基于桥函数重组研究的一种扩频序列设计
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摘要
序列设计研究是很多工程领域的重要课题。随着第三代、第四代移动通信技术的发展,码分多址技术逐渐成为一支主流力量,其特点包括：抗干扰能力强,抗截获能力强和通信系统容量大等,这些优势的提升很大程度上要依赖于扩频序列设计。实验表明,桥函数在码序列设计方面有很大的应用前景,本文在现有杂交桥函数序列设计研究的基础上,进一步研究了基于桥函数的序列生成方式和最佳序列设计方法。
文章提出了一种新型三值函数序列——重组杂交桥函数序列的生成方法,对其基本性质、相关性质进行了研究,对其最佳扩频序列设计方法和设计结果进行了说明,并进一步讨论了其他基于桥函数的序列(族)生成方式和设计方法。创新性工作主要包括：
(1)用重组杂交的方式,构造了一种新型三值函数序列,命名为重组杂交桥函数序列,该函数序列突破了桥函数序列中零元素的规律性分布,扩大了扩频序列的可研究范围；
(2)研究了重组杂交桥函数矩阵的一些基本性质,包括行正交和列正交的特性特征,并给出了严格的数学证明；重点讨论了重组杂交桥函数序列的相关性,并通过仿真实验得到了一系列结论；
(3)给出了基于重组杂交桥函数序列的最佳序列族设计方法,针对零相关区、主旁瓣比、相对影响因子等特征参数,用计算机搜索算法实现了对广义同类杂交桥函数序列的最佳扩频序列设计,得出了一系列优选序列族；
(4)从新的角度,提出了一种序列生成方式和一种序列族构造方法,分别称之为最佳零相关区交织桥函数序列和重构序列族,并分别对其相关性质进行了实验讨论和结果分析,得到了两种新的具有良好相关性的序列族设计方法。
通过本文的研究工作,扩展了杂交桥函数序列的生成思想,不仅完善了桥函数理论体系,也为序列码设计提供了更广阔的研究基础,使桥函数理论在无线通信等工程领域的应用进一步成为可能。
The design of code sequences is an important topic in many engineering fields.With the fast development of the 3G and the 4G mobile communication technology,Code Division Multiple Access (CDMA) technology has become a mainstream.It's key features include:huge capacity, good anti-interference and anti-interception capability, etc. It deeply dependents on the spread-spectrum sequences design to enhance these advantages. As research demonstrates,the bridge function has a great prospect in the code sequences design.Based on the learning and designing of the Hybrid Bridge Function sequence,this paper make further study on sequence generating methods and optimal sequences designing.
This paper proposes a new kind of sequence generating method.It's used to form a new ternary function sequence which is named as Restructed-Hybrid Bridge Function sequence.It analyzes the basic characters and the correlation characteristics of Restructed-Hybrid Bridge function sequence,and describes a design method as a kind of optimum spread-spectrum sequences designing with the new sequence.Further more, it also talks about some other sequence(s) generating methods and design methods based on the bridge functions. Specifically,this paper takes the following innovative contents:
(1)Create Restructed-Hybrid Bridge Function sequence with the method of Restructed-Hybrid,which breaks through the regular distribution of zero elements in the Bridge Function sequence.It expands the scope of the spread-spectrum sequences'study.
(2)Study some basic characters of Restructed-Hybrid Function matrix, including the pair wise orthogonal character of the row vectors and the group orthogonal characters of the column vectors, and give strict mathematical proves.Focus on correlation functions of Restructed-Hybrid Bridge Function sequences, and obtain some conclusions out through simulation.
(3)Further elaborate the design methods of optimal Restructed-Hybrid Bridge Function sequences sets.For the characteristic parameters such as zero correlation zones (ZCZs),main-side lobe ratio and relative influence factor,raise a sequence design based on the generalized-similar Restructed-Hybrid Bridge Function sequences with the computer search algorithm, and give out a series of preferred sequence sets.
(4)From new perspective, raise a generating method of optimal ZCZ Interwoven Bridge Function sequence and a reconstructing method of sequences family.Through taking analysis on simulation results of them,get two design methods of sequences family with good correlation characters. As manifested by experiments, the optimal ZCZ Interwoven Bridge Function sequence could apply to communication system.
