新型扩频序列及其理论界研究
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摘要
在码分多址(CDMA)技术中,扩频序列扮演着十分重要的角色。扩频序列特性的好坏在很大程度上决定了码分多址通信系统的多址接入干扰与多径干扰的大小,从而直接影响着系统性能优劣和系统容量大小。扩频序列理论包含扩频序列理论界与扩频序列设计两个主要研究方面。本文研究了常规扩频序列理论界、新型扩频序列理论界、新型扩频序列构造及其性能分析、扩频序列在准同步(QS)CDMA通信系统中的应用等重要问题。
首先,论文推广了Levenshtein提出的“权重向量法”,并通过选用特殊的权重向量,建立了常规二元直接扩频序列集和常规单位复根直接扩频序列集新的理论界,导出了序列长度、序列数目、最大非周期自相关边峰值和最大非周期互相关值等参数所满足的一些新的数学不等式。研究表明,本文得到的这些新理论界比已有的Sarwate界,Welch界、Levenshtein界和Boztas界更紧。
基于广义正交直接扩频序列的概念,通过将“权重向量法”与低/零相关区(LCZ/ZCZ)的理论结合在一起,本文提出了研究广义正交(GO)扩频序列集理论界的有效方法,即“相关区法”。使用相关区法,建立了广义正交二元序列周期和非周期相关函数理论界、广义正交单位复根序列周期和非周期相关函数理论界。论文研究表明,这些新的理论界包含了已有的关于广义正交序列的Tang-Fan界;而关于常规序列的Sarwate界、Welch界、Levenshtein界和彭-范界则是新结果的特殊情况,并且在很多情形下广义相关函数理论界更紧。
其次,论文研究了跳频(FH)扩频序列的理论界。对于常规跳频扩频序列集,建立了其序列长度、序列数目、频隙数目、最大周期(非周期)汉明自相关边峰值和最大周期(非周期)汉明互相值等参数所满足的几个理论约束关系(理论界)。对于所得到的周期汉明相关理论界,分析表明它们是已知Lempel-Greenberger界和Seay界的推广;而对于所得到的非周期汉明相关函数理论界,则是本论文首次导出。
论文详细阐述了无/低碰撞区(NHZ/LHZ)跳频序列的概念,建立了广义正交跳频扩频序列集周期汉明相关函数的理论界。即对于广义正交跳频扩频序列集,建立了其序列长度、序列数目、频隙数目、相关区、在相关区内的最大周期汉明自相关边峰值和在相关区内的最大周期汉明互相关值等参数所满足的几个理论界。分析表明,常规跳频序列的Lempel-Greenberger界、Seay界、彭-范界和无碰撞区序列的Ye-Fan界只是本文结果的特殊情况。
The spreading sequences play a very important role in Code Division Multiple Access (CDMA) techniques. In general, the goodness of the spreading sequences determines largely the level of the multiple-access interference and multipath interference of CDMA system, therefore directly influences the performance and capacity of the CDMA systems. The theory of spreading sequence design includes two primary research aspects, i.e. the theoretical bounds and sequence design. In this thesis, theoretical bounds for the conventional spreading sequences and the new type of spreading sequences are investigated; the constructions and analysis of novel spreading sequences are also carried out, together with their applications in quasi-synchronous (QS) CDMA communication systems.First of all, based on Levenshtein's "weight vector method", several new theoretical bounds for the conventional binary direct spreading sequences and the conventional direct spreading sequences over complex roots of unity are established by selecting special weight vector. That is, new mathematics inequalities are derived to disclose the relationship between the sequence length, the family size, the maximum aperiodic autocorrelation sidelobe and the maximum aperiodic crosscorrelation value. It is shown that these new theoretical bounds are tighter than the existing bounds, such as Sarwate bounds, Welch bounds, Levenshtein bounds and Boztas bounds.Based on the concepts of generalized orthogonal (GO) direct spreading sequences, by merging "weight vector method" with the theory of low/zero correlation zone (LCZ/ZCZ), an effective new method called "correlation zone method' is proposed for deriving theoretical bounds of GO sequence sets. Using "correlation zone method', the theoretical bounds for the periodic (aperiodic) GO binary sequence and the periodic (aperiodic) GO sequences over complex roots of unity are established. It is shown that these new theoretical bounds include the existing Tang-Fan bounds on GO sequences, the known Sarwate bounds, Welch bounds, Levenshtein bounds and Peng-Fan bounds on conventional sequences, as special cases. In addition, the theoretical bounds for GO functions are tighter under some circumstances.
