需要控制在一个或几个码片周期之内。于是人们只要求扩频序列在同步误差范围内具有或接近理想相关特性。ZCZ序列恰能满足这一特性。使用性能良好的ZCZ序列,可以降低甚至消除多径干扰和多址干扰(MAI)。但是,由于ZCZ序列的设计受到许多条件的限制,目前它的寻找还存在一定的困难。ZCZ序列偶作为ZCZ序列的扩展,用于AS-CDMA系统中的扩频序列,可以获得更多数量的地址码。
首先,本文提出了ZCZ序列偶集及大容量ZCZ序列偶集的构造方法。通过对最佳序列偶进行不同的移位,再与一定阶数的酉矩阵进行相关积运算,构造出了近似最优及最优两类ZCZ序列偶集;通过对已有的ZCZ序列偶集进行适当的移位再与相应的酉矩阵进行相关积运算,构造出了更大容量和更长零相关区的ZCZ序列偶集。
其次,通过对正交矩阵偶进行移位、交织运算,再进行n次递归,构造出ZCZ序列偶集;通过对已知的ZCZ序列偶集进行移位、交织运算,再进行n次递归,构造出新的大容量ZCZ序列偶集。
最后,本文还提出了一种扩大ZCZ序列偶集零相关区宽度的构造方法,对已知ZCZ序列偶集进行交织运算,再通过m次递归构造,在保持序列偶数目M不变的条件下,序列偶的零相关区宽度和长度都变成了原序列偶的M m倍。
上述方法适用于二元、三元、四相及多相情况。构造出的ZCZ序列偶集性能优良,在同步误差允许的范围内,能够满足多用户AS-CDMA系统的要求。
In the Approximately-synchronized code-division multiple-access (AS-CDMA) system, the synchronization error can be controlled in a few cycles within the chip. So people only requires spreading sequence in the synchronization error range (such as one or chip period) associated with or close to the ideal characteristics. ZCZ sequences satisfy this characteristic. ZCZ sequences with good performance, can reduce or eliminate multipath interference and multiple access interference (MAI). However, the ZCZ sequence design by many conditions, there are still some difficulties to look for them. ZCZ sequence pairs as the expansion of ZCZ sequence , as the AS-CDMA system of spread spectrum sequence can get more number of address code.
First of all, in this paper, new methods for constructing set of ZCZ sequence pairs and ZCZ sequence pairs with large family size are proposed. First, almost optimal or optimal ZCZ sequence pairs set can be generated from the correlation product of unitary matrix and perfect sequence pairs with difference shift operation. Second, a new method for constructing ZCZ sequence pairs set with larger family size and longer zero correlation zone from a known one is presented.
Secondly, a ZCZ sequence pairs set can be generated form orthogonal matrix pair with different shift, interleaved operation and n times recursive constructions; A new method for constructing ZCZ sequence pairs set with large family size from a known one is presented.
Finally, in this paper, a new method for constructing ZCZ sequence pairs set with large zero correlation zone from a known one is presented, new ZCZ sequence pairs set can be generated from the original one with interleaved operation. The zero correlation zone of ZCZ sequence pairs set is M mtimes than the known one by m times recursive constructions with the new method.
In addition, The methods are suitable for binary, ternary, four-phase and multiphase conditions. And the new ZCZ sequence pairs set has excellent performance that can satisfy Multi-users of AS-CDMA system.
首先,本文提出了ZCZ序列偶集及大容量ZCZ序列偶集的构造方法。通过对最佳序列偶进行不同的移位,再与一定阶数的酉矩阵进行相关积运算,构造出了近似最优及最优两类ZCZ序列偶集;通过对已有的ZCZ序列偶集进行适当的移位再与相应的酉矩阵进行相关积运算,构造出了更大容量和更长零相关区的ZCZ序列偶集。
其次,通过对正交矩阵偶进行移位、交织运算,再进行n次递归,构造出ZCZ序列偶集;通过对已知的ZCZ序列偶集进行移位、交织运算,再进行n次递归,构造出新的大容量ZCZ序列偶集。
最后,本文还提出了一种扩大ZCZ序列偶集零相关区宽度的构造方法,对已知ZCZ序列偶集进行交织运算,再通过m次递归构造,在保持序列偶数目M不变的条件下,序列偶的零相关区宽度和长度都变成了原序列偶的M m倍。
上述方法适用于二元、三元、四相及多相情况。构造出的ZCZ序列偶集性能优良,在同步误差允许的范围内,能够满足多用户AS-CDMA系统的要求。
In the Approximately-synchronized code-division multiple-access (AS-CDMA) system, the synchronization error can be controlled in a few cycles within the chip. So people only requires spreading sequence in the synchronization error range (such as one or chip period) associated with or close to the ideal characteristics. ZCZ sequences satisfy this characteristic. ZCZ sequences with good performance, can reduce or eliminate multipath interference and multiple access interference (MAI). However, the ZCZ sequence design by many conditions, there are still some difficulties to look for them. ZCZ sequence pairs as the expansion of ZCZ sequence , as the AS-CDMA system of spread spectrum sequence can get more number of address code.
