CN101662304B

CN101662304B - Method for designing zero correlation zone sequence on quadrature amplitude modulation constellation

Info

Publication number: CN101662304B
Application number: CN 200910023703
Authority: CN
Inventors: 马文平; 张晓�; 孙绍辉
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2009-08-26
Filing date: 2009-08-26
Publication date: 2013-04-10
Anticipated expiration: 2029-08-26
Also published as: CN101662304A

Abstract

The invention discloses a method for constructing a zero-correlation zone sequence cluster on a quadrature amplitude modulation constellation, which belongs to the technical field of digital communication and mainly solves the problem that the number of sequences of the existing zero-correlation sequence cluster is too small and the information bits transmitted in each sequence period are too small. The problem of too few numbers and the zero correlation interval of the series is too small. The construction process is: using 4×4 order 4-phase complex Hadamard matrix, constructing a 4-phase zero-correlation zone sequence cluster in a recursive manner; dividing this 4-phase zero-correlation zone sequence cluster into disjoint sequence sets , the number of sequences contained in each sequence set is the same; according to this disjoint sequence set, the zero-correlation zone sequence cluster on the quadrature amplitude modulation constellation is constructed. The sequence cluster constructed by the present invention has the advantages of a large number of sequences, a large number of information bits transmitted in each sequence cycle and a large zero-correlation interval, and can be applied to medium and large-capacity digital microwave communications, high-speed data transmission of cable TV networks, and satellite communications field.

Description

ZCZ Sequence Design Method for Quadrature Amplitude Modulation Constellation

技术领域 technical field

本方案属于数字通信技术领域，涉及正交幅度调制星座上的零相关序列簇的构造，可应用于中、大容量数字微波通信、有线电视网络高速数据传输、卫星通信等领域。The scheme belongs to the technical field of digital communication, and involves the construction of zero-correlation sequence clusters on the quadrature amplitude modulation constellation, and can be applied to medium and large-capacity digital microwave communication, high-speed data transmission of cable TV network, satellite communication and other fields.

背景技术 Background technique

码分多址(Code Division Multiple Access，CDMA)是第三代移动通信系统的一项主要技术。该技术给不同的用户分配一个独特的地址码，是一种允许不同的用户在同一时间、同一频谱上同时工作的通信方式。码分多址克服了时分多址和频分多址的缺点，容纳的用户数目大幅度提高。CDMA技术在20世纪40年代开始用于军事通信，到70年代末期开始用于蜂窝移动通信和卫星通信系统。1993年，美国电信协会TIA确定的美国第二代蜂窝移动通信标准IS-95采用了Qualcomm公司制订的CDMA技术规范。目前CDMA技术除已应用于移动通信外，在数据传输、卫星通信以及遥控遥测、空间通信等许多领域也得到越来越广泛的应用。Code Division Multiple Access (CDMA) is a main technology of the third generation mobile communication system. This technology assigns a unique address code to different users, which is a communication method that allows different users to work simultaneously on the same frequency spectrum at the same time. Code division multiple access overcomes the shortcomings of time division multiple access and frequency division multiple access, and the number of users accommodated is greatly increased. CDMA technology began to be used in military communications in the 1940s, and began to be used in cellular mobile communications and satellite communications systems in the late 1970s. In 1993, IS-95, the second-generation cellular mobile communication standard in the United States determined by TIA, adopted the CDMA technical specification formulated by Qualcomm. At present, in addition to being used in mobile communication, CDMA technology is also widely used in many fields such as data transmission, satellite communication, remote control telemetry, and space communication.

在CDMA通信系统中，序列的相关性准则是衡量序列设计的工程准则。人们希望CDMA通信系统中使用的序列应具有理想的相关特性，从而消除CDMA通信系统的多址干扰(MAI)，使得系统的性能达到最佳。具体而言，应用于CDMA通信系统的序列应具有如下相关特性：In the CDMA communication system, the correlation criterion of the sequence is an engineering criterion to measure the sequence design. It is hoped that the sequence used in the CDMA communication system should have ideal correlation characteristics, so as to eliminate the multiple access interference (MAI) of the CDMA communication system and make the system performance optimal. Specifically, the sequence applied to the CDMA communication system should have the following relevant characteristics:

(1)每个序列的自相关函数是一个冲激函数，即除了零时延外，其值应处处为零。(1) The autocorrelation function of each sequence is an impulse function, that is, its value should be zero everywhere except zero time delay.

(2)每对序列的互相关函数值处处为零。(2) The value of the cross-correlation function of each pair of sequences is zero everywhere.

