基于分数阶傅立叶变换的水声信道多参数估计算法研究

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基于分数阶傅立叶变换的水声信道多参数估计算法研究摘要由于海洋经济和海洋军事的战略地位，使得水声通信技术成为当今的研究热点。为了保证水声通信的可靠性和有效性，我们需要对水声信道的多参数进行估计。本论文选用的是数据辅助算法，采用的是Chirp信号。因此研究Chirp信号的检测与参数估计对水下声信道的多参数估计具有很重要的实用价值。本文在FRFT法的基础上进行了深入的研究，采用Chirp信号作为水下的探测信号，针对Chirp信号的两种接收模型(恒k模型和变k模型)，根据Chirp信号与FRFT的联系，对水声信道的多参数进行了估计。本文的工作首先是针对恒k模型提出了三种创新的水声信道估计算法。(1)FRFT估计法：该方法的优点是可以准确的估计出多径数，并且时延估计比较准确，频偏估计也比较精确，不足在于只能估计多径频偏都相同的情况，并且需要预先精确知道直达波时延的位置。(2)双Chirp信号估计法：该方法的优点是不管多径频偏如何，我们都能估计出多径数、多径频偏以及多径时延。不足是FRFT快速算法引入了计算误差，造成了频偏和时延估计误差较大，且计算量较大。(3)联合估计法：该方法的优点是不管多径频偏如何，我们都能精确的估计出多径数、多径频偏以及多径时延。不足是FRFT快速算法引入的计算误差，需要进行小范围搜索校正，信号处理算法复杂，计算量较大。其次针对变k模型又创新的提出了一种新颖的水声信道估计算法Chirp基法和两种基于FRFT水声通信系统的数据包结构设计。(1)FRFT的Chirp基解法：该方法的优点是精确的估计出了多径数、多径频偏以及多径时延。采用FRFT的Chirp基特性来估计水声信道多参数，避免了FRFT快速算法带来的计算误差，计算速度快，估计精度高，是一种可以实时处理的算法。(2)第一种数据包结构，适用于水况变化较快的水域，优点是可以做到一包一估，数据传输可靠性更高，不足在于传输效率相对较低。(3)第二种数据包结构，适用于水况变化缓慢的水域，需要每隔一定时间发射一定脉宽的单频信号估计信道的多径频偏，优点是传输效率相对较高，不足在于数据传输可靠性不如第一种数据包结构。最后，本文做了大量仿真，仿真结果验证了上述的算法都是有效的，并且仿真详细解释了两种数据包的处理过程。关键词：水声信道；多普勒频偏；时延；FRFI,Ohirp基特性 ResearchonmuIti—parameterestimationaIgorithmsofunderwateracousticchanneIbasedonFRFTAbstFactUnderwateracousticcommunicationhasbecometheresearchfocusowingtotheeconomicandmilitarysignificanceofocean．Theparametersofunderwateracousticchannelneedtobeestimatedinordertoensurethereliabilityandeffectivenessofunderwateracousticcommunication．Thedata-aidedalgorithmsareadoptedinthisdissertation，andnowadaysexistingpreamblesinunderwatertelemetryarealmostexclusivelybasedonLFMsignals，alsoknownasChirpsignals．Therefore，itissignificanttoresearchthemulti—parameterestimationalgorithmsofunderwateracousticchannel．Thein—depthresearchinthisdissertationisbasedonFRFTalgorithms．WetreatChirpsignalsastheunderwaterdetectionsignal，andtheparametersofunderwateracousticchannelareestimatedaimingatthetwomodelsofreceivedChirpsignals(theconstantkmodelandthevariablekmodel)andaccordingtotherelationofChirpsignalsandFRFT．Theworkofthisdissertationisasfollows．Firstly,threenovelalgorithmsforthemulti·parameterestimationofunderwateracousticchannelareproposedfortheconstantkmodelofChirpsignals．(1)TheFRFTbasedestimationalgorithm：。TheadvantageisthatitCanestimatetheprecisemulti—pathnumber,thedelaysandaccurateDopplershift．However,thisalgorithmisjustsuitabletothesituationwhereeachofthepathshasthesanleDopplershiftandtheexactdelayestimationofdirectpathisknowninanticipation．(2)Thedouble-chirpsignalestimationalgorithm：ThestrengthisthatitCandirectlydeterminethemulti—pathnumber,theDopplershiftsandthedelaysregardlessoftheDopplershiftsbeingthesame，similarorverydifferent．However,theshortcomingisthattheestimationerrorsofDopplershiftanddelayarequitelargeduetotheintroductionofthefastalgorithmofFRFTanditmakescomputationaloverload．(3)Thejointestimationalgorithm：ThevirtueisthatitCandirectlyandaccuratelydeterminethemulti—pathnumberandthedelaysandDopplershiftsregardlessoftheDopplershiftsbeingthesame，similarorverydifferent．AnditCanalsodirectlyandaccuratelyestimatethemulti—parameterofunderwateracousticchannelnomatterhowshortorlongthedelaysofthereceivedsignalare．However,theshortcomingisthatthecalculationerrorsneedtObesearchedfinelyinsmallrange，whichresultsincomplex algorithmandcomputationaloverload．Secondly,forthevariablekmodeloftheChirpsignal，anovelmulti—parameterestimationforunderwateracousticchannelbasedontheChirp-basedcharacterofFRFTisproposed，andthentwodesignsofpacketstructurebasedoncommunicationsystemofFRFTfordifferentwatersarealsogivenforthevariablekmodeloftheChirpsignal．(1)TheChirp-basedofFI心T：themeritisthatwecanaccuratelyandquicklyestimatetheparametersofunderwateracousticchannel．Theishighaccurateandsimple，aswellasthespeedofcalculationisveryfast．WhatisthemostimportantiSthatitcarlbeimplementedinreal-timeprocessing．HoweveLtheestimationperformancewilldecreasewhentheDopplershiftsareapproximate，andtheweakpathofthetwopathswithapproximateDopplershiftwillbeseverelyinfluenced，buttheproblemCanbesolvedbyhighresolutionandlongsinesignal．(2)Thestructuredesignofthefirstpacketsuitableforwatersoffastchange：Thestrongpointisthatitmakesthemulti—parameterestimationperpackagepossible，whichgreatlyincreasesthereliabilityofdatatransmission．However,itreducestransmissionefficiency．