First of all, in this paper, new methods for constructing set of ZCZ sequence pairs and ZCZ sequence pairs with large family size are proposed. First, almost optimal or optimal ZCZ sequence pairs set can be generated from the correlation product of unitary matrix and perfect sequence pairs with difference shift operation. Second, a new method for constructing ZCZ sequence pairs set with larger family size and longer zero correlation zone from a known one is presented.
Secondly, a ZCZ sequence pairs set can be generated form orthogonal matrix pair with different shift, interleaved operation and n times recursive constructions; A new method for constructing ZCZ sequence pairs set with large family size from a known one is presented.
Finally, in this paper, a new method for constructing ZCZ sequence pairs set with large zero correlation zone from a known one is presented, new ZCZ sequence pairs set can be generated from the original one with interleaved operation. The zero correlation zone of ZCZ sequence pairs set is M mtimes than the known one by m times recursive constructions with the new method.
In addition, The methods are suitable for binary, ternary, four-phase and multiphase conditions. And the new ZCZ sequence pairs set has excellent performance that can satisfy Multi-users of AS-CDMA system.
引文
1曾兴雯,刘乃安,孙献璞.扩展频谱通信及其多址技术.西安:西安电子科技大学出版社, 2004:134-196
2朱进康.扩展频谱通信及其应用.合肥:中国科技大学出版社, 1988:289-321
3 Shannon C E.A mathematical theory of communication.The Bell System Technical Journal, 1948, 27(7):379-423 623-656
4梅文华,杨义先.跳频通信地址编码理论.北京:国防工业出版社,1996:21-36
5孙立新,邢宁霞. CDMA(码分多址)移动通信技术.北京:人民邮电出版社, 1996:71-88
6竺南直,肖辉,刘景波.码分多址(CDMA)移动通信系统.北京:电子工业出版社,1999:25-32
7吴晓文,段晓明,蒲迎春.第三代移动通信标准化研究的最新进展.电子学报,1999,27(11A):21-24
8尤肖虎,曹淑敏,李建东.第三代移动通信系统发展现状与展望.电子学报, 1999,27(11A):3-8
9胡建栋,郑朝晖,龙必起.码分多址与个人通信.北京:人民邮电出版社, 1996:154-202
10吴伟陵.移动通信中的关键技术.北京:北京邮电大学出版社, 2000:49-71
11 Omura J K, Yang P T. Spread spectrum S-CDMA for personal communication services. Military Communications Conference, 1992:269-273
12 Pickholtz R L, Milstein L B, Schilling D L. Spread spectrum for mobile communications. IEEE Trans.Veh. Technol. 1991, 40(2):313-322
13 N. Suehiro. A Signal Design without Co-channel Imefference for Approximately Synchronized CDMA Systems. IEEE Journal on Selected Areas in Communicatiom,1994, 12(5):837-841
14 L.R.Welch. Lower Bounds on the Maximum Cross Correlation of Signals. IEEETransactions on Information Theory, 1974, 20(3):397-399
15 D. V. Sarwate. Bounds on Crosscorrelation and Autocorrelation of Sequences. IEEE Transactions on Information Theory, 1979, 25(6):720-724
16 V. I. Levenshtein. New Lower Bounds on Aperiodic Cross Correlation of Binary Codes. IEEE Transactions on Information Theory, 1999, 45(1):284-288
17 P. Z. Fan, N. Suehiro, N. Kuroyanagi. A Class of Binary Sequences with Zero Correlation Zone. Electronics Letters, 1999, 35(10):777-779
18 B. Q. Long, P. Zhang, J. D. Hu. A Generalized QS-CDMA System and the Design of New Spreading Codes. IEEE Transactions on Vehicular Technology, 1998, 47(4):1268–1275
19 X. H. Tang, P. Z. Fan. A Class of Pseudonoise Sequences over GF(p) with Low Correlation Zone. IEEE Transactions on Information Theory, 2001,47(4):1644-1649
20 S. Matsufuji. Two Families of Sequence Pairs With Zero Correlation Zone. International Conference on Parallel and Distributed Computing, Applications and Technologies, Chengdu, China, 2003:899-903