所述的第一条性质对诸如遥测系统、雷达系统和扩频通信系统来说是十分重要的。而对同时遥测多个目标的系统、多个终端识别系统和码分多址通信系统来说，第二条性质则更为重要。遗憾的是，无论二元、多元还是复数序列，理论界已表明：具有这种理想相关特性的扩频序列集是不存在的。为了解决理想相关特性与理论界的矛盾，也为了减少系统对扩频码设计和对同步精度的要求，人们提出了准同步码分多址(QS-CDMA)系统，其同步误差可根据需要控制在几个码片周期之内。QS-CDMA系统中最初使用的序列都是传统的正交序列(Wash码)，同步误差被控制在一个码片以内。随着零相关区(Zero Correlation Zone，ZCZ)序列理论的逐渐深入，人们认识到QS-CDMA系统中最大相对时延可以超过一个码片的限制而达到几个码片。ZCZ序列因此也成为理想的QS-CDMA通信系统的扩频序列，ZCZ序列设计的优劣是直接关系到QS-CDMA系统性能好坏的问题。The first property stated is very important for systems such as telemetry systems, radar systems and spread spectrum communication systems. The second property is even more important for systems that telemeter multiple targets at the same time, multiple terminal identification systems, and code division multiple access communication systems. Unfortunately, regardless of binary, multivariate or complex sequences, the theoretical circles have shown that there is no spread spectrum sequence set with such ideal correlation characteristics. In order to solve the contradiction between the ideal correlation characteristic and the theoretical circle, and to reduce the system's requirements for spreading code design and synchronization accuracy, a quasi-synchronous code division multiple access (QS-CDMA) system is proposed, and its synchronization error can be controlled as needed within a few chip periods. The sequences initially used in the QS-CDMA system are traditional orthogonal sequences (Wash codes), and the synchronization error is controlled within one chip. With the gradual deepening of the Zero Correlation Zone (ZCZ) sequence theory, people realized that the maximum relative delay in the QS-CDMA system can exceed the limit of one chip and reach several chips. Therefore, the ZCZ sequence has also become an ideal spread spectrum sequence of the QS-CDMA communication system. The quality of the ZCZ sequence design is directly related to the performance of the QS-CDMA system.

参照图1，ZCZ序列用于QS-CDMA通信系统的原理如下：首先，将各个用户经过信道编码之后的数据送入系统中；接着，分别用为每个用户分配的ZCZ序列来对这些数据进行扩频；然后，分别将这些扩频数据进行调制，并将调制后的信号合并后送入信道中进行传输；之后，在接收端进行解调；最后，再分别利用分配给每个用户的ZCZ序列进行解扩，由于ZCZ序列在一定的区间内具有理想的相关特性，对于准同步CDMA系统，就恢复出了各个用户未经过信道译码的数据。Referring to Figure 1, the principle of ZCZ sequence used in QS-CDMA communication system is as follows: First, the data of each user after channel coding is sent into the system; then, the ZCZ sequence assigned to each user is used to process these data respectively Spread spectrum; then, these spread spectrum data are modulated separately, and the modulated signals are combined and sent to the channel for transmission; after that, demodulation is performed at the receiving end; finally, the ZCZ allocated to each user is used The sequence is despread, because the ZCZ sequence has ideal correlation characteristics in a certain interval, for the quasi-synchronous CDMA system, the data of each user that has not been decoded by the channel is recovered.

目前，针对ZCZ序列集的研究，已经取得了不少的成果。范平志等人提出了零相关区(ZCZ)序列集的概念，并在非周期正交互补序列对基础上构造了ZCZ序列集。Hayashi运用任意一对Hadamard矩阵构造了二元ZCZ序列集。虽然二元ZCZ序列集与多元序列集相比在硬件上更容易实现，但二元ZCZ序列集的理论界仅能达到多元ZCZ序列集理论界的一半。李道本提出了一种LA序列的构造方法，这实际上是一种在周期相关、非周期相关函数以及周期奇相关函数意义下的三元ZCZ序列。Matsufuji基于完备序列构造了三元和多元ZCZ序列。但目前现有的ZCZ序列存在以下一些问题：At present, many achievements have been made in the research on the ZCZ sequence set. Fan Pingzhi and others proposed the concept of zero-correlation zone (ZCZ) sequence set, and constructed the ZCZ sequence set on the basis of aperiodic orthogonal complementary sequence pairs. Hayashi used any pair of Hadamard matrices to construct a set of binary ZCZ sequences. Although binary ZCZ sequence sets are easier to realize in hardware than multivariate sequence sets, the theoretical bounds of binary ZCZ sequence sets can only reach half of the theoretical bounds of multivariate ZCZ sequence sets. Li Daoben proposed a construction method of LA sequence, which is actually a ternary ZCZ sequence in the sense of periodic correlation, non-periodic correlation function and periodic odd correlation function. Matsufuji constructed ternary and multivariate ZCZ sequences based on complete sequences. However, the existing ZCZ sequence has the following problems:

1、序列簇中的序列个数太少，直接限制了CDMA通信系统中用户的数量。1. The number of sequences in the sequence cluster is too small, which directly limits the number of users in the CDMA communication system.

2、每个序列周期可传递的比特信息太少，直接影响CDMA通信系统中用户的信息传输速度。2. The bit information that can be transmitted in each sequence period is too little, which directly affects the information transmission speed of the user in the CDMA communication system.

3、序列的零相关区间太小，即抗多址干扰的区间太小。3. The zero-correlation interval of the sequence is too small, that is, the interval against multiple access interference is too small.

发明内容 Contents of the invention

本发明的目的在于针对目前零相关区序列设计中存在的不足，提出了一种正交幅度调制星座上的零相关序列簇的构造方法，以增加序列簇中序列的个数、每个序列周期所传递的信息比特数以及序列的零相关区间大小，提高准同步CDMA系统的通信性能。The purpose of the present invention is to address the deficiencies in the current zero-correlation zone sequence design, and propose a method for constructing zero-correlation sequence clusters on the quadrature amplitude modulation constellation, so as to increase the number of sequences in the sequence cluster and the number of each sequence period. The number of transmitted information bits and the size of the zero-correlation interval of the sequence improve the communication performance of the quasi-synchronous CDMA system.