(3)Thestructuredesignofthesecondpacketsuitableforwatersofslowchange：Thestrengthisthatithashighertransmissionefficiency．However，itgreatlyreducesthereliability．Finally,alotofsimulationexamplesaregiventoverifytheeffectivenessoftheestimationalgorithms．Andthesimulationshowsextensivelyhowthetwopacketsareprocessed．Keywords：UnderwaterAcousticChannel，DopplerShift，Delay,FRFT,Chirp—basedCharacteristic 目录1．引言⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．11．1课题来源⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯11．2研究背景及研究意义⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯l1．3水声信道特性及问题描述⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯21．4国内外的研究现状及发展动态⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯31．5本文所做的工作⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯42．三种基于FRFT的水声信道多参数估计算法⋯⋯⋯⋯⋯⋯⋯⋯．．62．1水声信道模型⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯62．2Chirp信号的恒七模型⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．72．3立论基础⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯72．3．1FRFT定义⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯72．3．2基于FRFT的水声信道多参数估计分析⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯72．4三种新颖的信道估计算法⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯82．4．1FRF，I’估计法⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯82．4．2双Chirp信号估计法⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯122．4．3联合估计法⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯172．5本章小结⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．313．一种基于FRFT的Chirp基特性的水声信道多参数估计算法⋯．323．1Chirp信号的变七模型⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯323．2立论基础⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．323．3测试信号的结构及信号处理算法⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．333．3．1测试信号的结构⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯333．3．2信号处理算法⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯333．4数值仿真⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．343．5本章小结⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．444．基于FRFT水声通信系统的数据包结构设计⋯⋯⋯⋯⋯⋯⋯⋯454．1两种数据包结构⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．454．2数据包处理算法流程⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯454．3数据包处理仿真⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯一464．3．1第一种数据包仿真⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯464．3．2第二种数据包仿真⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．484．4本章小结⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯505．总结及展望⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯5l参考文献⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．53致谢⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯55个人简历⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．56发表的学术论文与研究成果⋯⋯⋯⋯⋯⋯⋯⋯：⋯⋯⋯-⋯⋯⋯．．56 I】 基于分数阶傅立叶变换的水声信道多参数估计算法研究1引言1．1课题来源本论文采用分数阶傅立叶变换(FRFT)估计水下声信道的多参数，即水声信道的多径数、多普勒频偏以及多径时延。本论文来源于以下两个国家课题：(1)国家高技术研究和发展计划(863计划)基于传感器网络的深远海环境监测关键技术研究No．2006AA092115(2006．12-2009．7)(2)国家自然科学基金水声传感器网络控制系统的模糊控制方法研究No．60704023(2008．1—2010．12)这两个国家课题的总体目标是：提出深远海环境监测的水下声学传感器网络(UW-ASNs)的整体解决方案，解决节点硬件(体系结构)设计、水声通信物理接入技术、水声信道多参数估计算法、模糊控制算法、通信协议以及能源管理等关键技术问题，实现海洋数据实时可靠的采集、处理、传输与分析。本文的工作是研究这两个课题中的水声信道多参数估计算法。1．2研究背景及研究意义随着世界各国对海洋的开发，水声通信被广泛的应用于海洋数据的收集、污染监测、近海的探测、灾难预防、导航、军事监视、自然海底资源探测、海洋考古以及海洋搜寻营救等方面。水声信道的准确估计是水声通信高效和可靠传输的重要保证【l】【2】，因此，对水声信道的多参数进行准确估计是有重要意义的。因为水声信道与空间无线信道有很大的不同，所以尽管空间无线信道的理论和相关技术已经发展的非常成熟，我们也不能将空间无线信道的理论和技术直接应用到水声信道中。因此，我们在研究水声通信设备的设计时，必须考虑到水声信道的具体情况，发展适用于水声通信的相关理论和相关技术【3】【41。水声信道与空间无线信道的比较如表1-1所示。由表卜1可见，水声信道与空间无线信道相比，具有载波频率低、带宽窄、多径时延特别严重、多普勒频偏影响大和传输速率低等特点。所以说空间无线信道的多参数估计算法在水声信道的多参数估计时失效了。因此，我们必须提出基 基于分数阶傅立叶变换的水声信道多参数估计算法研究于水声信道的多参数估计算法【3】【4】，来保障水下通信的高效和可靠传输。表1-1水声信道与空间无线信道的比较1．3水声信道特性及问题描述信道实际上是一种物理媒质，用来将来自发射设备的信号传送到接收端。在无线信道中，信道可以是自由空间；在有线信道中，可以是明线、电缆和光纤。有线信道和无线信道均有多种物理媒质。信道既给信号以通路，也会对信号产生各种干扰和噪声。信道的固有特性和引入的干扰直接影响到通信的质量15J。因为本文研究的是水声信道的多参数估计，所以下面将从载波和水声信道特性两方面进行概述。在水下通信中所应用的各种能量辐射形式，以声波的传播性能为最好。声波在水中的传播速度约为1500m／s，比声波在空气中的传播速度340m／s要大四倍。在海水中，光波和电磁波的衰减都非常大，传播距离较短，远不能满足人类在海洋活动中的需要。因此，到目前为止，在水下目标探测、通讯和导航等方面均以声波做为水下唯一有效的辐射能16儿川。水声信道属于不平整双界面随机不均匀介质信道，是时间弥散的慢衰落信道。因为主动声纳探测的目标或水声通信节点间又通常是运动的，所以水声信道具有时变、空变、多径延时和多径频偏特性，水声通信除受到这些方面的影响外，还受到路径损耗和噪声等因素的影响【弘13】。因此，信号经水声信道后，接收波形发生畸变，这是影响水声通信可靠性的主要原因。为了克服水声信道的影响，我们需要对水声信道进行多参数估计。下面将从水声通信系统的模型和浅海声场基本线路图这两方面对本文要解决的问题进行描述。2 基于分数阶傅立叶变换的水声信道多参数估计算法研究水声通信的目的是传输信息。