Through the research, this paper extends the generation thoughts of the Hybrid Bridge Function sequences.It not only improves the Bridge Function theory system,but also provides a broader research base on the code sequences design.And it makes it further possible that the Bridge Function theory is to be used in the field of wireless communication applications and other projects.
文章提出了一种新型三值函数序列——重组杂交桥函数序列的生成方法,对其基本性质、相关性质进行了研究,对其最佳扩频序列设计方法和设计结果进行了说明,并进一步讨论了其他基于桥函数的序列(族)生成方式和设计方法。创新性工作主要包括：
(1)用重组杂交的方式,构造了一种新型三值函数序列,命名为重组杂交桥函数序列,该函数序列突破了桥函数序列中零元素的规律性分布,扩大了扩频序列的可研究范围；
(2)研究了重组杂交桥函数矩阵的一些基本性质,包括行正交和列正交的特性特征,并给出了严格的数学证明；重点讨论了重组杂交桥函数序列的相关性,并通过仿真实验得到了一系列结论；
(3)给出了基于重组杂交桥函数序列的最佳序列族设计方法,针对零相关区、主旁瓣比、相对影响因子等特征参数,用计算机搜索算法实现了对广义同类杂交桥函数序列的最佳扩频序列设计,得出了一系列优选序列族；
(4)从新的角度,提出了一种序列生成方式和一种序列族构造方法,分别称之为最佳零相关区交织桥函数序列和重构序列族,并分别对其相关性质进行了实验讨论和结果分析,得到了两种新的具有良好相关性的序列族设计方法。
通过本文的研究工作,扩展了杂交桥函数序列的生成思想,不仅完善了桥函数理论体系,也为序列码设计提供了更广阔的研究基础,使桥函数理论在无线通信等工程领域的应用进一步成为可能。
The design of code sequences is an important topic in many engineering fields.With the fast development of the 3G and the 4G mobile communication technology,Code Division Multiple Access (CDMA) technology has become a mainstream.It's key features include:huge capacity, good anti-interference and anti-interception capability, etc. It deeply dependents on the spread-spectrum sequences design to enhance these advantages. As research demonstrates,the bridge function has a great prospect in the code sequences design.Based on the learning and designing of the Hybrid Bridge Function sequence,this paper make further study on sequence generating methods and optimal sequences designing.
This paper proposes a new kind of sequence generating method.It's used to form a new ternary function sequence which is named as Restructed-Hybrid Bridge Function sequence.It analyzes the basic characters and the correlation characteristics of Restructed-Hybrid Bridge function sequence,and describes a design method as a kind of optimum spread-spectrum sequences designing with the new sequence.Further more, it also talks about some other sequence(s) generating methods and design methods based on the bridge functions. Specifically,this paper takes the following innovative contents:
(1)Create Restructed-Hybrid Bridge Function sequence with the method of Restructed-Hybrid,which breaks through the regular distribution of zero elements in the Bridge Function sequence.It expands the scope of the spread-spectrum sequences'study.
(2)Study some basic characters of Restructed-Hybrid Function matrix, including the pair wise orthogonal character of the row vectors and the group orthogonal characters of the column vectors, and give strict mathematical proves.Focus on correlation functions of Restructed-Hybrid Bridge Function sequences, and obtain some conclusions out through simulation.
(3)Further elaborate the design methods of optimal Restructed-Hybrid Bridge Function sequences sets.For the characteristic parameters such as zero correlation zones (ZCZs),main-side lobe ratio and relative influence factor,raise a sequence design based on the generalized-similar Restructed-Hybrid Bridge Function sequences with the computer search algorithm, and give out a series of preferred sequence sets.
(4)From new perspective, raise a generating method of optimal ZCZ Interwoven Bridge Function sequence and a reconstructing method of sequences family.Through taking analysis on simulation results of them,get two design methods of sequences family with good correlation characters. As manifested by experiments, the optimal ZCZ Interwoven Bridge Function sequence could apply to communication system.
Through the research, this paper extends the generation thoughts of the Hybrid Bridge Function sequences.It not only improves the Bridge Function theory system,but also provides a broader research base on the code sequences design.And it makes it further possible that the Bridge Function theory is to be used in the field of wireless communication applications and other projects.