Thereafter, the theoretical bounds on frequency hopping (FH) sequences are investigated. For the conventional FH sequence sets, several new theoretical restriction relations (theoretical bounds) that are satisfied by some parameters, such as the sequence length, the family size, the size of the frequency slot set, the maximum periodic (aperiodic) Hamming autocorrelation sidelobe and the maximum periodic (aperiodic) Hamming crosscorrelation value, are established. It is shown that the new periodic FH bounds include the known Lempel-Greenberger bounds and Seay bounds as special cases. Besides, the aperiodic FH bounds have not yet been previously reported.The concepts and properties of the no/low hit zone (NHZ/LHZ) on the FH sequences are then discussed in details, together with the theoretical bounds of periodic Hamming correlation functions on generalized orthogonal FH sequence sets. For GO FH sequence set, new theoretical inequalities are derived to disclose the relationship between sequence length, family size, size of the frequency slot set, correlation zone, maximum periodic Hamming autocorrelation sidelobe in the correlation zone and maximum periodic Hamming crosscorrelation value in the correlation zone. It is shown that the existing bounds on the conventional FH sequences, such as Lempel-Greenberger bounds, Seay bounds and Peng-Fan bounds, as well as the known Ye-Fan bounds on FH sequences with the no hit zone, are only special cases of the presented bounds.Next, the constructions and characteristics of the direct sequences are discussed. In order to judge the goodness of ZCZ direct sequence sets, a new concept, called ZCZ characteristic, is proposed. Then by defining a sequence operation called "correlation product", and establishing its basic properties, a new approach to construct sets of sequences with large zero correlation zone is presented. According to the proposed ZCZ characteristic measure, the new construction is near optimal with respect to the ZCZ bound. Besides, constructions and characteristics of frequency/time hopping (TH) sequences are also discussed. A general quadratic FH/TH sequences, a general cubic FH/TH sequences and polynomial FH/TH sequences are proposed and investigated in details. Based on the finite field theory, it is shown that the new frequency/time hopping sequence sets possess large family size and good Hamming correlation properties. Moreover, accurate analytical formulas for the average number of hits, the probability of full collisions on general
首先,论文推广了Levenshtein提出的“权重向量法”,并通过选用特殊的权重向量,建立了常规二元直接扩频序列集和常规单位复根直接扩频序列集新的理论界,导出了序列长度、序列数目、最大非周期自相关边峰值和最大非周期互相关值等参数所满足的一些新的数学不等式。研究表明,本文得到的这些新理论界比已有的Sarwate界,Welch界、Levenshtein界和Boztas界更紧。
基于广义正交直接扩频序列的概念,通过将“权重向量法”与低/零相关区(LCZ/ZCZ)的理论结合在一起,本文提出了研究广义正交(GO)扩频序列集理论界的有效方法,即“相关区法”。使用相关区法,建立了广义正交二元序列周期和非周期相关函数理论界、广义正交单位复根序列周期和非周期相关函数理论界。论文研究表明,这些新的理论界包含了已有的关于广义正交序列的Tang-Fan界;而关于常规序列的Sarwate界、Welch界、Levenshtein界和彭-范界则是新结果的特殊情况,并且在很多情形下广义相关函数理论界更紧。
其次,论文研究了跳频(FH)扩频序列的理论界。对于常规跳频扩频序列集,建立了其序列长度、序列数目、频隙数目、最大周期(非周期)汉明自相关边峰值和最大周期(非周期)汉明互相值等参数所满足的几个理论约束关系(理论界)。对于所得到的周期汉明相关理论界,分析表明它们是已知Lempel-Greenberger界和Seay界的推广;而对于所得到的非周期汉明相关函数理论界,则是本论文首次导出。
论文详细阐述了无/低碰撞区(NHZ/LHZ)跳频序列的概念,建立了广义正交跳频扩频序列集周期汉明相关函数的理论界。即对于广义正交跳频扩频序列集,建立了其序列长度、序列数目、频隙数目、相关区、在相关区内的最大周期汉明自相关边峰值和在相关区内的最大周期汉明互相关值等参数所满足的几个理论界。分析表明,常规跳频序列的Lempel-Greenberger界、Seay界、彭-范界和无碰撞区序列的Ye-Fan界只是本文结果的特殊情况。
The spreading sequences play a very important role in Code Division Multiple Access (CDMA) techniques. In general, the goodness of the spreading sequences determines largely the level of the multiple-access interference and multipath interference of CDMA system, therefore directly influences the performance and capacity of the CDMA systems. The theory of spreading sequence design includes two primary research aspects, i.e. the theoretical bounds and sequence design. In this thesis, theoretical bounds for the conventional spreading sequences and the new type of spreading sequences are investigated; the constructions and analysis of novel spreading sequences are also carried out, together with their applications