水声通信系统的作用是将信息从信源发送到一个或多个目的地。以声信号为例，首先要把信息变成声信号，然后经过发送设备，将信号送入信道，在接收端利用接收设备对接收信号作相应的处理后，送给信宿再转换为原来的消息【51。这一过程可用图卜1所示的水声数字通信系统模型来概括。图1—1水声数字通信系统模型由图1-1可直接看出本文的工作就是对水声信道进行研究，目的是要估计出水声信道的多径频偏和多径时延。现在我们来看浅海声场基本线路图如图1-2。声图卜2浅海声场基本线路图我们由图1-2可以看出，从声源到接收端共有三条路径，声线1为直达波，声线2、3为多径，声线2为海面反射波，声线3为海底反射波。本文要解决的水声信道多径时延估计即为声线1与接收信号起始点的时间间隔，声线1与声线2的时间间隔以及声线2与声线3的时间间隔。对于要解决的多径频偏估计即为声线l的频偏、声线2的频偏和声线3的频偏。1．4国内外的研究现状及发展动态目前，关于信道的多参数估计问题已经涌现出了很多算法，信道估计算法从大的角度可以分为盲估计算法和数据辅助算法。盲估计算法主要是利用循环前缀【141、虚拟子载波【151等先验信息，并用二阶或高阶统计量进行信道估计，计算比较复杂，收敛速度较慢。相对而言，数据辅助算法的数学原理比较成熟，算法比较简单，实用性也较强。数据辅助算法主要采用导频和训练序列来进行信道估计，实现准则可以基于最小平方(Least3 基于分数阶傅立叶变换的水声信道多参数估计算法研究Square，LS)、最小均方误差(MinimumMeanSquareError，MMSE)【16】【171、最大似然估计(MaximumLikehoodEstimator，MLE)【18】㈣等。其中，MLE算法不需要知道信道的统计特性和信噪比(SNR)的信息，它是假设h为确定而未知的向量来进行估计。本论文选用的是数据辅助算法，而现有的水下导频信号主要是采用线性调频(LFM)信号，也被称为Chirp信号【20】【2I】，因此研究Chirp信号的检测与参数估计对水下声信道的多参数估计具有很重要的实用价值。当前，针对Chirp信号的参数估计常用的有3类方法：(1)基于Cohen类的时频分布法【221，此类方法对单分量信号具有较好的时频积聚性，能够有效地进行信号检测和参数估计；其不足之处在于，对多分量信号的情况，存在严重的交叉项【231。尽管人们对核函数【24，251提出了改进以抑制交叉项，但均以牺牲自项为代价。(2)RWT法【26I署flRAT法【271，Radon—Wigner变换(RWT)法和Radon—Ambiguity变换(RAT)法适用于多分量信号的检测，其主要思想是将检测问题转化为峰值搜索， 基于分数阶傅市叶变换的水声信道多参数估计算法研究信道多参数估计算法，并对该算法进行了仿真和分析；第四章针对不同的水况，提出了两种基于FRFT通信系统的数据包结构设计；第五章总结了本论文的全部工作，并对后续工作进行了展望。 基于分数阶傅立叶变换的水声信道多参数估计算法研究2三种基于FRFT的水声信道多参数估计算法本章简要介绍了水声信道模型和Chirp信号的恒k模型，然后又简要介绍了FRFT的定义，同时采用FRFT对Chirp信号进行分析处理，最后，提出了三种新颖的水声信道多参数估计算法，并对这三种算法的处理效果及应用范围进行了总结。2．1水声信道模型水下声信道可以看成是缓慢时变的相干多途信道，声信号自声源发出沿不同途径的声线到达接收点，忽略介质吸收特性，假定没有色散现象，以直达波为基准，则多途冲击响应函数可以表示为：_^，-I㈨=鸽万(，)+∑48(t-r,)(2—1)，昌I假定发射信号为x(，)，信道噪声为胛(f)，4(扛O⋯N一1)为幅值，根据公式(2—1)可得相应的接收信号ro(t)为：Ⅳ一1％(f)=Aox(t)+∑A,x(t一一)+门(f)(2—2)i=1假定直达波有延时，且存在多径多普勒频偏，那么接收信号，．∥可表示为【1011111：|Ⅳ一l，(f)=Aox(t-ro)e72础训+∑4x(t-r,)e腑‘卜。’+门(，)(2—3)i=1公式(2-1)、(2-2)、(2-3)的参数含义如表2—1(待1⋯Ⅳ一1)。表2-1信道参数参数含义本征声线数直达波幅值第i径幅值直达波时延第i径的时延直达波频偏第，径的频偏高斯白噪声6■JⅣA4％‘岛吣’以 摹于分数阶傅屯叶变换的水声信道多参数估计算法研究2．2Chirio信号的恒k模型ChirpYN-号的瞬时频率随时问而变化，是一种典型的非平稳信号，设彳是Chirp信号的初始频率，石是chirp信号的终止频率，石是信号的时域长度，A为发射信号幅值，七为调频斜率，且七=TL-A，则发射端的chirp信号s(，)可以表示为【30l：∞，=Asinhz+钏(2-4)基：JZChirp信号的。N_k模型，设毛为第f径的频偏，‘为第i径的时延，4为第f径的幅值(i=0，．．．，N一1)，fo为Chirp信号中心频率，N为本征声线数，即多径数，则接收信号公式可以表示为【291：‘(，)=艺4sin[2万×((foi=O+乞)×。一。)+兰×(，一乃)2)](2—5)‘(归∑4snl万×I(+乞)×(卜0)+鲁×(f-乃)2l(2—5)L＼z／_|2．3立论基础2．3．1分数阶Fourier变换定义定义在“’域的函数朋，的p阶FRFT是一个线性积分运算131,32]：‘(“)=F吖厂@-)】}(甜)=ffKp(铭，“’)厂(甜I)幽’其中：～1-jcotc。ff唧c／竿cot口一》∽幽一胍厂(甜-)厂(一"．)f，翮l口三三一IL2／2．3．2基于FRFT的水声信道多参数分析对公式(2-3)进行FRFT，可得：7口=2nrc(2-6)口=(2n±1)re 基于分数阶傅立叶变换的水声信道多参数估计算’法研究R。(“)=4Xp(材一80sina—roCOS口)xexp(jn-r02sin口cos口一／2万(“一气sina)rosine)xexp(一jxe02sinacosa—j2_7rueoCOSg)^，一l+∑4巧(甜一蜀sina-r,COS口)l=lxexp(jxri2sin口cos口一／2万(甜一qsina)r_fsina)xexp(-jxe_f2sinacosa-j2xusiCOSg)+坼(材)(2—7)从公式(2—7)可以看出，当取“最佳”分数阶数p时，接收信号的FRFT模值I彤(")12将在相应的“域上形成一系列峰，直达声坐标相对于标准直达声坐标移动了Eosina+ToCOSOf，各多途信号对应的峰值位置相对于标准直达声坐标移动了幺sina+LCOSOf(f=0，．．．，N一1)‘121。2．4三种新颖的信道估计算法通过上述的分析，我们可知，通过FRFT可以估计出水声信道的多参数。下面我们针对恒k模型分别提出TFRFT估计法、双Chirp信号估计法以及联合估计法来估计水声信道的多参数。2．4．1FRFT估计法发射一个脉宽为互，调频斜率为k，中心频率为石，带宽为B的Chirp信号。经过水声信道后，Chirp信号因为水声信道的影响产生了多径时延和多径频偏，假定多径频偏都相同，通过接收到的Chirp信号估计出水声信道的多径频偏和多径时延。设△f为时域的时间长度，s为频率变化大小，因为Chirp信号为线性调频信号，可得k为【33】k=二(2-8)△f设接收信号的中心频率石频偏‰，对接收信号进行FRFT，在角度为口时，接收信号可在相应的U域形成一系列峰值，设多途的峰值坐标为Z(b0，．．．，N—1)，假定多径频偏都相同，根据公式(2-7)可以推出相邻两个波的延时公式：8 基于分数阶傅立叶变换的水声信道多参数估计算法研究l+·一t2丽+1两B4(2—9)COSl口J在接收信号的开始处，重构Chirp信号，对重构的Chirp信号做FRFT，此时的峰值坐标即为标准参考值sta__peak。则多普勒频偏为：FRF1’法算法流程如图2—1。岛2紫sin(口)(2-10)图2—1FRFT法算法流程图注：A为将接收信号进行FRFT：B为取出甜域里的各峰值坐标；C为通过峰值数得出多径数；假定多径频偏都相同，我们可以直接通过峰值坐标的间隔求出时延；通过直达波的峰值和标准参考值求出多径频偏。综上，信道参数估计步骤如下：(1)将接收信号进行FRFT，根据峰值的个数确定多径数。(2)根据公式(2—9)求出多径延时，‘+。一‘(汪0⋯．，N一1)。(3)根据公式(2—10)求出频偏％。为了验证上述算法的有效性，下面进行了数值仿真。例1：设Chirp信号的中心频率为3kHz，带宽为4kHz，脉宽为0．4s，采样频率为40kHz(1s采样40000点)。信道参数如下：三条途径：海面反射波比直达波延时120点，海面反射后的幅值为0．7；海底反射波比海面反射波又延时160点，海底反射后的幅值为0．5；信噪比为0dB；三径频偏都为17．6Hz。则无噪声且频偏都相同的直达波、海面波及海底波的波形图如图2-2。9 基于分数阶傅直叶变换的水声信道多参数估计算法研究时间，s藿。黝瑟凇渊潲㈣蟊蕊勰一{。f—o面百1一一疏r一打⋯五西一面一百墨～丽—帚5时问，sO0050101502O250303504噍惦时间，s图2—2发射信号经过信道后的三径波形图无噪声的接收信号波形图以及SNR=OdB的接收信号波形图如图2-3。OO．05n’n15乱2025O．3035O．4O．惦时问，s燃蜘I,'iI删黼,II'It俐PO0．∞n1n’5020为0，3n350．40．朽时问，s图2-3无噪声与SNR=OdB的接收信号波形图在SNR=OdB时，将接收信号进行FRFT处理后的甜域图如图2—4。．蓝色方框为将标准信号进-行FRFT处理后的甜域图，红色五角星为将实际接收信号进行FRFT处理后的材域图。j一⋯一⋯．-山-曲-_扯l图2—4SNR=OdB接收信号的FRFT图我们将图2-4进行局部放大可得图2—5，可以明显的看出有一个蓝色方框的峰值和lO4202●505魁孥博馨 桀于分数阶傅立叶变换的水声信道多参数估计算法研究三个红色五角星的峰值。蓝色方框的峰值坐标为标准信号的材域坐标，三个红色五角星的峰值坐标为直达、海面和海底的甜域坐标。