21 S. Matsufuji, N.Kuroyanagi, N.Suehiro. Two Types of Polyphase Sequence Sets for Approximately Synchronized CDMA Systems. IEICE Trans. Fundamentals, 2003, E86-A(1): 274-279
22 S. Matsufuji. Families of Sequence Pairs with Zero Correlation Zone. IEICE Trans. Fundamentals, 2006, E89-A(11):3013-3017
23 H. Torii, M. Nakamura, N. Suehiro. A New Class of Zero-Correlation Zone Sequences. IEEE Transactions on Information Theory, 2004, 50(3):559-565
24 H. Torii, M. Nakamura. Enhancement of ZCZ Sequence Set Construction Procedure. IEICE Trans. Fundamentals, 2007, E90-A(2):535-538
25 J. S. Cha, S. Kameda, M. Okoyama. New Binary Sequences with Zero-Correlation During for Approximately Synchronized CDMA. Electronics Letters, 2000, 36 (11): 991-993
26 J. S. Cha. Class of Ternary Spreading Sequences with Zero Correlation Duration. Electronics Letters, 2001, 37(10):636-637
27 P. Z. Fan, W. H. Mow. On Optimal Training Sequence Design for Multiple-Antenna Systems over Dispersive Fading Channels and its Extensions. IEEE Transactions on Vehicular Technology, 2004, 53(5):1623-1626
28 Fan P Z, Suehiro N, Kuroyanagi N. Class of binary sequences with zero correlation zone.Electronics Letters ,1999,35(10):777-779
29 Deng X M, Fan P Z. Spreading sequence sets with zero correlation zone. Electronics Letters, 2000, 36(11): 993-994
30 G. L. Ye, J. Li, A.P.Huang. A Novel ZCZ Code Based on m-Sequences and its Applications in CDMA Systems. IEEE Communications Letters, 2007,11(6):465-467
31曾凡鑫.适用于近似同步CDMA系统的扩频序列.通信学报, 2003, 24(11):34-39
32胡飞,文红,陈华伟.一类新型准同步CDMA系统扩频序列.西南交通大学学报,2004,39(1):104-107
33 T. Hayashi. A Class of Two-Dimensional Binary Sequences with Zero Correlation Zone. IEEE Signal Processing Letters, 2002, 9(7):217-221
34 T.Hayashi. Ternary Array Set Having a Zero Correlation Zone. IEICE Trans. Fundamentals, 2003, E86-A(8):2163-2167
35 T.Hayashi, S.Okawa. Binary Array Set Having a Cross-Shaped Zero-Correlation Zone. IEEE Signal Processing Letters, 2004, 11(4):423-426
36 Matsufuji S. Families of sequence pairs with zero correlation zone. IEICE Trans Fund Electron Commun Comput Sci 2006 , E89-A(11): 3013–3017
37梁清梅,刘金明,许成谦.一种达到理论上限的新型扩频序列集.无线电工程,2006,36(10): 27-30
38 Gao Junping, Li Qi, Dai Junfeng. A new construction technique of ZCZ sequence pairs set. IET Conference on Wireless, Mobile and Sensor Networks. United Kingdom: Institution of Engineering and Technology, 2007:970-973
39刘凯,许成谦,刘洺辛.由平方剩余差集与差集偶构造二元ZCZ序列偶集.北京邮电大学学报, 2009, 32 (4): 50-53
40许蕾,蒋挺,周正.最佳屏蔽二进序列偶在低/零相关区中的应用研究.通信学报, 2006, 10(27):19-24
41李兆斌,蒋挺,周正.基于伪随机序列的零相关区三元序列偶集的研究.通信学报, 2009, 30(8):27-31
42李兆斌,蒋挺,周正. ZCZ屏蔽阵列偶集的研究.电子学报, 2009 , 37(3): 288-291
43 Peng Daiyuan, Fan Pingzhi, Suehiro N. Construction of sequences with large zero correlation zone. IEICE Transaction on Fundamentals of Electronics,Communications and Computer Sciences, 2005 , E88-A(11): 3256-3259
44 WANG Jing-song, QI Wen-feng. A large class of binary zcz sequence families constructed by period doubling. Journal of Electronics (China), 2005, 24 (3): 341-344
45刘凯,许成谦,李刚.二元二值周期自相关序列偶的应用研究.电子与信息学报, 2009, 31(7):1536-1541
46王龙业,唐小虎.基于交织方法的ZCZ序列设计.西南交通大学学报, 2005, 40(3):422-425
47汪劲松,戚文峰.一类由交织方式构造的二元ZCZ序列簇.电子与信息学报, 2007, 29(7):1573-1575
48杨义先.最佳信号理论与设计.北京:人民邮电出版社, 1996:35-39.