实现本发明目的技术方案是：首先，利用4×4阶4-相复Hadamard矩阵，构造一种4-相零相关区序列簇；然后，将此序列簇划分成不相交的序列集合，每个序列集合包含相同个数的序列；最后，根据得到的序列集合来构造正交幅度调制星座上的零相关区序列簇。具体构造步骤包括：The technical solution for realizing the object of the present invention is: at first, utilize 4 * 4 orders 4-phase complex Hadamard matrix, construct a kind of 4-phase zero-correlation zone sequence cluster; Then, this sequence cluster is divided into disjoint sequence set, each The sequence set contains the same number of sequences; finally, according to the obtained sequence set, the zero-correlation zone sequence cluster on the quadrature amplitude modulation constellation is constructed. The specific construction steps include:

(1)利用4×4阶4-相复Hadamard矩阵，采用递归的方式得到4-相零相关区序列簇：S＝{s_p(t)|1≤p≤2ⁿ⁺²，1≤t≤2²ⁿ⁺²}，其中n≥1，2ⁿ⁺²为序列的数量，2²ⁿ⁺²为序列的长度，s_p(t)为S中第p个序列在位置t处的取值；(1) Using a 4×4-order 4-phase complex Hadamard matrix, a 4-phase zero-correlation zone sequence cluster is obtained in a recursive manner: S={s _p (t)|1≤p≤2 ⁿ⁺² , 1≤t ≤2 ²ⁿ⁺² }, where n≥1, 2 ⁿ⁺² is the number of sequences, 2 ²ⁿ⁺² is the length of the sequence, s _p (t) is the value of the pth sequence in S at position t;

(2)将4-相零相关区序列簇S划分成个不相交的序列集合：{g_q，0≤q＜Q}，其中 $g_{q} = {s_{p_{i}}^{q} (t) | 1 \leq i \leq m, 1 \leq t \leq 2^{2 n + 2}},$ m为每个序列集合中所包含的序列个数，为序列簇S中第p_i个序列在位置t处的取值；(2) Divide the 4-phase zero correlation zone sequence cluster S into A set of disjoint sequences: {g _q , 0≤q<Q}, where $g_{q} = {{the s}_{p_{i}}^{q} (t) | 1 \leq i \leq m, 1 \leq t \leq 2^{2 no + 2}},$ m is the number of sequences contained in each sequence set, is the value of the p _i- th sequence in the sequence cluster S at position t;

(3)根据{g_q，0≤q＜Q}，得到正交幅度调制星座上的零相关区序列簇：(3) According to {g _q , 0≤q<Q}, the zero-correlation zone sequence cluster on the quadrature amplitude modulation constellation is obtained:

${CQ CQ}_{{M m}^{22}} = = {{s the s (({g g}_{q q},, {κ κ}_{q q},, t t)) | | {κ κ}_{q q} &Element; &Element; {Z Z}_{44}^{m m},, 11 \leq \leq q q \leq \leq Q Q,, 11 \leq \leq t t \leq \leq 22^{22 n no + + 22}}},,$

其中 $s (g_{q}, κ_{q}, t) = \sqrt{2 j} (Σ_{k = 0}^{m - 1} 2^{k} s_{n_{k}}^{q} (t) j^{κ_{k}^{q}}),$ κ_q为m维4元向量，κ_kq为向量κ_q中位置k处的取值，j为虚数单位，

为序列簇S中第p_k个序列在位置t处的取值，2²ⁿ⁺²为序列长度。in

the s (g_{q}, κ_{q}, t) = \sqrt{2 j} (Σ_{k = 0}^{m - 1} 2^{k} {the s}_{{no}_{k}}^{q} (t) j^{κ_{k}^{q}}),

κ _q is an m-dimensional 4-element vector, κ _kq is the value at position k in the vector κ _q , j is an imaginary number unit,

is the value of the p _kth sequence in the sequence cluster S at position t, and 2 ²ⁿ⁺² is the sequence length.

所述的正交幅度调制星座的星座点共有M²个，其中M＝2^m，m为集合g_q中序列的个数。The quadrature amplitude modulation constellation has M ² constellation points in total, where M=2 ^m , and m is the number of sequences in the set g _q .

所述的4×4阶4-相复Hadamard矩阵为The 4×4 order 4-phase complex Hadamard matrix is

$H (0) = \begin{matrix} \end{matrix} (\begin{matrix} 1 & 1 & 1 & 1 \\ 1 & j & - j & 1 \\ 1 & - j & j & - 1 \\ 1 & - 1 & - 1 & 1 \end{matrix}),$ 其中j²＝-1。 $h (0) = \begin{matrix} \end{matrix} (\begin{matrix} 1 & 1 & 1 & 1 \\ 1 & j & - j & 1 \\ 1 & - j & j & - 1 \\ 1 & - 1 & - 1 & 1 \end{matrix}),$ where j ² =-1.