图2—5SNR=OdB援收信号的FRFT局部放大图由此我们可得：共有三条途径。通过公式(2-9)，可得：海面波比直达波的延时估计为：■-ro=121。0518≈121点海底波比海面波的延时估计为：乃-‘=158．2985≈158点通过公式(2-10)，可得：三径的频偏估计为：‰217．6018Hz信道参数误差率为：海面波一直达波的延时估计误差率：警=o．833％海底波一海面波的延时估计误差率：警=1．25％频偏估计误差率：鱼青≠=o．。1023％综上，统计数据列于表2-2。通过上述分析可知，该方法的优点是可以准确的估计出多径数，并且时延估计比较准确，频偏估计比较精确，但时延估计误差比高于频偏估计误差比，不足之处在于该方法只适用于多径频偏都相同且能准确抓取直达波时延的情况。 基于分数阶傅立叶变换的水声信道多参数估计算法研究表2-2FRFT法信道估计对比表为了能够估计出水声信道多径不同频偏的情况，弥补FRFT法应用范围的不足，本章提出了双Chirp信号估计法。2．4．2双Chirp信号估计法采用发射间隔为时间丁的两个Chirp信号—chirpl和Chirp2，脉宽都为Z，调频斜率都为七，中心频率分别为石。和丘：(fo。≠fo：)。经过水声信道后，Chirpl与Chirp2在甜域的信号间隔产生了变化，这个变化是由于Chirpl和Chirp2的多径频偏不同造成的。通过这个变化的大小，我们可以求出多径频偏。再通过多径频偏求出多径信号间的时延。发射信号的结构图如图2-6所示：I中心频率工．I调频斜率^一脉宽7：一间隔r中心频率厶调频斜率t一脉宽7=一cIlirplChirp2图2—6双Chirp信号法发射信号结构图设接收信号中心频率fo。偏移了岛，，中心频率fo：偏移了％，‰为信号的中心频偏，五为信号的中心频率。设物体运动速率为y，载波速率为c，可得公式【34】：兰：皂。因此我们可以推出：c】o孕：孚(2—11)五。厶、若接收信号Chirpl和Chirp2都无频偏的话，对接收信号进行FRFT，在角度为口时，接收信号可在相应的甜域形成一系列峰值，由公式(2-7)和公式(2-8)可得材域的Chirpl和Chirp2各自的最高峰对应的甜域间隔为：觚=卜掣卜㈤》蚴12 基于分数阶傅立叶变换的水声信道多参数估计算法研究若Chirpl信号的多径有不同的频偏，根据公式(2—11)，Chirp2的频偏随之相应变化。此时对接收信号进行FRFT，设Au2．，为Chirpl和Chirp2第i条途径的甜域间隔，岛1．，为Chirpl第i条途径的中心频偏(i=0⋯．，N一1)，i=0时为直达波。由公式(2—7)、(2-8)和(2一11)，以及含有频偏的接收信号Chirpl和Chirp2进行FRFT后的U域图，我们可以得出每一对相对应的峰值U域间隔为：毗，地懒t×(1一舡半∽13)由公式(2—13)可得：‰=警×赤∽Ⅲ(1一华)w泌“，Jol设Chirpl的峰值坐标为谚(i=0⋯．，N一1)，再根据公式(2-7)和(2-8)可以推出相邻两个波的延时公式：％中丽+1--4+等孚(2_15)双Chirp信号法算法流程如图2—7。图2—7双Chirp信号法算法流程图注：A为将接收信号进行FRFT；B为取出甜域里的各峰值坐标；C为求出两信号无频偏时的甜域间隔；D为求出两信号有频偏时的材域间隔；E为求出多径频偏；最后，求出多径时延。综上，信道参数估计步骤如下：(1)由公式(2—12)求取无频偏的Chirpl、Chirp2信号的U域间隔△％。(2)由公式(2一13)求取含有频偏的Chirpl、Chirp2第f条途径的甜域间隔△甜2，(f=0，．．．，N—1)。(3)由公式(2—14)求取Chirpl的多途频偏‰1．『(kO⋯．，N一1)。(4)由公式(2—15)求取相邻两条途径的延时f，+l一一(江0，．．．，N一1)。 基于分数阶傅市叶变换的水声信道多参数估计算法研究下面将举出两个仿真实例来验证该算法的有效性。例1：设Chirpl信号的中心频率为3kHz，Chirp2信号的中心频率为6kHz，脉宽都为O．4s，带宽都为4kHz，采样频率也都为40kHz(1秒为40000点)，两个信号间隔时间为1S。信道参数如下：三条途径；直达波延时30点，直达波幅值为1；海面反射波比直达波又延时160点，海面反射后的幅值为0．7；海底反射波比海面反射波又延时180点，海底反射后的幅值为0．5；信噪比为OdB；直达波频偏为19．595Hz；海面反射波频偏为12．67Hz；海底反射波频偏为-18．333Hz。发射双Chirp信号，经过SNR=OdB的水声信道后，信号接收波形图如图2—8。00．5t1．S时间，s图2—8SNR=OdB接收端双Chirp信号波形图对接收信号进行FRFT，可得图2-9。∞型加罂100．I--．．．．．_o～⋯／⋯17451751755'761765177u域，点数x104图2—9接收信号的“域图及Chirpl部分的放大图由图2—9我们可以确定Chirp信号有3条途径，表明本算法确定信号多径有效。14 基于分数阶傅立叶变换的水声信道多参数估汁算法研究35；．∞I广—一虬为l【r‘。。。。。。。。。。’’’。。。’。。。。’。。。。‘。。。。。’’。‘‘。。。。。1。—df171892212324252627u域，点数xlo．图2-10接收信号的甜域放大图我们由图2-10可以直接看出经过水声信道后的Chirpl和Chirp2在材域中的相对应的多径距离，通过公式(2—12)、(2一13)、(2—14)和(2一15)，我们可以估计出多径频偏和多径时延。综上，统计数据列于表2—3。表2—3双Chirp法信道估计对比表例2：发射信号同上，设信道参数如下：直达波的频偏由Om／s—lOm／s的相对运动产生，幅值为l；海面反射波的频偏为12．67Hz，幅值为0．7：海底反射波的频偏为-18．333Hz，幅值为0．5；直达一海面反射延时160点；海面反射一海底反射延时180点；信噪比为OdB。针对上述水声信道环境的参数，我们得到的仿真结果如图2一11、图2—12和图2—13所示。图2-11为直达波的频偏估计。图2-12为海面反射和海底反射波的频偏估计。图2-13为海面一直达、海底一海面的延时估计。15 基于分数阶傅立叶变换的水声信道多参数估计算法研究速度m／s图2-11直达波的频偏估计图注：黑点为真实信道值，红星为估计值。图2-12海面反射和海底反射波的频偏估计图注：黑点为真实信道值，蓝三角为海面的频偏估计，洋红色方框为海底的频偏估计。裁咂富毅}——母．，睁——E卜—B，日口日，卢户、，一一苗一——，一1西÷|＼／速度m／s图2-13海面一直达、海底—海面的延时估计图注：黑点为真实信道，蓝三角为海面一直达的延时估计，洋红色方框为海底一海面的延时估计。图2—11、图2-12矛13图2-13表明，直达波、海面反射波、海底反射波的频偏估计，以及海底一海面和海面一直达的时延估计始终在水声信道真实值附近波动，16 基于分数阶傅立叶变换的水声信道多参数估计算法研究估计的偏差并不随着频偏和时延的增大而增大。图2-11和图2-12所示，在6m／s时直达波的频偏与海面反射波的频偏仅仅相差0．913Hz，但是依然分别估计出了直达波和相对应的海面反射波的水声信道参数，表明本算法可以区分频率非常相近的多径。图2—14为同样的条件下，不同信噪比的直达波频偏估计图。N工霹粕晒图2—14不同信噪比下，直达波频偏估计图注：黑点为真实信道值，蓝色三角为信噪LL-IOdB的估计，洋红色方框为信噪比-5dB的估计，红色星为信噪LLOdB的估计。图2一14表明，信噪比在OdB和一5dB时，估计值在真实信道值附近波动，而一lOdB波动个别点略大些。由上表明FRFT估计水声信道参数抗噪性很好，随着噪声的增大，估计性能变化不大。综上，我们可以得出，双Chirp信号法优点是能估计出多径不同的频偏以及时延。当频偏接近且含有负频偏时，该算法依然有效。不足是采用了FRFT快速算法，带来了计算误差，造成了多径频偏和多径时延估计误差偏大。为了能够精确的估计出水下声信道的多参数，弥补双Chirp信号法的估计准确度的不足，本章又提出了联合估计法。2．4．3联合估计法采用发射间隔为丁的Chirp信号和正弦信号。Chirp信号的中心频率为．磊，脉宽为五，调频斜率为k，带宽为B。正弦信号载频也为石，脉宽为正。经过水声信道后，Chirp信号和正弦信号都产生了多径时延和频偏。在接收信号开始处重构Chirp信号，使得重构信号与接收信号等长。通过FRFT和解相关在时域和甜域分别与标准重构信号对比列方程，求出多径频偏和时延的关系表，再通过正弦信号求出多径频偏，通过估计出的频偏提取信道估计值。发射信号结构如图2-15所示。 基于分数阶傅立叶变换的水声信道多参数估计算法研究圈l竺竺竺兰!I问隔7’—————一图2—15发射信号结构图设接收酐JChirp信号中心频率五频偏了岛，则正弦信号也频偏了‰。设Uc．，(i=0，．．．，N—1)为接收信号FRFT与标准重构信号FRFT的U域间隔。设f。，(i=0一．，N—1)为接收信号与标准重构信号的解相关峰值与标准重构信号自相关峰值的时域间隔点数。设乞。，(f=O，．．．，N-1)为多径信号的延时点数，岛。，(扛0⋯．，N—1)为多径信号的频偏。．设接收信号FRFT的最佳角度为口，因此，我们可以列出两个方程：“叫=td，，×cos(a)+eo。fxsin(a)(2—16)，c广”半×z(2-17)由方程(2-16)、(2—17)可以推出：‰：≠_芷!盟(2-18)J七SXCOS(口)-sin(口)么，嘞一甓黜∽坳因为FRF1’的快速算法带来一定的计算误差可以在小范围内进行搜索，得出频偏和时延估计表，根据正弦信号的频偏估计，我们可以提取出最佳的频偏和时延。联合估计法算法流程图如图2一16。18 基于分数阶傅立叶变换的水声信道多参数估计算法研究正弦求D频F偏提R0取F时接T频延收偏C信时延号解表相占关图2一16联合估计算法流程图注：彳为将接收信号进行FRFr；B为将接收信号进行解相关；C为A和B联立方程，列出频偏时延估计表；D为正弦信号求出多径频偏；最后，根据D得出的多径频偏从表中提取多径时延。