引文
[1]张其善,李植华.信息传输新方法[M].北京：宇航出版社,1989
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[3]郭梯云,邬国扬,李建东.移动通信[M].西安：西安电子科技大学出版社,2002
[4]钱雪荣.扩频通信系统的扩频序列设计研究[D].南京：南京理工大学,2004
[5]朱近康.CDMA通信技术[M].合肥：人民邮电出版社,2001
[6]R.L.Pickholtz,L.B.Milstein,D.L.Schilling.Spread Spectrum for Mobile Communications [J]. IEEE Transactions on Vehicular Technology,1991,40(2):313-322
[7]R.Gaudenzi,C.Elia,R.Viola.Bandlimited Quasi-Synchronous CDMA:A Novel Satellite Access Technique for Mobile and Personal Communication Systems[J].IEEE Journal on Selected Areas in Communications,1992,10(2):328-343
[8]V.M.Dasilva,E.S.Sousa.Multicarrier Orthogonal CDMA Signals for Quasi-Synchronous Communication Systems[J].IEEE Journal on Selected Areas in Communications, 1994,12(5):842-852
[9]W.J.Houtum.Quasi-Synchronous Code-Division Multiple Access with High-Order Modulation[J].IEEE Transactions on Communications,2001,49(7):1240-1249
[10]J.K.Omura,P.T.Yang. Spread Spectrum S-CDMA for Personal Communication erviees [J].IEEE Conference in Military Communications,San Diego,USA,1992:269-273
[11]易雄书,崔华,余少波,王常远.扩频通信系统中基本扩频序列性能分析与设计[J].计算机仿真,2008,25(6)
[12]ZENG Fan-xi. On generalized orthogonal spreading sequences for quasi synchronous CDMA system [J]重庆邮电学院学报,2003,15(4)
[13]Waleej Haider, Seema Ansari. Method for Allocating Walsh Codes by Complete Group Information Walsh Code in CDMA Cellular System [J]计算机系统应用,2009,(6)
[14]TD-SCDMA系列\CDMA2000-1X系统.中国第三代移动通信网,3G网络课堂,2003.Copyright(?)2002-2003 www.china-3g.com
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[16]张其善,常青.桥函数理论综述[J].航空学报,2002,23(5)
[17]张其善,张凤元,杨东凯.信息传输与正交函数[M].北京：国防工业出版社,2008
[18]张其善,王钢.桥函数及广义桥函数的研究进展[J].北京航空航天大学学报,2001,27(3)
[19]张其善,金明录.信号复制生成理论及应用[M].北京：人民邮电出版社,2001
[20]竺南直,张其善.广义沃尔什函数的复制理论及其应用[J].电子学报,1994,22(1)
[21]王钢,张军,张其善.一种新型混合进制广义级联桥函数系生成算法及其主要性质[J1.自然科学进展,2007,17(5)
[22]王钢,张其善.一种新型非正弦函数——混合进制广义桥函数的复制生成算法及其主要性质[J].中国科学,2005,35(10)：1064-1071
[23]李岩,常青,张其善.一种基于Walsh函数生成的杂交桥函数[J].自然科学进展,2009,19(2)
[24]张凤元,吴今培,张其善.复制生成序列的自相关函数研究[J].信号处理,2004,20(3)：241—244
[25]张凤元,吴今培,张其善.混合进制复制生成序列的相关函数[J].电子学报,2004,32(9)：1472—1474
[26]邓琼.基于杂交桥函数的序列设计及其应用[D].北京：北京航空航天大学,2010
[27]张其善,张凤元,吴今培.沃尔什函数的一种新定义及其复制本质[J].通信学报,2004,25(2)：144—148
[28]窦中兆,雷湘.CDMA无线通信原理[M].北京：清华大学出版社,2004
[29](美)Kazimierz Siwak, Debra McKerwn著.张中兆,沙学军等泽.《超宽带无线电技术》[M].北京：电子工业出版社,2005
[30](意) Maria-Gabriella Di Benedetto, Guerino Giancola著.葛利嘉,朱林,袁晓芳,陈帮富等译.《超宽带无线电基础》[M].北京：电子工业出版社,2005
[31]李岩.基于桥函数的序列设计及其在无线通信系统中的应用[D].北京：北京航空航天大学,2009
[32]郭磊.一种特殊扩频序列设计与应用[D].北京：北京化工大学,2010
[33]Fan PZ, Darnell M. Sequence design for communications applications[J]. Research Studies Press, John Wiley & Sons ltd, London,1996