所述的正交幅度调制星座上的零相关区序列簇 ${CQ}_{M^{2}} = {s (g_{q}, κ_{q}, t) | κ_{q} &Element; Z_{4}^{m}, 1 \leq q \leq Q, 1 \leq t \leq 2^{2 n + 2}}$ 的序列数量为

零相关区间长度为2ⁿ-1。The zero-correlation zone sequence clusters on the quadrature amplitude modulation constellation

{CQ}_{m^{2}} = {the s (g_{q}, κ_{q}, t) | κ_{q} &Element; Z_{4}^{m}, 1 \leq q \leq Q, 1 \leq t \leq 2^{2 no + 2}}

The number of sequences is

The length of the zero-correlation interval is ²ⁿ -1.

本发明所设计的正交调制星座上的零相关序列簇具有如下优点：The zero-correlation sequence cluster on the orthogonal modulation constellation designed by the present invention has the following advantages:

1.序列的数量大，可增加系统容量，确保了CDMA通信系统中用户的数量能满足实际的需求；1. The large number of sequences can increase the system capacity and ensure that the number of users in the CDMA communication system can meet the actual needs;

2.在一个序列周期内可传递的比特信息较多，有利于高速数据调制，提高了CDMA通信系统中用户的的信息传输速率；2. There are more bit information that can be transmitted in a sequence period, which is conducive to high-speed data modulation and improves the information transmission rate of users in the CDMA communication system;

3.所使用的正交调制星座的大小可变，可用于CDMA系统中逆向链路中可变速率的数据传输；3. The size of the quadrature modulation constellation used is variable, which can be used for variable rate data transmission in the reverse link in the CDMA system;

4.序列的零相关区间比较大，确保了CDMA通信系统中有较大的抗多址干扰的区间；4. The zero-correlation interval of the sequence is relatively large, which ensures a large anti-multiple access interference interval in the CDMA communication system;

5.序列的长度大，增加了信号的抗攻击能力；5. The length of the sequence is large, which increases the anti-attack ability of the signal;

6.由于采用了正交幅度调制，同一用户的不同数据比特对应的调制信号具有大的欧几里得距离，可增加通信的可靠性。6. Due to the use of quadrature amplitude modulation, the modulated signals corresponding to different data bits of the same user have a large Euclidean distance, which can increase the reliability of communication.

附图说明 Description of drawings

图1传统的准同步CDMA系统框图；Fig. 1 traditional quasi-synchronous CDMA system block diagram;

图2本发明构造正交幅度调制星座上零相关区序列流程图；Fig. 2 present invention constructs the sequence flowchart of zero correlation zone on the quadrature amplitude modulation constellation;

图3本发明中的准同步QAM-CDMA系统框图。Fig. 3 is a block diagram of quasi-synchronous QAM-CDMA system in the present invention.

具体实施方式 Detailed ways

参照图2，本发明构造正交幅度调制星座上零相关区序列的步骤如下：With reference to Fig. 2, the step that the present invention constructs the zero-correlation zone sequence on the quadrature amplitude modulation constellation is as follows:

步骤1，选取一个4×4阶4-相复Hadamard矩阵。Step 1, select a 4×4 order 4-phase complex Hadamard matrix.

本发明中所选取的4×4阶4-相复Hadamard矩阵为：The selected 4 * 4 order 4-phase complex Hadamard matrix in the present invention is:

$H^{'} (0) = \begin{matrix} \end{matrix} (\begin{matrix} 1 & 1 & 1 & 1 \\ 1 & j & - j & 1 \\ 1 & - j & j & - 1 \\ 1 & - 1 & - 1 & 1 \end{matrix}),$ 其中j²＝-1。 $h^{'} (0) = \begin{matrix} \end{matrix} (\begin{matrix} 1 & 1 & 1 & 1 \\ 1 & j & - j & 1 \\ 1 & - j & j & - 1 \\ 1 & - 1 & - 1 & 1 \end{matrix}),$ where j ² =-1.

步骤2，构造4-相零相关区序列簇S。Step 2. Construct a 4-phase zero-correlation zone sequence cluster S.

利用步骤1选取的4×4阶4-相复Hadamard矩阵，采用递归的方式得到4-相零相关区序列簇S，具体构造步骤如下：Using the 4×4 order 4-phase complex Hadamard matrix selected in step 1, the 4-phase zero-correlation zone sequence cluster S is obtained in a recursive manner. The specific construction steps are as follows:

(2.1)根据(2^k×4)×(2^k×4)阶矩阵H′(k)，构造(2^k+1×4)×(2^k+1×4)阶矩阵H′(k+1)；(2.1) According to (2 ^k × 4) × (2 ^k × 4) order matrix H'(k), construct (2 ^k+1 ×4) × (2 ^k+1 ×4) order matrix H'(k+ 1);

将(2^k×4)×(2^k×4)阶矩阵H′(k)记为：The (2 ^k × 4) × (2 ^k × 4) order matrix H′(k) is recorded as:

${H h}^{' '} ((k k)) = = (\begin{matrix} {a a}_{1111} ((k k)) & {a a}_{1212} ((k k)) & \cdot \cdot & \cdot \cdot & \cdot \cdot & {a a}_{11 ((22^{k k} \times \times 44))} ((k k)) \\ {a a}_{21 twenty one} ((k k)) & {a a}_{22 twenty two} ((k k)) & \cdot \cdot & \cdot \cdot & \cdot \cdot & {a a}_{22 ((22^{k k} \times \times 44))} ((k k)) \\ \cdot \cdot & \cdot \cdot & \cdot &Center Dot; \\ \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; & \cdot \cdot & \cdot &Center Dot; & \cdot \cdot \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ {a a}_{((22^{k k} \times \times 44)) 11} ((k k)) & {a a}_{((22^{k k} \times \times 44)) 22} ((k k)) & \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; & {a a}_{((22^{k k} \times \times 44)) ((22^{k k} \times \times 44))} ((k k)) \end{matrix});;$

其中0≤k≤n-1，n≥1；Where 0≤k≤n-1, n≥1;

根据H′(k)构造H′(k)的扩展矩阵： $H (k + 1) = (\begin{matrix} A_{11} (k) & A_{12} (k) \\ A_{21} (k) & A_{22} (k) \end{matrix}),$ 其中Construct the extended matrix of H'(k) according to H'(k): $h (k + 1) = (\begin{matrix} A_{11} (k) & A_{12} (k) \\ A_{twenty one} (k) & A_{twenty two} (k) \end{matrix}),$ in

A₁₂(k)＝A₂₁(k)，A₁₁(k)＝A₂₂(k)，A ₁₂ (k)=A ₂₁ (k), A ₁₁ (k)=A ₂₂ (k),

${A A}_{1111} ((k k)) = = (\begin{matrix} {a a}_{1111} ((k k)) {a a}_{1111} ((k k)) & {a a}_{1212} ((k k)) {a a}_{1212} ((k k)) & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & {a a}_{11 ((22^{k k} \times \times 44))} ((k k)) {a a}_{11 ((22^{k k} \times \times 44))} ((k k)) \\ {a a}_{21 twenty one} ((k k)) {a a}_{21 twenty one} ((k k)) & {a a}_{22 twenty two} ((k k)) {a a}_{22 twenty two} ((k k)) & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & {a a}_{22 ((22^{k k} \times \times 44))} ((k k)) {a a}_{22 ((22^{k k} \times \times 44))} ((k k)) \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot \cdot \\ \cdot &Center Dot; & \cdot \cdot & \cdot &Center Dot; & \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ {a a}_{((22^{k k} \times \times 44)) 11} ((k k)) {a a}_{((22^{k k} \times \times 44)) 11} ((k k)) & {a a}_{((22^{k k} \times \times 44)) 22} ((k k)) {a a}_{((22^{k k} \times \times 44)) 22} ((k k)) & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & {a a}_{((22^{k k} \times \times 44)) ((22^{k k} \times \times 44))} ((k k)) {a a}_{((22^{k k} \times \times 44)) ((22^{k k} \times \times 44))} ((k k)) \end{matrix});;$

${A A}_{1212} ((k k)) = = (\begin{matrix} (({- - a a}_{1111} ((k k)))) {a a}_{1111} ((k k)) & (({- - a a}_{1212} ((k k)))) {a a}_{1212} ((k k)) & \cdot \cdot & \cdot \cdot & \cdot \cdot & (({- - a a}_{11 ((22^{k k} \times \times 44))} ((i i)))) {a a}_{11 ((22^{k k} \times \times 44))} ((k k)) \\ (({- - a a}_{21 twenty one} ((k k)))) {a a}_{21 twenty one} ((k k)) & (({- - a a}_{22 twenty two} ((k k)))) {a a}_{22 twenty two} ((k k)) & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & (({- - a a}_{22 ((22^{k k} \times \times 44))} ((i i)))) {a a}_{22 ((22^{k k} \times \times 44))} ((k k)) \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ \cdot &Center Dot; & \cdot \cdot & \cdot &Center Dot; & \cdot \cdot & \cdot \cdot & \cdot \cdot \\ \cdot &Center Dot; & \cdot \cdot & \cdot &Center Dot; \\ (({- - a a}_{((22^{k k} \times \times 44)) 11} ((k k)))) {a a}_{((22^{k k} \times \times 44)) 11} ((k k)) & (({- - a a}_{((22^{k k} \times \times 44)) 22} ((k k)))) {a a}_{((22^{k k} \times \times 44)) 22} ((k k)) & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & (({- - a a}_{((22^{k k} \times \times 44)) ((22^{k k} \times \times 44))} ((k k)))) {a a}_{((22^{k k} \times \times 44)) ((22^{k k} \times \times 44))} ((k k)) \end{matrix})$

记：a_ij(k+1)＝a_ij(k)a_ij(k)，1≤ i，j≤2^k×4，Note: a _ij (k+1)＝a _ij (k)a _ij (k), 1≤ i, j≤2 ^k ×4,

${a a}_{((i i + + 22^{k k} \times \times 44)) ((j j + + 22^{k k} \times \times 44))} ((k k + + 11)) = = {a a}_{ij ij} ((k k)) {a a}_{ij ij} ((k k)),, 11 \leq \leq i i,, j j \leq \leq 22^{k k} \times \times 44,,$

${a a}_{((i i + + 22^{k k} \times \times 44)) j j} ((k k + + 11)) = = (({- - a a}_{ij ij} ((k k)))) {a a}_{ij ij} ((k k)),, 11 \leq \leq i i,, j j \leq \leq 22^{k k} \times \times 44,,$