综上，信道参数估计步骤如下：(1)通过Chirp信号的甜域图，列出公式(2-16)。(2)通过Chirp信号的解相关图，列出公式(2—17)。(3)通过公式(2-18)和公式(2-19)得出多径时延和频偏，小范围搜索，得出多径时延和频偏的关系表。(4)发射一定脉宽的正弦信号求出多径频偏，从表中提取估计的信道参数。下面举了三个不同信道情况下的仿真实例。在信道噪声比为零的前提下，分别仿真了多径时延相差小，多径频偏相差较大、多径时延相差小，多径频偏接近以及多径时延相差大，多径频偏接近的情况。通过三种不同水声信道的多参数估计，来验证该算法的有效性。例1：设Chirp信号的初始频率为100Hz，终止频率为500Hz，调频斜率为2kHz／s，脉宽为0．5s，采样频率为4kHz。正弦信号频率为300Hz，脉宽为0．6s。两个信号间隔时间为1s。信道参数如下：三条途径；直达波延时120点(1秒为4000点)，直达波的幅值为1；海面反射波比直达波又延时160点，海面反射后的幅值为0．7；海底反射波比海面反射波又延时180点，海底反射后的幅值为O．5；信噪比为0dB；直达波频偏为8．333Hz；海面反射波频偏为15．777Hz；海底反射波频偏为一10．777Hz。无噪声且含有不同频偏和时延的直达、海面及海底的三径波形如图2-17。19 基于分数阶傅寺叶变换的水声信道多参数估计算法研究《盈礴㈣匿j譬j西两瓣匾疆j00102030405080．7时间，s图2—17三径不同频偏时延的波形图无噪声的接收信号波形图以及SNR=OdB的接收信号波形图如图2-18。图2一18不含噪声和SNR=OdB的接收信号波形图对接收信号进行解相关运算。此时接收信号的解相关图如图2一r9所示。图2-19接收信号的解相关图将图2-19进行局部放大，如图2-20所示。20 基于分数阶傅立叶变换的水声信道多参数估计算法研究型毒丑辱彩至鏊O；OL阪妊睡菡鑫矗鑫蓝料【叶；5f≯ok厶k五矗《如氢采200021∞22002300“oo2S00时域，点数图2—20接收信号的解相关局部放大图从图2—20可以得出：tc,O=103,氘tc．12248点；to,2=482,点。对接收信号进行FRFT。此时接收信号的U域及局部放大如图2-21、图2-22所示。倒馨毛霹卜L叱u．创擎习臻卜-u-芷k图2—21接收信号的U域图由图2—22可以直接得出：图2—22接收信号的“域局部放大图2l 基于分数阶傅立叶变换的水声信道多参数估计算法研究点123．4032123．1696122．9359122．7023122．4687122．235122．0014121．7677121．5341121．3004Hz10．201610．08489．9689．85129．73439．61759．50079．38399．2679．1502111213141516．17181920点121．0668120．8331120．5995120．3658120．1322119．8985119．6649119．4312119．1976118．964Hz9．03348．91668．79978．68298．56618．44938．33248．21568．09887．982212223242526：。：27282930点118．7303118．4967118．263118．0294117．7957117．5621117．3284116．861l116．6275116．3938Hz7．86527．74837．63157．51477．39797．2817．16426．93066．81376．6969通过正弦信号可以很容易得出估计的频偏值，从表中可以直接提取出信道估计值：％，o28．3324Hz；ta。o≈120点。海面波频偏时延估计表如表2-5。表2-5海面波频偏时延估计表12345678910点280．092280．0622280．0324280．0026279．9728279．943279．9132279．8834279．8537279．8239Hz16．04616．031116．016216．001315．986415．971515．9566lg．941715．926815．9119ll12131415161718．1920点279．7941279．7643279．7345279．7047279．6749279．6451279．6153279．5855279．5558279．526Hz15．89715．882l15．867215．852415．837515．822615．807715．792815．777915．7632l222324252627282930点279．4962279．4664279．4366279．4068279．377279．3472279．3174279．2876279．2579279．2281Hz15．748115．733215．718315．703415．688515．673615．658715．643815．628915．614通过正弦信号可以很容易得出估计的频偏值，从表2-5中可以直接提取出信道估计值：‰，l215．7779Hz；fd，I一‰≈160点。22 幕于分数阶傅立叶变换的水声信道多参数估计算法研究点461．2678461．2094461．151461．0925461．0341460．9757460．9173460．8589460．8005460．7421Hz-i0．3661—10．3953—10．4245一10．4537一10．4829一lO．5121—10．5413一10．5705一10．5998一i0．6291114．151820点460．6837460．6253460．5668460．5084460．45460．3916460．3332460．2748460．2164460．158Hz—10．6582一10．6874一10．7166-10．7458-10．775一10．8042一10．8334一10．8626一10．8918一10．92l222324252627282930点460．0996460．041459．9827459．9243459．8659459．8075459．7491459．6907459．6323459．5738Hz一10．9502一10．9794一11．0086一11．0378—11．067—11．0963—11．1255一11．1547—11．1839一11．2131通过正弦信号可以很容易得出估计的频偏值，从表中可以直接提取出信道估计值：E*0,2------lO．775Hz；td，2一td，l≈180A。．基于联合估计法的水声信道多参数的时延估计统计数据列于表2—7。表2—7联合估计法时延估计表该方法只作多径时延方面的讨论，多径频偏估计将在第三章详细讨论。我们可以看到在信道比较恶劣的情况下，多径频偏相差较大，时延相差较小时，时延估计误差为0，说明该方法在这种情况下是有效的。例2：发射信号同上，信道参数如下：三条途径；直达波延时120点(1秒为4000点)，海面反射后的幅值为1；海面反射波比直达波又延时160点，海面反射后的幅值为0．7；海底反射波比海面反射波又延时180点，海底反射后的幅值为0．5；信噪比为OdB；直达波频偏为8．333Hz；海面反射波频偏为9．777Hz；海底反射波频偏为-8．777Hz。无噪声且含有不同频偏和时延的直达、海面及海底的三径波形如图2—23。 基于分数阶傅立叶变换的水声信道多参数估计算法研究1藿。．1'藿。．，n5釜。-0．50O'02030405080．7时间，sOO．10．20．304O5060．7时问，s00．’020304050．60．7时间，s图2—23三径不同频偏时延的波形图无噪声的接收信号波形以及SNR=OdB的接收信号波形如图2—24。魁馨5譬。．50n10．20304050．60．7时间，s图2—24不含噪声和SNR=OdB的接收信号波形图对接收信号进行解相关，此时接收信号的解相关如图2-25所示。由图2-25可以得出：魁馨丑攥斗K罂鐾{哒喹丑辞}K罂譬时域／点数Il乙一上⋯一j～C。一莨。±女高时域／点数图2—25接收信号的解相关图和局部放大图tc,o：103点；7叫2261点；l，22478,点。24 基于分数阶傅立nl’变换的水声信道多参数估计算法研究对接收信号进行FRFT，此时接收信号的“域图如图2-26所示。由图2—26得出：型∞厂——————————————]矍加}I耋，。}i衙4E10}训1匿嗵_-_鳓----___-_-逸舀_·—嘞u域，点数恻粤丑僻卜L叱u-j赫jj上u域，点数图2-26接收信号的U域图和局部放大图U。,0=--3l点；甜。．1—79点；Uc,2=--145点；sin(a)=一0．9525；COS(a、=一0．3045。根据公式(2-18)、(2-19)，可以求出多径频偏和时延，进行小范围搜索，得出频偏和时延估计表。直达波频偏时延估计表如表2—8。表2-8直达波频偏时延估计表l23456789点122．8392122．6063122．3734122．1404121．9075121．6745121．4416121．2087120．9757120．7428Hz9．91969．80319．68679．57029．45379．33739．22089．10438．98798．8714点118．1805117．9475117．7146117．4817117．2487117．0158116．7828116．5499116．317116．084Hz7．59027．47387．35737．24087．12447．00796．89146．77496．65856．542通过正弦信号可以很容易得出估计的频偏值，根据频偏值，我们可以从表中可以直接提取出信道估计值：‰，028．4055Hz；td，o≈120A。 幕于分数阶傅立叶变换的水声信道多参数估计算法研究点281．0292280．9995280．9698280．9402280．