直接序列扩频通信系统中的序列设计
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摘要
扩频通信因其具有保密性好、截获概率低、抗干扰性能强以及多址复用等优点,目前已经在现代军事通信、卫星通信、移动通信以及指挥控制通信中得到了广泛应用。直接序列扩频系统是扩频通信中应用最多、技术最成熟的一种频谱扩展方式。在直接序列扩频系统中,扩频序列性能的优劣在很大程度上决定了通信系统的多址干扰和符号间干扰的大小,从而直接影响到系统的性能。因此,深入研究扩频序列的性质、设计性能优良的扩频序列是直接序列扩频系统的核心课题。本文针对直接序列扩频系统中的扩频序列设计问题进行了研究,取得了如下研究结果:
1.研究了对于奇数n,GMW序列与WG序列间的互相关函数以及GMW序列与WG某一采样序列间的互相关函数,并给出了GMW序列与WG序列间互相关函数的最大峰值。同时,分析了WG序列间的互相关特性,在一定条件下,WG序列间的互相关函数可为3-值或5-值的。
2.分别针对n为奇数和n为偶数两种情形,构造了两类基于迹函数的二元低相关序列集。新的序列集不仅具有较多序列数目而且具有较大线性复杂度。
3.构造了一类新的p-元低相关序列集。新构造的p-元序列集不仅具有低相关性,而且具有较大的线性复杂度和较多的序列数目。
4.提出了两种由已知的零相关区序列集构造出具有周期更长、序列数目更多、零相关区更宽的零相关区序列集的方法。另外,提出了由完备序列和酉矩阵构造零相关区序列集的方法,得到了最优零相关区序列集。
5.构造了一类在原点周围的一个矩形区内周期相关函数和非周期相关函数都为0的三元阵列集。新阵列集中包含的阵列数目接近理论界,其性能参数达到了近似最优的状态。
6.构造了一类在原点周围的一个十字形区内周期相关函数和非周期相关函数都为0的三元阵列集。
Spread spectrum communication system has many advantages such as good security, low probability of being intercepted and captured, strong anti-jamming ability and multiple-access communication ability and so on. Owing to the above advantages, spread spectrum communication system has been widely used in modern military communications, satellite communications, mobile communications and command-control communications. Direct sequence spread spectrum (DS-SS) system is the most widely used and its technology is the most mature in spread spectrum communication system. The preference of the spread spectrum sequences decide the inter symbol interference (ISI) and multi-access interference (MAI) in DS-SS system to a large extent. Therefore, the investigation of sequences' properties and their constructions are the core technologies in DS-SS system. In this thesis, we study the sequences design for DS-SS system. The main contributions of this work are as follows:
1. For odd n, the cross-correlations between GMW sequences and WG sequences (decimated WG sequences with one particular exponent) and that of WG sequences are investigated in detail. Moreover, the maximum magnitude of the cross- correlation between GMW sequences and WG sequences are given. Furthermore, the cross-correlation of WG sequences can be 3-valued or 5-valued under a certain condition.
2. A new family of binary sequences with low correlation property is constructed for odd n and even n, respectively. The new sequence sets are proved to have not only large linear span but large family size as well.
3. A new family of p-ary sequences with low correlation property is presented. It is proved that the proposed sequence set has not only large linear span but also large family size.
4. Two new methods of constructing zero correlation zone (ZCZ) sequence set with large family size from an known one are presented. Compared with the original ZCZ sequence set, the proposed sequence sets have longer period, larger family size, and wider zero correlation zone. In addition, we present two new methods for constructing ZCZ sequence set from an arbitrary perfect sequence and unitary matrices.
5. A novel construction method of ternary two dimensional array sets having a rectangular zero correlation zone is presented. The new class of array sets have rectangular zero correlation zones for both periodic and aperiodic correlation functions. The member size of the proposed two dimensional array sets is close to the methmatical bound, and its performance parameter is almost optimal.
6. A construction of ternary two dimensional array sets having a cross-shaped zero correlation zone is presented. The new class of array sets has a cross-shaped zero correlation zone for both periodic and aperiodic correlation functions.
1.研究了对于奇数n,GMW序列与WG序列间的互相关函数以及GMW序列与WG某一采样序列间的互相关函数,并给出了GMW序列与WG序列间互相关函数的最大峰值。同时,分析了WG序列间的互相关特性,在一定条件下,WG序列间的互相关函数可为3-值或5-值的。
2.分别针对n为奇数和n为偶数两种情形,构造了两类基于迹函数的二元低相关序列集。新的序列集不仅具有较多序列数目而且具有较大线性复杂度。
3.构造了一类新的p-元低相关序列集。新构造的p-元序列集不仅具有低相关性,而且具有较大的线性复杂度和较多的序列数目。
4.提出了两种由已知的零相关区序列集构造出具有周期更长、序列数目更多、零相关区更宽的零相关区序列集的方法。另外,提出了由完备序列和酉矩阵构造零相关区序列集的方法,得到了最优零相关区序列集。
5.构造了一类在原点周围的一个矩形区内周期相关函数和非周期相关函数都为0的三元阵列集。新阵列集中包含的阵列数目接近理论界,其性能参数达到了近似最优的状态。
6.构造了一类在原点周围的一个十字形区内周期相关函数和非周期相关函数都为0的三元阵列集。
Spread spectrum communication system has many advantages such as good security, low probability of being intercepted and captured, strong anti-jamming ability and multiple-access communication ability and so on. Owing to the above advantages, spread spectrum communication system has been widely used in modern military communications, satellite communications, mobile communications and command-control communications. Direct sequence spread spectrum (DS-SS) system is the most widely used and its technology is the most mature in spread spectrum communication system. The preference of the spread spectrum sequences decide the inter symbol interference (ISI) and multi-access interference (MAI) in DS-SS system to a large extent. Therefore, the investigation of sequences' properties and their constructions are the core technologies in DS-SS system. In this thesis, we study the sequences design for DS-SS system. The main contributions of this work are as follows:
1. For odd n, the cross-correlations between GMW sequences and WG sequences (decimated WG sequences with one particular exponent) and that of WG sequences are investigated in detail. Moreover, the maximum magnitude of the cross- correlation between GMW sequences and WG sequences are given. Furthermore, the cross-correlation of WG sequences can be 3-valued or 5-valued under a certain condition.
2. A new family of binary sequences with low correlation property is constructed for odd n and even n, respectively. The new sequence sets are proved to have not only large linear span but large family size as well.
3. A new family of p-ary sequences with low correlation property is presented. It is proved that the proposed sequence set has not only large linear span but also large family size.
4. Two new methods of constructing zero correlation zone (ZCZ) sequence set with large family size from an known one are presented. Compared with the original ZCZ sequence set, the proposed sequence sets have longer period, larger family size, and wider zero correlation zone. In addition, we present two new methods for constructing ZCZ sequence set from an arbitrary perfect sequence and unitary matrices.
5. A novel construction method of ternary two dimensional array sets having a rectangular zero correlation zone is presented. The new class of array sets have rectangular zero correlation zones for both periodic and aperiodic correlation functions. The member size of the proposed two dimensional array sets is close to the methmatical bound, and its performance parameter is almost optimal.
6. A construction of ternary two dimensional array sets having a cross-shaped zero correlation zone is presented. The new class of array sets has a cross-shaped zero correlation zone for both periodic and aperiodic correlation functions.
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