${a a}_{i i ((j j + + 22^{k k} \times \times 44))} ((k k + + 11)) = = (({- - a a}_{ij ij} ((k k)))) {a a}_{ij ij} ((k k)),, 11 \leq \leq i i,, j j \leq \leq 22^{k k} \times \times 44,,$

扩展矩阵H(k+1)表示为一个(2^k+1×4)×(2^k+1×4)矩阵H′(k+1)为：The extended matrix H(k+1) is expressed as a (2 ^k+1 ×4)×(2 ^k+1 ×4) matrix H′(k+1) as:

${H h}^{' '} ((k k + + 11)) = = (\begin{matrix} {a a}_{1111} ((k k + + 11)) & {a a}_{1212} ((k k + + 11)) & \cdot \cdot & \cdot \cdot & \cdot \cdot & {a a}_{11 ((22^{k k + + 11} \times \times 44))} ((k k + + 11)) \\ {a a}_{21 twenty one} ((k k + + 11)) & {a a}_{22 twenty two} ((k k + + 11)) & \cdot \cdot & \cdot \cdot & \cdot \cdot & {a a}_{22 ((22^{k k + + 11} \times \times 44))} ((k k + + 11)) \\ \cdot \cdot & \cdot \cdot & \cdot \cdot \\ \cdot \cdot & \cdot \cdot & \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; & \cdot \cdot \\ \cdot \cdot & \cdot \cdot & \cdot \cdot \\ {a a}_{((22^{k k + + 11} \times \times 44)) 11} ((k k + + 11)) & {a a}_{((22^{k k + + 11} \times \times 44)) 22} ((k k + + 11)) & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & {a a}_{((22^{k k + + 11} \times \times 44)) ((22^{k k + + 11} \times \times 44))} ((k k + + 11)) \end{matrix});;$

(2.2)根据步骤1中选取的4×4阶4-相复Hadamard矩阵H′(0)，采用步骤(2.1)中的方法，递归地生成矩阵H′(1)，H′(2)，…，H′(n)，最终得到(2ⁿ×4)×(2ⁿ×4)阶的矩阵H′(n)，其中，n≥1；(2.2) According to the 4 × 4 order 4-phase complex Hadamard matrix H'(0) selected in step 1, adopt the method in step (2.1) to recursively generate matrix H'(1), H'(2), ..., H′(n), and finally obtain a matrix H′(n) of order (2 ⁿ ×4)×(2 ⁿ ×4), where n≥1;

例如，对于n＝1，最终得到的矩阵H′(1)为：For example, for n=1, the final matrix H'(1) is:

${H h}^{' '} ((11)) = = (\begin{matrix} 1111 & 1111 & 1111 & 1111 & ((- - 11)) 11 & ((- - 11)) 11 & ((- - 11)) 11 & ((- - 11)) 11 \\ 1111 & jj jj & ((- - j j)) ((- - j j)) & ((- - 11)) ((- - 11)) & ((- - 11)) 11 & ((- - j j)) j j & j j ((- - j j)) & 11 ((- - 11)) \\ 1111 & ((- - j j)) ((- - j j)) & jj jj & ((- - 11)) ((- - 11)) & ((- - 11)) 11 & j j ((- - j j)) & ((- - j j)) j j & 11 ((- - 11)) \\ 1111 & ((- - 11)) ((- - 11)) & ((- - 11)) ((- - 11)) & 1111 & ((- - 11)) 11 & 11 ((- - 11)) & 11 ((- - 11)) & ((- - 11)) 11 \\ ((- - 11)) 11 & ((- - 11)) 11 & ((- - 11)) 11 & ((- - 11)) 11 & 1111 & 1111 & 1111 & 1111 \\ ((- - 11)) 11 & ((- - j j)) j j & j j ((- - j j)) & 11 ((- - 11)) & 1111 & jj jj & ((- - j j)) ((- - j j)) & ((- - 11)) ((- - 11)) \\ ((- - 11)) 11 & j j ((- - j j)) & ((- - j j)) j j & 11 ((- - 11)) & 1111 & ((- - j j)) ((- - j j)) & jj jj & ((- - 11)) ((- - 11)) \\ ((- - 11)) 11 & 11 ((- - 11)) & 11 ((- - 11)) & ((- - 11)) 11 & 1111 & ((- - 11)) ((- - 11)) & ((- - 11)) ((- - 11)) & 1111 \end{matrix})$

(2.3)将(2ⁿ×4)×(2ⁿ×4)阶矩阵H′(n)的行向量看成序列，得到4-相零相关区序列簇，其参数为：序列长度为2²ⁿ⁺²，序列数量为2ⁿ⁺²，零相关区间长度为2ⁿ-1。(2.3) Treat the row vector of (2 ⁿ ×4)×(2 ⁿ ×4) order matrix H′(n) as a sequence, and obtain a 4-phase zero-correlation zone sequence cluster, whose parameters are: the sequence length is 2 ^{2n +2} , the number of sequences is 2 ⁿ⁺² , and the length of the zero correlation interval is 2 ⁿ -1.

步骤3，将4-相零相关区序列簇S划分成

个不相交 +的序列集合。Step 3, divide the 4-phase zero correlation zone sequence cluster S into

A set of disjoint + sequences.