9105280．8808280．8511280．8214280．7917280．762Hz10．01469．99989．98499．97019．95529．94049．92559．91079．89589．88lll12131416．17点280．7323280．7026280．6729280．6432280．6135280．5838280．5541280．5244280．4947280．465Hz9．86619．85139．83649．82169．80679．79199．7779．76229．74739．7325222324252627282930点280．4353280．4056280．3759280．3462280．3165280．2868280．2571280．2274280．1977280．168Hz9．71769．70289．68799．67319．65829．64349．62859．61379．59889．584通过正弦信号可以很容易得出估计的频偏值。从表2—9中可以直接提取出信道估计值：EO，l29．777Hz；ta，l—ta，o≈161点。海底波的频偏时延估计表如表2一10。表2—10海底波频偏时延估计表点460．624460．5658460．5076460．4493460．391l460．3329460．2746460．2164460．1582460．0999Hz-8．688—8．7171—8．7462—8．7753-8．8044-8．8336-8．8627-8．8918—8．9209—8．95222324252627282930点460．0417459．9835459．9252459．867459．8088459．7505459．6923459．6341459．5758459．5176Hz-8．979l一9．0083-9．0374-9．0665-9．0956—9．1247—9．1539-9．183—9．212l一9．2412通过正弦信号可以很容易得出估计的频偏值，我们可从表中可以直接提取出信道估计值：C0,2----'--8．7753Hz；乙，2一乙’l≈179A。 基于分数阶傅立叶变换的水声信道多参数估计算法研究基于联合估计法的水声信道多参数的时延估计统计表如表2-11所示。表2—11联合估计法时延估计表由本例可知，在信道比较恶劣的情况下，多径频偏相差较小，多径时延相差也较小时，多径时延估计误差依然很小，说明该方法依然适用这种情况的水声信道多参数估计。例3：发射信号同上，信道参数如下：三条途径；直达波延时1200点(1秒为4000点)，海面反射后的幅值为l；海面反射波比直达波又延时1600点，海面反射后的幅值为O．7；海底反射波比海面反射波又延时1800点，海底反射后的幅值为0．5；信噪比为OdB；直达波频偏为8．333Hz；海面反射波频偏为9．777Hz；海底反射波频偏为一8．777Hz。无噪声且含有不同频偏和时延的三径图如图2-27。羹jE麟蕊三三j鐾。卜一黝潮一一1鐾二E三三噩7图2—27三径不同频偏时延的波形图无噪声的接收信号波形图以及SNR=OdB的接收信号波形如图2-28。 基于分数阶傅立叶变换的水声信道多参数估计算法研究图2-28不含噪声和SNR=OdB的接收信号波形图对接收信号进行解相关运算，此时接收信号的解相关图如图2—29所示。图2-29接收信号的解相关图由图2-29可以得出：to．o=1183,点；to,,=2781点；乞．224618点；对接收信号进行FRFT。此时接收信号的U域图如图2—30所示。图2-30接收信号的U域图 基于分数阶傅立叶变换的水声信道多参数估计算法研究由图2—30得出：UC,0mmM759点；UC,1一----1785点；甜c．2—2964点sin(a)2—0．7667；cos(a)=一0．642。根据公式(2—18)和(2—19)可以求出多径频偏和时延，进行小范围搜索，得出频偏和时延估计表。直达波频偏时延估计表如表2-12。表2一12直达波频偏时延估计表12345678910点1197．3041197．4591197．6141197．7681197．9231198．0781198．2321198．3871198．5411198．696Hz7．15227．22957．30687．38417．46147．53887．61617．69347．77077．8481l12131415．1617181920点1198．8511199．0051199．161199．3151199．4691199．6241199．7791199．9331200．0881200．243Hz7．92548．00278．088．15738．23468．3128．38938．46668．54398．621221222324252627282930点1200．3971200．5521200．7061200．8611201．0161201．171201．3251201．481201．6341201．789Hz8．69868．77598．85328．93059．00789．08529．16259．23989．31719．3944通过正弦信号可以很容易得出估计的频偏值，从表2—12中可以直接提取出信道估计值：岛，o28．312Hz；岛，o≈1200点。海面波频偏时延估计表如表2一13。表2—13海面波频偏时延估计表12345678910点2800．2832800．3032800．3222800．3422800．3622800．3822800．4012800．4212800．4412800．461Hz9．64159．65149．66129．67119．68099．69089．70079．71059．72049．730211121314．151617181920点2800．482800．52800．522800．5392800．5592800．5792800．5992800．6182800．6382800．658tlz9．74019．74999．75989．76979．77959．78949．79929．80919．8199．82882l222324252627282930点2800．6772800．6972800．7172800．7372800．7562800．7762800．7962800．8152800．8352800．855tlz9．83879．84859．85849．86829．87819．8889．89789．90779．91759．9274通过正弦信号可以很容易得出估计的频偏值，从表2一13中可以直接提取出信道估计值： 基于分数阶傅立叶变换的水声信道多参数估计算法研究点4599．8664599．9054599．9444599．9824600．0214600．0594600．0984600．1374600．1754600．214Hz-9．0669-9．0476-9．0283-9．0089-8．9896-8．9703-8．9509—8．9316—8．9123-8．893点4600．6394600．6784600．7174600．7554600．7944600．8334600．8714600．914600．9494600．987Hz一8．6803—8．661—8．6417—8．6223-8．603-8．5837-8．5643-8．545-8．5257-8．5064通过正弦信号可以很容易得出估计的频偏值，从表2-14中可以直接提取出信道估计值：岛，2—8．777Hz；ta，2一ta，l=1799,点。基于联合估计法的水声信道多参数的时延估计统计数据列于表2一15。表2-15联合估计法时延估计表由本例可以知，我们可以看到在信道比较恶劣的情况下，多径频偏相差较小，时延相差较大时，时延估计误差依然很小，说明该方法在这种情况下也是有效的。综上，我们可以得出，联合估计法优点是能精确的估计出多径不同的频偏以及时延。不管是频偏接近还是相差较大、或是时延相差较小或是相差较大时，该算法都可精确的估计出水下声信道的多参数。不足之处是该算法采用了联立方程，且需要进行小范围的搜索，算法流程复杂，计算量较大。 摹于分数阶傅立叶变换的水声信道多参数估计算法研究2．5本章小结本章主要介绍了三种基于FRFT的水声信道多参数估计算法。第一种是FRFT法，该算法的优点在于发射信号的结构简单，只有一个Chirp信号即可估计出水下声信道的频偏和时延，信号处理算法简单。不足在于需要先精确的估计出同步头，同时要求多径频偏都相同，满足这两点才能估计出水下声信道的多参数。第二种是双Chirp信号法，该算法的优点是可以估计出水下声信道的多径频偏和多径时延，不管多径频偏接近还是多径频偏相差较大时，多径时延相差较小还是多径时延相差较大时，都可以估计出水下声信道的多参数。不足在于该方法发射结构相对复杂，由两个Chirp信号构成，且采用了FRFT快速算法，带来了一定的计算误差，参数估计误差较大，信号处理算法相对复杂，计算量较大。第三种是联合估计法，该算法的优点是精确的估计出了水下声信道的多参数，不管多径频偏接近还是多径频偏相差较大，多径时延相差较小还是多径时延相差较大时，都可以精确的估计出水下声信道的多参数。不足在于发射信号相对复杂，由一个Chirp信号和一个正弦信号构成，且需要联立方程同时进行小范围的搜索，信号处理算法复杂，计算量较大。 基于分数阶傅专叶变换的水声信道多参数估计算法研究3一种基于FRFT的Chirp基特性的水声信道多参数估计算法在估计水声信道多参数时，上一章采用了FRFT快速算法，引入了计算误差，虽然经过小范围搜索精确估计出了水声信道的多参数，但代价是信号处理算法复杂，计算量大。本章利用FRFT的Chirp基分解特性，在保证精确估计水声信道多参数的同时，避免了FRFT快速算法的使用，信号处理算法简单，计算量小，可实现水下声信号的实时处理。3．1接收端Chirp信号的变k模型设s(，)为发射信号，r(t)为经过水声信道后的接收信号。多普勒频偏系数△为物体运动速率y与载波速率c之比。