49左会娟,佟鑫,温巧燕.由完备序列构造零相关区序列集的方法.北京邮电大学学报, 2008, 31(4):122-125
50 Xin TONG, Qiaoyan WEN. New Construction of ZCZ Sequence Set with Large Family Size. proc. 3rd, Int. Workshop on Signal Design and its Application in Communications (IWSDA2007), Chengdu, China , 2007:99-103
51唐小虎.低/零相关区理论与扩频通信系统序列设计. [西南交通大学工学博士学位论文]. 2001:92-96
52梁青梅.准同步CDMA系统中零相关区序列偶集合的设计. [燕山大学工学硕士学位论文]. 2005:33-49
2朱进康.扩展频谱通信及其应用.合肥:中国科技大学出版社, 1988:289-321
3 Shannon C E.A mathematical theory of communication.The Bell System Technical Journal, 1948, 27(7):379-423 623-656
4梅文华,杨义先.跳频通信地址编码理论.北京:国防工业出版社,1996:21-36
5孙立新,邢宁霞. CDMA(码分多址)移动通信技术.北京:人民邮电出版社, 1996:71-88
6竺南直,肖辉,刘景波.码分多址(CDMA)移动通信系统.北京:电子工业出版社,1999:25-32
7吴晓文,段晓明,蒲迎春.第三代移动通信标准化研究的最新进展.电子学报,1999,27(11A):21-24
8尤肖虎,曹淑敏,李建东.第三代移动通信系统发展现状与展望.电子学报, 1999,27(11A):3-8
9胡建栋,郑朝晖,龙必起.码分多址与个人通信.北京:人民邮电出版社, 1996:154-202
10吴伟陵.移动通信中的关键技术.北京:北京邮电大学出版社, 2000:49-71
11 Omura J K, Yang P T. Spread spectrum S-CDMA for personal communication services. Military Communications Conference, 1992:269-273
12 Pickholtz R L, Milstein L B, Schilling D L. Spread spectrum for mobile communications. IEEE Trans.Veh. Technol. 1991, 40(2):313-322
13 N. Suehiro. A Signal Design without Co-channel Imefference for Approximately Synchronized CDMA Systems. IEEE Journal on Selected Areas in Communicatiom,1994, 12(5):837-841
14 L.R.Welch. Lower Bounds on the Maximum Cross Correlation of Signals. IEEETransactions on Information Theory, 1974, 20(3):397-399
15 D. V. Sarwate. Bounds on Crosscorrelation and Autocorrelation of Sequences. IEEE Transactions on Information Theory, 1979, 25(6):720-724
16 V. I. Levenshtein. New Lower Bounds on Aperiodic Cross Correlation of Binary Codes. IEEE Transactions on Information Theory, 1999, 45(1):284-288
17 P. Z. Fan, N. Suehiro, N. Kuroyanagi. A Class of Binary Sequences with Zero Correlation Zone. Electronics Letters, 1999, 35(10):777-779
18 B. Q. Long, P. Zhang, J. D. Hu. A Generalized QS-CDMA System and the Design of New Spreading Codes. IEEE Transactions on Vehicular Technology, 1998, 47(4):1268–1275
19 X. H. Tang, P. Z. Fan. A Class of Pseudonoise Sequences over GF(p) with Low Correlation Zone. IEEE Transactions on Information Theory, 2001,47(4):1644-1649
20 S. Matsufuji. Two Families of Sequence Pairs With Zero Correlation Zone. International Conference on Parallel and Distributed Computing, Applications and Technologies, Chengdu, China, 2003:899-903
21 S. Matsufuji, N.Kuroyanagi, N.Suehiro. Two Types of Polyphase Sequence Sets for Approximately Synchronized CDMA Systems. IEICE Trans. Fundamentals, 2003, E86-A(1): 274-279
22 S. Matsufuji. Families of Sequence Pairs with Zero Correlation Zone. IEICE Trans. Fundamentals, 2006, E89-A(11):3013-3017
23 H. Torii, M. Nakamura, N. Suehiro. A New Class of Zero-Correlation Zone Sequences. IEEE Transactions on Information Theory, 2004, 50(3):559-565
24 H. Torii, M. Nakamura. Enhancement of ZCZ Sequence Set Construction Procedure. IEICE Trans. Fundamentals, 2007, E90-A(2):535-538
