Gold序列的仿真研究

Gold序列的仿真研究摘要:Gold序列是R·Gold提出的一种基于m序列的码序列，这种序列有较优良的自相关和互相关特性，构造简单，产生的序列数多，因而获得了广泛的应用。本文对Gold序列进行仿真研究，首先介绍了扩频通信中常用的m序列和Gold序列码产生的方法原理和性质，运用Matlab对Gold码的生成和性能进行了仿真分析。关键词：伪随机序列；Gold序列；m序列；Matlab仿真SIMULATIONOFGOLDSEQUENCESAbstract:GoldsequencesisproposedbyR•Goldwhichisbasedonmsequences.Goldsequenceshasgoodproperties,suchasgoodautocorrelationandcross-correlation,easytoconstructandmoresequences,etc,thereforeithaswideapplications.ThispaperinvestigatestheGoldsequences.TheprincipleandperformanceofmsequencesandGoldsequencesinspreadspectrumcommunicationarefirstintroducedinthepaper.SimulationbyMatlabisalsoprovidedinthepapertoanalyzethenatureofGoldsequences.Keywords:Pseudo-randomsequence；Goldsequence；msequence；Matlabsimulation目录1引言······································································································11.1研究的背景及意义················································································11.2CDMA通信技术简介·············································································11.2.1扩频的理论基础··············································································11.2.2扩频通信的分类··············································································21.2.3CDMA扩频通信系统的构成······························································21.2.4伪随机序列在CDMA通信系统中的应用··············································22M序列····································································································32.1伪随机序列相关概念·············································································32.1.1伪随机序列的数学定义····································································32.1.2随机序列的相关特性·······································································42.2M序列的产生原理·················································································53GOLD序列······························································································63.1GOLD序列的产生原理············································································63.2GOLD序列的基本性质············································································74MATLAB仿真实现···················································································84.1产生M序列························································································84.2产生GOLD序列···················································································94.3相关性仿真························································································104.3.1相关性的理论分析·········································································104.3.2Matlab仿真···················································································115结束语··································································································14致谢·········································································································16参考文献··································································································16作者：唐思远第1页共17页1引言1.1研究的背景及意义移动通信由于具有时实性、机动性、具有不受时空限制等特点，己经成为一种深受人们欢迎的通信方式，并融入了现代生活当中。自美国Qualcomm公司提出在蜂窝移动通信系统中应用码分多址(CodeDivisionMultipleAccess，简称CDMA)技术的系统实现方案至今，CDMA通信系统相对于其它无线通信系统在客户容量和高质量的优势越来越显现出来。在短短的二、三十年中，移动通信系统已从第一代的模拟蜂窝系统发展到第二代全球数字移动电话蜂窝系统(2G)，目前己经开始向第三代宽带多媒体蜂窝系统(3G)发展，并且处于第二代和第三代之间的2.5G已经趋于成熟。虽然第二代移动通信系统中，GSM系统仍占有很大的市场份额。但是，因为具有伪随机编码调制和信号相关处理两大特点而使CDMA通信方式具有抗干扰、抗噪音、抗多径衰落、能在低功率谱密度下工作、有保密性、可多址复用和任意选址、可高精度测量等优点，使CDMA技术成为第三代移动通信和个人通信系统的核心技术，以扩频理论为基础的CDMA技术已成为当前移动通信领域的研究热点。在CDMA系统的众多用户都工作在同一时间同一频段内，系统给各个用户分配一个唯一的扩频码来进行频谱的扩展，在发送和接收时，系统更是利用各地址码之间的互相关特性值来区分不同的用户。因此，扩频码的特性直接影响到CDMA系统的捕获同步性能、抗干扰性能和多址能力。从理论上说，独立、均匀分布的随机序列是扩频码的理想模型，然而它由于不易产生、无法时实分发等缺陷而被认为难以在实际的CDMA系统中应用。CDMA自其理论提出到投入商业营运、直至称为第三代移动通信系统的核心技术，一直是通信领域的关注热点。作为CDMA的基础技术之一的PN码的选择和产生也是倍受业内人士关注的，如何找到易生成且相关特性好的PN码成为研究人员追求的目标之一。为此，人们设计了各种确定性的伪随机序列来代替随机序列作为扩频码。迄今为止，世界各国的学者在伪随机序列的设计与选择方面己做了大量的工作，例如，由m序列优选对生成的Gold序列己被用作第三代移动通信系统中WCDMA的扩频码；以及通过对m序列添加一个全“0”状态得到的M序列和m序列也已被用作第三代移动通信系统中CDMA2000的扩频码。m序列、Gold序列等线性序列多由线性移位寄存器所产生，有易于实现、具备较好的相关特性等优点。实际应用的CDMA通信系统采用复合扩频技术，即用正交码(Walsh函数序列，OVSF码族)作为信道化码来区分小区、用Gold序列或M序列作为扰码来区分用户。因此，本文所研究的Gold序列，在扩频通信系统中发挥着重要的作用，通过Matlab仿真，对其自相关性能进行分析，能够更好的理解CDMA系统的通信原理。1.2CDMA通信技术简介1.2.1扩频的理论基础在信息论中，对于连续信道，如果信道带宽为B，且受到加性高斯白噪声干扰，则其信道容量的理论公式(香农公式)为：)/1(log2NSBC(1.1)其中C—信道容量，单位bit/s;B一信道带宽，单位Hz；S一信号平均功率，单位w；N一噪声平均功率，单位w。从香农公式可知：(1)要增大信息传输速率，就必须增大信道带宽B或信噪比S。由于公式中对数部分变化得比较缓慢，因此增加B比增加S加更有效，也就是说如果传输信号的带宽变窄，将导致信号功率的大幅提高。而如果通过增加带宽去换取信号功率的减小，就能节省较大的信号功率能源。即B增加时，信道容量增加较快。浙江传媒学院本科毕业论文Gold序列的仿真研究作者：唐思远第2页共17页(2)当信道容量为常量时，信道带宽与信噪比存在互换关系。在C恒定的情况下，可以通过减少发送功率，增加信道带宽的方法保持信道容量不变的目标。也可以通过减小带宽，增强信号功率的方法。信道容量可以通过带宽与信噪比的互换而保持不变。(3)当带宽增加到一定程度时，信道容量也不能无限增加。这是因为噪声功率N=n0B，当信道带宽B增加时，N也随着增加，所以C有一个极限值。扩频通信是指系统所传输的信号(带宽为Bm)被扩展至一个很宽的频带Bc。用来传输信息的信号带宽远远大于信息本身带宽的一种通信方式。它利用高速率的扩频码来达到扩展传输信号的带宽，从而减小了发送功率。对扩频通信来说Bc/Bm的值一般为100～1000。1.2.2扩频通信的分类(1)直接序列(DS)扩频系统：用一组高速数字编码序列直接扩展频谱，由于编码序列的带宽远远大于原始信号的带宽，从而扩展了发射信号的频谱。(2)跳频(FH)扩频系统：使发射机频率在一组预先制定的频率上按照编码序列所规定的顺序离散的跳变，从而扩展发射波的频谱。一般来说，跳频图案由伪随机码控制，从而使载频的跳变具有均匀分布的性质。(3)线性调频(Chirp)系统：在这种系统中，载频在一给定的脉冲时间间隔内线性的扫过一个宽的频带，从