信号经过水声信道后，接收信号可以表示成【8】：吃(f)=s((1+△弘)(3—1)针对正弦信号频率为q，经过水声信道后，信号频率变为【8】：％’=％(1+△)(3-2)根据公式(2—4)、(3—1)，设△，为第f径的频偏系数，t为第i径的时延，4为第i径的幅值(扛02"''IPN-1)，彳为初始频率，石为终止频率，N为多径数，五为信号时域长度，那么我们可以推￡BChirp信号的变k模型接收公式【8】【30】：拍，=篓iv--i倒n卜(c-+△『M川吲+知训2)]》3，尔D2丢今inI2删卜△『)X小o-『『)+弘训2jI@_3’3．2立论基础根据FRFT的逆变换公式x(f)=e4(甜)K户(t,u)du可知，信号x(f)的FRFTX，@)可以解释为x(f)在以逆变换核疋P(f，“)为基的函数空间上的展开，而该核是甜域上的一组正交的Chirp基，这与Fourier变换原理是相近的，只是函数空间展开的基底不同，FRFT的基底是“域上的一组正交的Chirp基，这就是FRFT(约Chirp基分解特性【12】【32】。因此，一个Chirp信号在适当的FRFT域中将表现为一个冲激函数，即对于给定的Chirp信号(调频斜率一定)，存在一个分数阶数使线性调频信号的能量聚集于一最大值，我们称之为与此调频斜率相匹配的“最佳”分数阶数。理论上，调32 基于分数阶傅立叶变换的水声信道多参数估计算法研究频斜率七与‘‘最佳7’阶数P有如下确定的对应关系【12】：bcot(等)(3-4)我们可以看出，对于任意的调频斜率k都会有相应的阶数P与之对应，反之，对于任意的阶数P都会有相应的调频斜率k与之相对应，也就是说，FRFT里含有任意调频斜率的Chirp信号。之所以采用Chirp信号估计时延而不采用正弦信号估计时延的原因就在于，正弦信号产生频偏后，调频斜率依然为0，而Chirp信号产生频偏后，调频斜率改变，利用接收信号多径调频斜率的不同求取多径延时。3．3测试信号的结构及信号处理算法3．3．1测试信号的结构发射信号的参数如2．4．3联合估计法所示，发射信号的结构图如图2-15所示。经过水声信道后，Chirp信号和正弦信号都产生了多径时延和多径频偏。对接收到的正弦信号进行高分辨的FFT，确定多径数，同时求出多径频偏。根据估计出的多径频偏按先后到达的顺序依次重构信号与接收信号进行解相关运算，我们可以根据相应的峰值坐标的差值快速精确的估计出时延。3．3．2信号处理算法对接收信号的正弦信号部分做高分辨的FFT，我们可以直接得出多径数和精确的频偏估计值。根据FRFT的Chirp基分解特性，我们可以避免采用FRFT的快速算法来估计Chirp信号的同步头和时延，将估计出来的多径频偏值重构Chirp信号，将重构信号依次与接收信号进行解相关运算，获取解相关的峰值坐标，因为多径调频斜率不同，我们可以根据这些峰值坐标精确的估计出多径时延。Chirp基法的算法流程如图3-1。图3—1Chirp基法的算法流程图33 基于分数阶傅立nt。变换的水声信道多参数估计算法研究注：么为取出接收信号的Chirp信号部分；B为取出接收信号的正弦信号部分；C为将B进行高分辨的FFT，提取出多径数和多径频偏；最后，根据C得出的多径频偏重构Chirp信号与彳进行解相关运算估计出多径时延。综上，信道参数估计步骤如下：(1)对接收信号的正弦部分做高分辨的FFT，得出多径数和频偏估计值。(2)利用多径数和相应的频偏估计值重构Chirp信号，将重构的Chirp信号依次与接收信号进行运算，基于Chirp信号的调频斜率改变特性，我们可以精确的估计出多径时延。3．4数值仿真下面举了三个不同信道情况下的仿真实例。在信道噪声比为零的前提下，分别仿真了多径时延相差小，多径频偏相差大、多径时延相差小，多径频偏接近以及多径时延相差大，多径频偏接近的情况。通过三种不同水声信道的多参数估计，来验证该算法的有效性。例1：设Chirp信号的中心频率为lkHz，带宽为800Hz，脉宽为0．Ols，采样频率为12kHz(1秒采12000点)。正弦信号频率为lkHz，脉宽为0．6s。两个信号间隔时间为ls。信道参数如下：三条途径；直达波延时120点，海面反射后的幅值为1；海面反射波比直达波又延时133点，海面反射后的幅值为0．7；海底反射波比海面反射波又延时181点，海底反射后的幅值为0．5；信噪比为OdB；直达波频偏为3．777Hz；海面反射波频偏为100．777Hz；海底反射波频偏为一100．777Hz。发射信号中的正弦信号部分经过水声信道时的三径频偏时延波形图以及SNR=OdB时的接收信号波形图如图3—2。譬j嘲黝㈣勰贼鳓EO01020304050607O．0时问愚盏o}黜目阅跚嘲锄触慨勰疆一——1。占_～i1o：21：3i1百i——1盎———若F———言·时问，s鼙曼圃嬲斓劂㈣黜匾]Oo'02o3o405o6070．8时问岛盏。脚删删蝴脚嘲|II蝴蝴喇蝴荆黼蝴呐州{4占_—1汀—1百—1占——赢——赢——赢——亩——矗·时闻虑图3-2正弦信号多径频偏时延波形图及SNR=OdB的接收信号波形图发射信号中的Chirp信号部分经过水声信道时的三径频偏时延波形图以及SNR=OdB时的接收信号波形图如图3—3。34 基于分数阶傅立叶变换的水声信道多参数估计算法研究蓉j三要避E三三三三时间括耋oL————州6懒———一一1‘10～⋯0一．01⋯i．砭～。币j—一百万——丽r——孤时问，s耋曼E三三三三j圜日耋．。：E二二：二：：=：二=：盥璐避二二j时间舟墓!}删忡咿州州¨州讪州1-，--------------·--------------I---------------------．—-----l-．—．------u-．------------J----．------．--．--------．---1．------．--—-------．--------J．．．—．-．-—------．．--—．-----一时间舟图3—3Chirp信号多径频偏时延波形图及SNR=OdB的接收信号波形图将接收信号的正弦信号部分进行高分辨的FFT，可得图3-4。图3—4正弦信号的FFT高分辨图SNR=OdB将图3-4进行局部放大，可得图3—5。图3-5SNR=OdB的正弦信号的FFT高分辨局部放大图由图3-5可以直接读出三径频偏，如表3-1。35 基于分数阶傅立叶变换的水声信道多参数估计算法研究表3—1Chirp基法频偏估计表由表3—1可以看出，在多径时延相差小、多径频偏相差较大时，多径频偏估计性能非常好。我们根据估计出来的多径频偏和先验信号依次重构多径Chirp信号，分别与接收信号进行解相关，可得图3-6、图3-7和图3-8。一1选t一是后前坐．黼b『随‰·o100200300400500600700800时域，点数图3—6SNR=0dB直达波重构信号与接收信号的解相关图一鼻■援H挂*后的童话【f1．．燃濑越‰：时域，点数图3—7SNR=OdB海面波重构信号与接收信号的解相关图¨"¨帖¨"¨o越孥丑驿水罂鐾¨盯¨帖¨∞¨o避罂丑簿状霉饕 基于分数阶傅立叶变换的水声信道多参数估计算法研究O1002003004005006007∞800时域／点数图3—8SNR=0dB海底波重构信号与接收信号的解相关图取图3—6的第一个峰值与Z×石进行相减可得直达波延时，取图3—7的第二个峰值与图3—6的第一个峰值相减可得海面对直达的延时，取图3—8的第三个峰值与图3-7的第二个峰值进行相减可得海底对海面的延时。经过计算可得表3-2。表3—2Chirp基法时延估计表由表3—2可得，在多径频偏相差较大、且多径时延相差较小的情况下，多径时延估计非常精确。例2：发射信号同上，信道参数如下：三条途径；直达波延时120点，海面反射后的幅值为1；海面反射波比直达波又延时133点，海面反射后的幅值为O．7；海底反射波比海面反射波又延时181点，海底反射后的幅值为O．5；信噪比为0dB；直达波频偏为33．333Hz；海面反射波频偏为35．777Hz；海底反射波频偏为-33．373Hz。发射信号中的正弦信号部分经过水声信道时的三径频偏时延波形图以及SNR=0dB时的接收信号波形图如图3—9。37¨”¨”¨o煞；芒簿彬霉譬 基于分数阶傅立叶变换的水声信道多参数估计算法研究蓉．{鬣蕊黼蕊蕊溺蕊E00102O304050Bg70．8时间居蓉o}勰嘲湖跚嘲煳i黼——1。}o，02o3o‘4os一。百r——南——≮o时问，s蓉：ii嘲翮㈣绷黼jO0102030405060．7n0时阃屉鼙。脚嘞嘲嗍黼懈煳躺蝴槲喇脚黼嘲■1。5}—1汀——矗——赢——赢——若r一亩一1占—≮o时间舟图3—9正弦信号多径频偏时延波形图及SNR=OdB的接收信号波形图接收端的Chirp信号部分的三径图以及SNR=OdB时的接收的Chirp信号如图3一10。釜jE丑盈E三三三jO001O佗0030．040．惦n08时问，s鼙-oE二二=笾幽!==]时间伍譬曼E三三三三丑蕊曰譬．。：E=二=二二堋雠二一时问虑鼙!卜酬撕吣w㈣忡州w帅坤吣{-2时阃／s图3—10Chirp信号多径频偏时延波形图及SNR=OdB的接收信号波形图将接收信号的正弦信号部分进行高分辨的FFT，可得图3-11。I●01000200030(,0400050006900频率／Hz图3—11正弦信号的FFT高分辨图将图3-1l进行放大，可得图3-12。38 桀于分数阶傅立叶变换的水声信道多参数估计算法研究≮l：【[i}‘j一k．一～越渊5．溢随岫频率，№图3—12正弦信号的FFT高分辨局部放大图从图3—12中可直接读出三径频偏，如表3-3。表3—3Chirp基法频偏估计表由表3—3可以看出，在多径时延相差较小、多径频偏相差也较小时，多径频偏估计性能依然非常好。但是对于频偏接近的两个径估计性能有所下降，尤其是频偏接近的两径能量较弱的那一径，受影响大，可通过调高分辨率和增大信号时域长度来解决频偏接近情况下估计性能下降的问题。我们根据估计出来的多径频偏和先验信号依次重构多径Chirp信号，分别与接收信号进行解相关，可得图3—13、图3-14署I图3-15。