25 J. S. Cha, S. Kameda, M. Okoyama. New Binary Sequences with Zero-Correlation During for Approximately Synchronized CDMA. Electronics Letters, 2000, 36 (11): 991-993
26 J. S. Cha. Class of Ternary Spreading Sequences with Zero Correlation Duration. Electronics Letters, 2001, 37(10):636-637
27 P. Z. Fan, W. H. Mow. On Optimal Training Sequence Design for Multiple-Antenna Systems over Dispersive Fading Channels and its Extensions. IEEE Transactions on Vehicular Technology, 2004, 53(5):1623-1626
28 Fan P Z, Suehiro N, Kuroyanagi N. Class of binary sequences with zero correlation zone.Electronics Letters ,1999,35(10):777-779
29 Deng X M, Fan P Z. Spreading sequence sets with zero correlation zone. Electronics Letters, 2000, 36(11): 993-994
30 G. L. Ye, J. Li, A.P.Huang. A Novel ZCZ Code Based on m-Sequences and its Applications in CDMA Systems. IEEE Communications Letters, 2007,11(6):465-467
31曾凡鑫.适用于近似同步CDMA系统的扩频序列.通信学报, 2003, 24(11):34-39
32胡飞,文红,陈华伟.一类新型准同步CDMA系统扩频序列.西南交通大学学报,2004,39(1):104-107
33 T. Hayashi. A Class of Two-Dimensional Binary Sequences with Zero Correlation Zone. IEEE Signal Processing Letters, 2002, 9(7):217-221
34 T.Hayashi. Ternary Array Set Having a Zero Correlation Zone. IEICE Trans. Fundamentals, 2003, E86-A(8):2163-2167
35 T.Hayashi, S.Okawa. Binary Array Set Having a Cross-Shaped Zero-Correlation Zone. IEEE Signal Processing Letters, 2004, 11(4):423-426
36 Matsufuji S. Families of sequence pairs with zero correlation zone. IEICE Trans Fund Electron Commun Comput Sci 2006 , E89-A(11): 3013–3017
37梁清梅,刘金明,许成谦.一种达到理论上限的新型扩频序列集.无线电工程,2006,36(10): 27-30
38 Gao Junping, Li Qi, Dai Junfeng. A new construction technique of ZCZ sequence pairs set. IET Conference on Wireless, Mobile and Sensor Networks. United Kingdom: Institution of Engineering and Technology, 2007:970-973
39刘凯,许成谦,刘洺辛.由平方剩余差集与差集偶构造二元ZCZ序列偶集.北京邮电大学学报, 2009, 32 (4): 50-53
40许蕾,蒋挺,周正.最佳屏蔽二进序列偶在低/零相关区中的应用研究.通信学报, 2006, 10(27):19-24
41李兆斌,蒋挺,周正.基于伪随机序列的零相关区三元序列偶集的研究.通信学报, 2009, 30(8):27-31
42李兆斌,蒋挺,周正. ZCZ屏蔽阵列偶集的研究.电子学报, 2009 , 37(3): 288-291
43 Peng Daiyuan, Fan Pingzhi, Suehiro N. Construction of sequences with large zero correlation zone. IEICE Transaction on Fundamentals of Electronics,Communications and Computer Sciences, 2005 , E88-A(11): 3256-3259
44 WANG Jing-song, QI Wen-feng. A large class of binary zcz sequence families constructed by period doubling. Journal of Electronics (China), 2005, 24 (3): 341-344
45刘凯,许成谦,李刚.二元二值周期自相关序列偶的应用研究.电子与信息学报, 2009, 31(7):1536-1541
46王龙业,唐小虎.基于交织方法的ZCZ序列设计.西南交通大学学报, 2005, 40(3):422-425
47汪劲松,戚文峰.一类由交织方式构造的二元ZCZ序列簇.电子与信息学报, 2007, 29(7):1573-1575
48杨义先.最佳信号理论与设计.北京:人民邮电出版社, 1996:35-39.
49左会娟,佟鑫,温巧燕.由完备序列构造零相关区序列集的方法.北京邮电大学学报, 2008, 31(4):122-125
50 Xin TONG, Qiaoyan WEN. New Construction of ZCZ Sequence Set with Large Family Size. proc. 3rd, Int. Workshop on Signal Design and its Application in Communications (IWSDA2007), Chengdu, China , 2007:99-103
51唐小虎.低/零相关区理论与扩频通信系统序列设计. [西南交通大学工学博士学位论文]. 2001:92-96
52梁青梅.准同步CDMA系统中零相关区序列偶集合的设计. [燕山大学工学硕士学位论文]. 2005:33-49
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