[34]Darnell M. Sequence design for communications applications[J]. Research Studies Press,John Wiley & Sons ltd,London,1996
[35]L.R.Welch. Lower bounds on maximum cross-correlation of signals[J]. IEEE Trans. Inform, Theory, Vol. IT-20. pp.397-399,1974
[36]D.V.Sarwate. Bounds on crosscorrelation and autocorrelation of sequences[J]. IEEE Trans. Inform, Theory, Vol. IT-25. pp.720-724,1979
[37]P.Z. Fan, N. Suehiro, N. Kuroyanagi, X. M. Deng, A class of binary sequences with zero correlation zone[J]. IEE Electronic Leter, Vol.35. pp.773-779.1999
[38]Z. Zierler. Several binary sequence generator[J]. Technical report 95, MIT Lincoln Lab, 1995:1-3
[39]S. W. Golomb. Sequence with randomness properties[J]. Terminal Progress Report under Contract 639498, Glenn L. Martin Co., Baltimore,1995
[40]胡征,樊昌信.沃尔什函数及其在通信中的应用[M].北京：人民邮电出版社,1980
[41]郑维行,苏维宜.任福贤.沃尔什函数理论与应用[M].上海：上海科学技术出版社,1983
[42]袁超伟,陈德荣等.CDMA蜂窝移动通信[M],北京邮电大学出版社,2003
[43]张凤元,张其善.一类新型智能码序列的相关函数研究[J].遥测遥控,2005,26(5)：7—11
[44]任韩.图论[M].上海：上海科技教育出版社,2009
[45]Reinhard Diestel. Graph Theory[M]北京：世界图书出版社,2008
[46]周尚超,刘二根,王森.图的最大完全子图的一个算法[J].华东交通大学学报,2002,19(4)：71—72
[47]王扬志.零相关区序列与零相关区序列偶理论的研究[D].河北：燕山大学,2010
[48]邱刚.基于完全互补码的CDMA通信系统仿真研究[D].四川：西南交通大学,2002
[49]S.Matsufuji.Two Families of Sequence Pairs With Zero Correlation Zone.International Conference on Parallel and Distributed Computing[J]. Applications and Technologies, Chengdu,China,2003:899-903
[50]王龙业,唐小虎.零相关区序列的交织构造[J].西南交通大学学报,2006,5141(3)：319-323,340
[2]王钢,张军,张其善.非正弦函数理论及其在通信中的应用[M].北京：电子工业出版社,2006
[3]郭梯云,邬国扬,李建东.移动通信[M].西安：西安电子科技大学出版社,2002
[4]钱雪荣.扩频通信系统的扩频序列设计研究[D].南京：南京理工大学,2004
[5]朱近康.CDMA通信技术[M].合肥：人民邮电出版社,2001
[6]R.L.Pickholtz,L.B.Milstein,D.L.Schilling.Spread Spectrum for Mobile Communications [J]. IEEE Transactions on Vehicular Technology,1991,40(2):313-322
[7]R.Gaudenzi,C.Elia,R.Viola.Bandlimited Quasi-Synchronous CDMA:A Novel Satellite Access Technique for Mobile and Personal Communication Systems[J].IEEE Journal on Selected Areas in Communications,1992,10(2):328-343
[8]V.M.Dasilva,E.S.Sousa.Multicarrier Orthogonal CDMA Signals for Quasi-Synchronous Communication Systems[J].IEEE Journal on Selected Areas in Communications, 1994,12(5):842-852
[9]W.J.Houtum.Quasi-Synchronous Code-Division Multiple Access with High-Order Modulation[J].IEEE Transactions on Communications,2001,49(7):1240-1249
[10]J.K.Omura,P.T.Yang. Spread Spectrum S-CDMA for Personal Communication erviees [J].IEEE Conference in Military Communications,San Diego,USA,1992:269-273
[11]易雄书,崔华,余少波,王常远.扩频通信系统中基本扩频序列性能分析与设计[J].计算机仿真,2008,25(6)