从S中任意选取m个不相同的序列组成序列集合g₁，再从剩余的2ⁿ⁺²-m个序列中任意选取m个不相同的序列组成序列集合g₂，依此类推，直到S中剩余的序列个数不足m个，最多划分出

个序列集合，记划分出的不相交的序列集合为{g_q，1≤q≤Q}。Randomly select m different sequences from S to form a sequence set g ₁ , and then arbitrarily select m different sequences from the remaining 2 ⁿ⁺² -m sequences to form a sequence set g ₂ , and so on until S The number of remaining sequences in is less than m, and at most it can be divided into

Sequence sets, and the disjoint sequence sets divided by the score are {g _q , 1≤q≤Q}.

步骤4，根据{g_q，1≤q≤Q}，得到的正交幅度调制星座上的零相关区序列簇为：Step 4, according to {g _q , 1≤q≤Q}, the obtained zero-correlation zone sequence cluster on the quadrature amplitude modulation constellation is:

其中 $s (g_{q}, κ_{q}, t) = \sqrt{2 j} (Σ_{k = 0}^{m - 1} 2^{k} s_{p_{k}}^{q} (t) j^{κ_{k}^{q}}),$ κ_q为m维4元向量，κ_k ^q为向量κ_q中位置k处的取值，j为虚数单位，

为序列簇S中第p_k个序列在位置t处的取值。in

the s (g_{q}, κ_{q}, t) = \sqrt{2 j} (Σ_{k = 0}^{m - 1} 2^{k} {the s}_{p_{k}}^{q} (t) j^{κ_{k}^{q}}),

κ _q is an m-dimensional 4-element vector, κ _k ^q is the value at position k in the vector κ _q , j is the imaginary number unit,

is the value of the p _kth sequence in sequence cluster S at position t.

在本发明中，

是一簇正交幅度调制星座上的零相关区序列，该序列簇具有下列特性：序列周期为2²ⁿ⁺²；序列簇能提供给个用户；每个用户在每个序列周期可传递2m比特信息；序列的零相关区间为2ⁿ-1。该序列簇可以用在准同步CDMA系统中。In the present invention,

is a cluster of zero-correlation zone sequences on the quadrature amplitude modulation constellation, the sequence cluster has the following characteristics: the sequence period is 2 ²ⁿ⁺² ; the sequence cluster can provide users; each user can transmit 2m bits of information in each sequence period; the zero-correlation interval of the sequence is 2 ⁿ -1. This sequence cluster can be used in quasi-synchronous CDMA systems.

本发明中的所设计的序列是正交幅度调制星座上的零相关区序列。正交幅度调制是用两个独立的基带数字信号对两个相互正交的同频载波进行抑制载波的双边带调制，利用这种已调信号在同一带宽内频谱正交的性质来实现两路并行的数字信息传输，它是一种频率利用率很高的调制方式。The designed sequence in the present invention is a zero-correlation zone sequence on the quadrature amplitude modulation constellation. Quadrature Amplitude Modulation is to use two independent baseband digital signals to suppress carrier double sideband modulation of two mutually orthogonal co-frequency carriers, and realize two-channel Parallel digital information transmission, it is a modulation method with high frequency utilization.

正交幅度调制星座的星座点组成集合{a+bj|-N+1≤a，b≤N-1，a，b odd}，其中，N²为此集合的大小，也是这个正交幅度调制星座的星座点的个数。当N＝2ⁿ时，这个正交幅度调制星座被描述为：The constellation points of the quadrature amplitude modulation constellation form a set {a+bj|-N+1≤a, b≤N-1, a, b odd}, where N ² is the size of this set, and this quadrature amplitude modulation The number of constellation points of the constellation. When N = 2 ⁿ , this quadrature amplitude modulation constellation is described as:

${\sqrt{2 j} (Σ_{k = 0}^{n - 1} 2^{k} i^{a_{k}}) | &Element; Z_{4}}$ 其中

表示1+j。

{\sqrt{2 j} (Σ_{k = 0}^{no - 1} 2^{k} i^{a_{k}}) | &Element; Z_{4}}

in

Indicates 1+j.

在本发明中，使用的正交幅度调制星座的星座点数为M²，其中M＝2^m，m为{g_q，1≤q≤Q}中每个元素所包含的序列的个数。In the present invention, the number of constellation points of the quadrature amplitude modulation constellation used is M ² , where M=2 ^m , and m is the number of sequences contained in each element in {g _q , 1≤q≤Q}.

本发明的效果可以通过以下试验进一步说明：Effect of the present invention can be further illustrated by following test:

在传统的准同步系统中，ZCZ序列的设计与调制方式无关，而本发明中的正交幅度星座上的零相关区序列还涉及到了调制的内容，传统的准同步CDMA系统框图已不适用。In the traditional quasi-synchronous system, the design of the ZCZ sequence has nothing to do with the modulation method, but the ZCZ sequence on the quadrature amplitude constellation in the present invention also involves the modulation content, and the traditional quasi-synchronous CDMA system block diagram is no longer applicable.