in quasi-synchronous (QS) CDMA communication systems.First of all, based on Levenshtein's "weight vector method", several new theoretical bounds for the conventional binary direct spreading sequences and the conventional direct spreading sequences over complex roots of unity are established by selecting special weight vector. That is, new mathematics inequalities are derived to disclose the relationship between the sequence length, the family size, the maximum aperiodic autocorrelation sidelobe and the maximum aperiodic crosscorrelation value. It is shown that these new theoretical bounds are tighter than the existing bounds, such as Sarwate bounds, Welch bounds, Levenshtein bounds and Boztas bounds.Based on the concepts of generalized orthogonal (GO) direct spreading sequences, by merging "weight vector method" with the theory of low/zero correlation zone (LCZ/ZCZ), an effective new method called "correlation zone method' is proposed for deriving theoretical bounds of GO sequence sets. Using "correlation zone method', the theoretical bounds for the periodic (aperiodic) GO binary sequence and the periodic (aperiodic) GO sequences over complex roots of unity are established. It is shown that these new theoretical bounds include the existing Tang-Fan bounds on GO sequences, the known Sarwate bounds, Welch bounds, Levenshtein bounds and Peng-Fan bounds on conventional sequences, as special cases. In addition, the theoretical bounds for GO functions are tighter under some circumstances.
Thereafter, the theoretical bounds on frequency hopping (FH) sequences are investigated. For the conventional FH sequence sets, several new theoretical restriction relations (theoretical bounds) that are satisfied by some parameters, such as the sequence length, the family size, the size of the frequency slot set, the maximum periodic (aperiodic) Hamming autocorrelation sidelobe and the maximum periodic (aperiodic) Hamming crosscorrelation value, are established. It is shown that the new periodic FH bounds include the known Lempel-Greenberger bounds and Seay bounds as special cases. Besides, the aperiodic FH bounds have not yet been previously reported.The concepts and properties of the no/low hit zone (NHZ/LHZ) on the FH sequences are then discussed in details, together with the theoretical bounds of periodic Hamming correlation functions on generalized orthogonal FH sequence sets. For GO FH sequence set, new theoretical inequalities are derived to disclose the relationship between sequence length, family size, size of the frequency slot set, correlation zone, maximum periodic Hamming autocorrelation sidelobe in the correlation zone and maximum periodic Hamming crosscorrelation value in the correlation zone. It is shown that the existing bounds on the conventional FH sequences, such as Lempel-Greenberger bounds, Seay bounds and Peng-Fan bounds, as well as the known Ye-Fan bounds on FH sequences with the no hit zone, are only special cases of the presented bounds.Next, the constructions and characteristics of the direct sequences are discussed. In order to judge the goodness of ZCZ direct sequence sets, a new concept, called ZCZ characteristic, is proposed. Then by defining a sequence operation called "correlation product", and establishing its basic properties, a new approach to construct sets of sequences with large zero correlation zone is presented. According to the proposed ZCZ characteristic measure, the new construction is near optimal with respect to the ZCZ bound. Besides, constructions and characteristics of frequency/time hopping (TH) sequences are also discussed. A general quadratic FH/TH sequences, a general cubic FH/TH sequences and polynomial FH/TH sequences are proposed and investigated in details. Based on the finite field theory, it is shown that the new frequency/time hopping sequence sets possess large family size and good Hamming correlation properties. Moreover, accurate analytical formulas for the average number of hits, the probability of full collisions on general
引文
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