[12]ZENG Fan-xi. On generalized orthogonal spreading sequences for quasi synchronous CDMA system [J]重庆邮电学院学报,2003,15(4)
[13]Waleej Haider, Seema Ansari. Method for Allocating Walsh Codes by Complete Group Information Walsh Code in CDMA Cellular System [J]计算机系统应用,2009,(6)
[14]TD-SCDMA系列\CDMA2000-1X系统.中国第三代移动通信网,3G网络课堂,2003.Copyright(?)2002-2003 www.china-3g.com
[15]张其善,张有光.桥函数理论及其应用[M].北京：国防工业出版社,1992
[16]张其善,常青.桥函数理论综述[J].航空学报,2002,23(5)
[17]张其善,张凤元,杨东凯.信息传输与正交函数[M].北京：国防工业出版社,2008
[18]张其善,王钢.桥函数及广义桥函数的研究进展[J].北京航空航天大学学报,2001,27(3)
[19]张其善,金明录.信号复制生成理论及应用[M].北京：人民邮电出版社,2001
[20]竺南直,张其善.广义沃尔什函数的复制理论及其应用[J].电子学报,1994,22(1)
[21]王钢,张军,张其善.一种新型混合进制广义级联桥函数系生成算法及其主要性质[J1.自然科学进展,2007,17(5)
[22]王钢,张其善.一种新型非正弦函数——混合进制广义桥函数的复制生成算法及其主要性质[J].中国科学,2005,35(10)：1064-1071
[23]李岩,常青,张其善.一种基于Walsh函数生成的杂交桥函数[J].自然科学进展,2009,19(2)
[24]张凤元,吴今培,张其善.复制生成序列的自相关函数研究[J].信号处理,2004,20(3)：241—244
[25]张凤元,吴今培,张其善.混合进制复制生成序列的相关函数[J].电子学报,2004,32(9)：1472—1474
[26]邓琼.基于杂交桥函数的序列设计及其应用[D].北京：北京航空航天大学,2010
[27]张其善,张凤元,吴今培.沃尔什函数的一种新定义及其复制本质[J].通信学报,2004,25(2)：144—148
[28]窦中兆,雷湘.CDMA无线通信原理[M].北京：清华大学出版社,2004
[29](美)Kazimierz Siwak, Debra McKerwn著.张中兆,沙学军等泽.《超宽带无线电技术》[M].北京：电子工业出版社,2005
[30](意) Maria-Gabriella Di Benedetto, Guerino Giancola著.葛利嘉,朱林,袁晓芳,陈帮富等译.《超宽带无线电基础》[M].北京：电子工业出版社,2005
[31]李岩.基于桥函数的序列设计及其在无线通信系统中的应用[D].北京：北京航空航天大学,2009
[32]郭磊.一种特殊扩频序列设计与应用[D].北京：北京化工大学,2010
[33]Fan PZ, Darnell M. Sequence design for communications applications[J]. Research Studies Press, John Wiley & Sons ltd, London,1996
[34]Darnell M. Sequence design for communications applications[J]. Research Studies Press,John Wiley & Sons ltd,London,1996
[35]L.R.Welch. Lower bounds on maximum cross-correlation of signals[J]. IEEE Trans. Inform, Theory, Vol. IT-20. pp.397-399,1974
[36]D.V.Sarwate. Bounds on crosscorrelation and autocorrelation of sequences[J]. IEEE Trans. Inform, Theory, Vol. IT-25. pp.720-724,1979
[37]P.Z. Fan, N. Suehiro, N. Kuroyanagi, X. M. Deng, A class of binary sequences with zero correlation zone[J]. IEE Electronic Leter, Vol.35. pp.773-779.1999
[38]Z. Zierler. Several binary sequence generator[J]. Technical report 95, MIT Lincoln Lab, 1995:1-3
[39]S. W. Golomb. Sequence with randomness properties[J]. Terminal Progress Report under Contract 639498, Glenn L. Martin Co., Baltimore,1995
[40]胡征,樊昌信.沃尔什函数及其在通信中的应用[M].北京：人民邮电出版社,1980
[41]郑维行,苏维宜.任福贤.沃尔什函数理论与应用[M].上海：上海科学技术出版社,1983
[42]袁超伟,陈德荣等.CDMA蜂窝移动通信[M],北京邮电大学出版社,2003
[43]张凤元,张其善.一类新型智能码序列的相关函数研究[J].遥测遥控,2005,26(5)：7—11
[44]任韩.图论[M].上海：上海科技教育出版社,2009
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