河北工业大学 博士学位论文 阵列偶相关理论及其在扩频通信系统中的应用研究 姓名：李琦 申请学位级别：博士 专业：微电子学与固体电子学 指导教师：赵晓群 20090401 河北工业大学博士学位论文 i 阵列偶相关理论及其在扩频通信系统中的应用研究阵列偶相关理论及其在扩频通信系统中的应用研究 摘摘 要要 序列和阵列设计理论在现代通信、雷达、声纳、制导、空间测控、以及电子对抗等系 统中具有十分广泛的应用。结构优良的序列和阵列信号可以提高系统的抗干扰、抗噪声、 抗截获、抗衰落等性能，可以实现扩频多址通信等。因此对其进行深入研究在理论和应用 上都具有十分重要的意义。 本文主要对基于阵列偶相关理论的各种相关信号形式进行了深入研究。 首先推导出二元序列偶的周期相关理论界，这为进一步研究具有良好相关特性的二元 序列偶集提供了理论基础。 提出了广义伪随机屏蔽二进序列偶，给出了其变换性质、组合允许条件。搜索出若干 广义伪随机屏蔽二进序列偶，并与伪随机二进序列偶进行了对比分析。并将其推广到多维 广义伪随机屏蔽二进阵列偶，研究了其等价变换性质、频谱特性和组合允许条件，利用这 些条件对小体积广义伪随机屏蔽二进阵列偶进行搜索，并提出了广义伪随机屏蔽二进阵列 偶的折叠构造法。 提出了周期屏蔽二元互补序列偶集。研究了其等价变换性质，及其与非周期屏蔽二元 互补序列偶集的等价关系。提出了利用最佳屏蔽二进序列偶与阵列偶、列正交矩阵、周期 屏蔽二元互补序列偶集伙伴以及周期乘积法等多种构造方法。 在奇周期相关条件下提出了奇周期屏蔽二元互补序列偶集。给出了屏蔽序列偶的奇周 期相关函数的特性以及奇周期屏蔽二元互补序列偶集的等价变换性质，及其与非周期和周 期屏蔽二元互补序列偶集的等价关系。搜索出若干奇周期屏蔽二元互补序列偶集，并给出 了多种构造方法。结果表明其与奇周期二元互补序列集相比具有更大的存在空间。 提出了二元互补阵列偶集。对二元阵列偶的非周期相关特性以及二元互补阵列偶集的 等价变换性质进行了研究，得出二元互补阵列偶集的变维并不影响互补性的结论。搜索出 若干二元互补阵列偶集，提出多种二元互补阵列偶集的构造方法。研究了互正交二元互补 阵列偶集集合的生成方法，由此可生成大量具有更大阵列偶数与体积的互正交二元互补阵 列偶集集合。 研究了基于最佳序列偶和正交矩阵构造 ZCZ 序列偶集的方法。对其在 QS-CDMA 系统中 的应用进行了分析。结果表明该系统具有较好的性能，可满足多用户通信的要求，因此具 有一定的应用前景。并对基于序列偶的扩频通信系统设计方案进行了讨论。 阵列偶相关理论及其在扩频通信系统中的应用研究 ii 关键词：关键词：阵列偶，伪随机屏蔽，屏蔽互补，零相关区，扩频通信 河北工业大学博士学位论文 iii RESEARCH ON ARRAY PAIRS CORRELATION THEORY AND ITS APPLICATION IN SPREAD SPECTRUM COMMUNICATION SYSTEM ABSTRACT The design theory of sequences and arrays plays an increasingly important role in modern communications, radar, sonar, navigation, space ranging and controlling, and electronically countermeasures systems etc. Well-structured sequence and array signals can improve systems properties of anti-interference, anti-noise, anti-doubts, the decline of performance and achieve spread spectrum multiple access communication. Therefore, an in-depth study of these signals is of vital importance both in theory and applications. The thesis mainly studied various kinds of signals based on array pair correlation theory. Firstly, the periodic correlation bounds of binary sequence pair is educed, which provide the theory foundation for further research of binary sequence pair sets with good correlation property. Generalized pseudorandom punctured binary sequence pair along with the transformation properties and combinatorial limited conditions are presented. Some generalized pseudorandom punctured binary sequence pairs are searched out, and is compared with pseudorandom binary sequence pair. This concept is extended to generalized pseudorandom punctured binary array pair which is a kind of multi-dimension signal. The equivalent transformation properties, spectrum character and combinatorial limited conditions are discussed also. Based on these conditions, several generalized pseudorandom punctured binary array pairs with small volumes are obtained. The folding construction method is presented. Periodic punctured binary complementary sequence pair set is proposed. The equivalent transform properities and relation with aperiodic punctured binary complementary sequence pair set are studied. Many construction methods are presented, such as using perfect punctured binary sequence pair and array pair, column orthogonal matrix, periodic punctured binary complementary sequence pair sets mate and periodic product methods etc. Under odd-periodic correlation condition, the odd-periodic punctured binary complementary sequence pair set is proposed. The properities of punctured binary sequence pairs odd-periodic correlation function, the equivalent transformation properties of odd-periodic 阵列偶相关理论及其在扩频通信系统中的应用研究 iv punctured binary complementary sequence pair set and relations with aperiodic and periodic punctured binary complementary sequence pair set are presented also. Odd-periodic punctured binary complementary sequence pair sets are searched out, and several construction methods are proposed. The result shows that it has larger exist space compared with odd-periodic binary complementary sequence set. The binary complementary array pair set is proposed also. The aperiodic correlation properities of binary array pair and binary complementary array pair sets equivalent transformation properties are studied, and find that changing dimension doesnt affect its complementary properity. Some binary complementary array pair sets are obtained, and many kinds of construction methods are proposed. The synthesized methods of mutual orthogonal binary complementary array pair set are studied also, through this method amount of mutual orthogonal binary complementary array pair set with larger numbers and volumes can be obtained. The construction method of ZCZ sequence pair set is studied based on perfect sequence pair and orthogonal matrix, and analyzed its application in QS-CDMA system. The result shows that it has good performance, satisfies the requirement of multi-user communication, and has certain application foreground. The design scheme of spread-spectrum system based on sequence pairs is discussed. KEY WORDS: array pair, pseudorandom punctured, punctured complementary, zero correlation zone, sp