本试验所使用的准同步QAM-CDMA系统框图如图3所示。试验过程如下：The quasi-synchronous QAM-CDMA system block diagram used in this experiment is shown in Figure 3. The test process is as follows:

(a)将各个用户经过信道编码的数据送入系统中，送入的数据为连续的m维4元向量；(a) Send the channel-coded data of each user into the system, and the sent data is a continuous m-dimensional 4-element vector;

(b)分别用为每个用户分配的正交幅度上的零相关序列对送入系统的数据进行扩频和正交幅度调制；(b) Carry out spectrum spreading and quadrature amplitude modulation on the data sent into the system with the zero-correlation sequence on the quadrature amplitude allocated for each user, respectively;

(c)将各个用户经过扩频和调制后的信号合并后送入信道中进行传输；(c) Combine the spread spectrum and modulated signals of each user into the channel for transmission;

(d)利用分配给每个用户的正交幅度调制星座上的零相关区序列对接收到的信号分别进行解调和解扩；(d) Demodulate and despread the received signal using the zero-correlation zone sequence on the quadrature amplitude modulation constellation assigned to each user;

(e)得到各个用户未经过信道译码的数据。(e) Obtain the data of each user without channel decoding.

试验结果表明：在准同步QAM-CDMA系统中，通过使用本发明中设计的正交幅度调制星座上的零相关区序列，系统所能容纳的用户数更多，每个序列周期能够传输的数据比特更多且可变，系统的抗噪声性能更好，系统的抗攻击能力更强。The test result shows: in the quasi-synchronous QAM-CDMA system, by using the zero-correlation zone sequence on the quadrature amplitude modulation constellation designed in the present invention, the number of users that the system can accommodate is more, and the data that can be transmitted in each sequence period With more and variable bits, the system has better anti-noise performance and stronger anti-attack ability of the system.

Claims

1. the zero-correlation zone sequence method for designing on the quadrature amplitude modulation constellation comprises the steps:

(1) utilizes mutually Hadamard matrix again of 4 * 4 rank 4-, adopt the mode of recurrence to obtain 4-phase zero-correlation zone sequence bunch: S={s _p(t) | 1≤p≤2 ^N+2, 1≤t≤2 ²ⁿ⁺², n 〉=1,2 wherein ^N+2Be the quantity of sequence, 2 ²ⁿ⁺²Be the length of sequence, s _p(t) be among the S p sequence in the value at position t place;

(2) a 4-phase zero-correlation zone sequence bunch S is divided into

Individual disjoint arrangement set:

{ g _q, 0≤q＜Q}, wherein

The sequence number of m for comprising in each arrangement set,

Be p among the sequence cluster S _iIndividual sequence is in the value at position t place;

(3) according to { g _q, 0≤q＜Q} obtains the zero-correlation zone sequence bunch on the quadrature amplitude modulation constellation:

Wherein

к _qBe 4 yuan of vectors of m dimension,

Be vectorial к _qThe value at i place, middle position, j is imaginary unit, Be p among the sequence cluster S _iIndividual sequence is in the value at position t place, 2 ²ⁿ⁺²Be sequence length, M=2 ^m

2. sequences Design method according to claim 1, the constellation point of wherein said quadrature amplitude modulation constellation has M ²Individual, M=2 wherein ^m

3. sequences Design method according to claim 1, wherein said 4 * 4 rank 4-mutually again the Hadamard matrix be:

J wherein ²=-1.

4. sequences Design method according to claim 1, the described mutually Hadamard matrix again of 4 * 4 rank 4-that utilizes of step (1) wherein adopts the mode of recurrence to obtain 4-phase zero-correlation zone sequence bunch, carries out as follows:

(4.1) select 4 * 4 rank 4-to answer mutually Hadamard matrix H ' (0):

(4.2) according to (2 ^k* 4) * (2 ^k* 4) rank matrix H ' (k) is come structural matrix (2 ^K+1* 4) * (2 ^K+1* 4) rank matrix H ' (k+1), 0≤k≤n-1 wherein, n 〉=1;

(2 ^k* 4) * (2 ^k* 4) rank matrix H ' (k) be expressed as:

(k) construct H ' extended matrix (k) according to H ':

Wherein

A ₁₂(k)＝A ₂₁(k)，A ₁₁(k)＝A ₂₂(k)，

Note: a _lf(k+1)=a _lf(k) a _lf1 (k) ,≤ l, f≤2 ^k* 4,

Extended matrix H (k+1) is expressed as one (2 ^K+1* 4) * (2 ^K+1* 4) matrix H ' (k+1):

(4.3) according to step (4.2), generator matrix H ' (1) recursively, H ' (2) ..., H ' (n) finally obtains (2 ⁿ* 4) * (2 ⁿ* 4) matrix H on rank ' (n), wherein, n 〉=1;

(4.4) with (2 ⁿ* 4) * (2 ⁿ* 4) the capable vector of rank matrix H ' (n) is regarded sequence as, obtains 4-phase zero-correlation zone sequence bunch, and its parameter is: sequence length is 2 ²ⁿ⁺², sequence quantity is 2 ^N+2, the zero correlation siding-to-siding block length is 2 ⁿ-1.

5. sequences Design method according to claim 1, the zero-correlation zone sequence on the wherein said quadrature amplitude modulation constellation bunch Sequence quantity be

The zero correlation siding-to-siding block length is 2 ⁿ-1.