建“’●山{融时域，点数图3—13直达波重构信号与接收信号解相关图¨"¨旺"o魁孽习蒜枨罂譬 基于分数阶傅专叶变换的水声信道多参数估计算法研究●蚍凝剧础0100200300400500600700啪时域，点数图3-14海面波重构信号与接收信号解相关图●【毫{檄撼＆燃0100200300400500600700啪时域／点数图3—15海底波重构信号与接收信号解相关图取图3—13的第一个峰值与Z×石进行相减可得直达波延时，取图3—14的第二个峰值与图3—13的第一个峰值相减可得海面对直达的延时，取图3—15的第三个峰值与图3—14的第二个峰值进行相减可得海底对海面的延时。经过计算可得表3—4。表3—4Chirp基法时延估计表由表3-4可得，在多径频偏相差较小、且多径时延相差较小的情况下，多径时延估计非常精确。例3：发射信号同上，信道参数如下：三条途径；直达波延时1200点，海面反射后的幅值为1；海面反射波比直达波又延时1330点，海面反射后的幅值为0．7；海底反射波比海面反射波又延时1810点，海底反射后的幅值为O．5；信噪比为OdB；¨”¨"o魁馨兰簿水I甘譬¨舱"o魁馨薯箨水罂鐾 基于分数阶傅立叶变换的水声信道多参数估计算法研究直达波频偏为33．333Hz；海面反射波频偏为35．777Hz；海底反射波频偏为一33．373Hz。发射信号中的正弦信号部分经过水声信道时的三径频偏时延波形图以及SNR=OdB时的接收信号波形图如图3-16。蓉．}口嬲潮嬲匾三三]O0204O60．811．21．4时间愚时问，s釜曼E三三嬲黝翮姗圃二]时问，s5r二—一⋯——一————一墨!—蚺蝴螂嘲黼㈣嗍嘲黼{时问屉图3—16正弦信号多径频偏时延波形图及SNR=OdB的接收信号波形图接收的Chirp信号部分的三径以及SNR=OdB时的接收的Chirp信号如图3-17。图3—17Chirp信号多径频偏时延波形图及SNR=OdB的接收信号波形图将接收信号的正弦信号部分进行高分辨的FFT，可得图3-18。一-～⋯一▲一一一●一一■●一一一．0100020003000400050006000频率／Hz图3—18正弦信号的FFT高分辨图4lOn趔馨越警螂譬一趟馨¨啦¨o魁罂丑舞．LkL 基于分数阶傅寺叶变换的水声信道多参数估计算法研究将图3—18放大，可得图3—19。nBO5型馨0．4弓j罂03u-n2n'由表3-5可以看出，在多径时延相差较大、多径频偏相差较小时，多径频偏估计性能虽然依然良好，但是对于频偏接近的两个径估计性能有所下降，尤其是频偏接近的两径中能量较弱的那一径受影响大，但是这个影响可通过调高分辨率和增大信号时域长度来解决。我们根据估计出来的多径频偏和先验信号依次重构多径Chirp信号，分别与接收信号进行解相关，可得图3—20、图3—2l和图3—22。图3-20直达波重构信号与接收信号的解相关图42 基于分数阶傅．、'￡叶变换的水声信道多参数估计算法研究图3-22海底波重构信号与接收信号的解相关图取图3—20的第一个峰值与Z×互进行相减可得直达波延时，取图3—2l的第二个峰值与图3-20的第一个峰值相减可得海面对直达的延时，取图3—22的第三个峰值与图3—2l的第二个峰值进行相减可得海底对海面的延时。经过计算可得表3—6。表3—6Chirp基法时延估计表由表3-6可得，在多径频偏相差较小、且多径时延相差较大的情况下，多径时延估计依然非常精确。43，¨”¨墼肇H{箨米毒譬 基于分数阶傅立叶变换的水声信道多参数估计算法研究3．5本章小结本章采用FRFT的Chirp基特性来估计水声信道多参数，避免了FRFT快速算法带来的计算误差，解决了水声信道的多径判断，多径频偏估计，以及多径时延估计。共举了三个仿真实例，分别仿真了三种不同的水声信道情况，依次是多径时延相差较小，多径频偏相差大、多径时延相差较小，多径频偏接近以及多径时延大，多径频偏接近的情况。当多径频偏较接近时，多径频偏估计性能仍然良好，但是对于频偏接近的两个径估计性能有所下降，尤其是两径中的能量较弱的那一径受影响大，但是这个影响可通过调高分辨率和增大信号的时域长度来解决。仿真结果表明，该算法能快速精确的估计出水声信道的多参数，估计精度高，信号处理算法简单，计算速度快，可以有效的处理实时水声信号。 基于分数阶傅立叶变换的水声信道多参数估汁算法研究4基于FRFT通信系统的数据包结构设计信道是通信系统必不可少的组成部分之一，也是系统数据包结构设计所必须考虑的关键问题。针对不同的信道特性，会有不同的设计方案。本章根据不同的信道，提出了两种基于FRFT通信系统的数据包结构，针对水况变化较快的信道，设计了第一种数据包结构，针对水况变化较慢的信道，设计了第二种数据包结构。4．1两种数据包的结构根据信道变化情况的不同，本章提出了两种基于FRFT通信系统的数据包结构，分另lJ如图4—1和图4—2。图4一l第一种数据包结构图第一种数据包结构适用于水况变化较快的信道，这种数据包采用Chirp信号作为同步头，脉宽为墨，采用正弦信号估计信道频偏，脉宽为正，数据采用BPSK，脉宽为五。为了防止信号干扰，Chirp信号和正弦信号间隔时间为△，1，正弦信号和BPSK间隔为△，，。这种数据包的优点是可以做到一包一估，数据传输可靠性更高，不足在于传输效率降低。图4—2第二种数据包结构图第二种数据包结构适用于水况变化缓慢的信道，这种数据包采用Chirp信号作为同步头，脉宽为正，数据采用BPSK，脉宽为正，每隔一定的时间发段正弦信号估计信道频偏，脉宽为兀。为了防止信号干扰，Chirp信号和BPSK间隔时间为△，。这种数据包的优点是传输效率高，不足在于不能一包一估，数据传输可靠性不如第一种数据包结构。4．2数据包处理算法流程将接收信号的正弦信号部分做高分辨的FFT，我们可以得出多径数，并精确的估计出多径频偏值。根据Chirp基分解特性，我们可以避免采用FRFT的快速算法来估计Chirp信号的多径时延，根据估计出来的多径频偏重构Chirp信号，将重45 基于分数阶傅立叶变换的水声信道多参数估计算法研究构信号依次与接收信号进行解相关运算，因为多径调频斜率的不同，我们可以根据这些峰值坐标精确的估计出多径时延。根据估计出的水声信道多参数，解调出BPSK真实数据。第一种数据包处理算法流程图如图4—3。接收信号lBPSKChirpSineC—l口求多径频偏口求多径时延占I解调BPSK图4—3第一种数据包处理算法流程图注：A为接收信号的Chirp信号部分：B为接收信号的正弦信号部分；C为BPSK数据；D为B经过高分辨FFT后所求得的多径数和多径频偏：E为根据D重构信号，依次与爿进行解相关运算，根据这些解相关的峰值坐标精确的估计出多径时延；最后，根据水下声信道的参数D和E解调出BPSK数据。综上，信道参数估计步骤如下：(1)对接收信号的正弦部分做高分辨的FF1I，得出多径数和频偏估计值。(2)利用多径数和相应的频偏估计值重构Chirp信号，根据Chirp信号的Chirp基分解特性，我们可以精确的估计出多径时延。(3)通过估计出的水声信道多参数，解调BPSK数据。4．3数据包处理仿真4．3．1第一种数据包仿真例1：设Chirp信号的中心频率为lkHz，带宽为800Hz，脉宽为0．Ols，采样频率为12kHz(1秒采样12000点)。正弦信号频率为lkHz，脉宽为0．6s。两个信号间隔时间为1s。信道参数如下：三条途径；直达波延时120点，海面反射后的幅值为1；海面反射波比直达波又延时160点，海面反射后的幅值为0．7；海底反射波比海面反射波又延时180点，海底反射后的幅值为0．5；信噪比为20dB；直达波频偏为3．777Hz；海面反射波频偏为10．777Hz；海底反射波频偏为一10．777Hz。图4-4为发射信号的波形图，由Chirp信号、正弦信号以及BPSK组成。46 基于分数阶傅立叶变换的水声信道多参数估汁算法研究25354时域地图4—4第一种数据包发射信号结构图信号发射经过水声信道后，产生了多径频偏和多径时延，为了便于分析，假定无噪声，则接收信号波形图如图4—5。00511．522．533．5●时域，s图4-5无噪声第一种数据包接收波形图我们将无噪声接收信号的Chirp信号和正弦信号进行局部放大，可得图4—6。覆102n30．40．50．60．7时域，s图4-6无噪声第一种数据包接收波形的局部放大图SNR=20dB的第一种数据包接收信号波形图如图4-7。47jiijjiii，iijii。H信萨．#薛n§h¨一ih订¨"jlhrli∥“钉．．r1。#“，¨j。ioj．。自d¨i"●；，i2侣，¨。：；J舢右趟馨 基于分数阶傅立叶变换的水声信道多参数估计算法研究丑㈣。。恻㈣j确i阿之5}——言r——寺——彳}——专——-j言——芎———苦—一时域／s图4-7SNR=20dB第一种数据包接收波形图图4-8为SNR=20dB的第一种数据包接收信号的局部放大图。o．’n2O．30．40．50．6n70．●时域，s图4-8SNR=20dB的第一种数据包接收波形局部放大图’．_实际上，我们发射的信号由三部分组成，第一部分Chirp信号部分，第二部分为正弦信号部分，第三部分为BPSK部分。接收信号的处理分三步，首先，取第二部分，将其做高分辨的FFT，求出多径数及多径频偏，其次，根据Chirp信号的先验知识和估计出的多径频偏重构Chirp信号，依次与第一部分做解相关运算，即可精确的估计出多径时延，最后根据估计出的频偏和时延，解调BPSK部分。4．3．2第二种数据包仿真例2：发射信号同上，发射信号由Chirp信号和BPSK构成，信道参数如下：三条途径；直达波延时120点，海面反射后的幅值为l；海面反射波比直达波又延时160点，海面反射后的幅值为0．7；海底反射波比海面反射波又延时180点，海底反射后的幅值为0．5；信噪比为20dB；直达波频偏为3．777Hz；海面反射波频偏为10．777Hz；海底反射波频偏为-10．777Hz。第二种发射信号的波形图如图4—9，由一个Chirp信号和BPSK构成。48“陋撼搿¨i．"“，pj⋯n飙。孵础洲㈣孙㈧擞一晰．锄种●●h"引j¨黔．”I．，：．一。=『iii¨P．ul+iii¨¨●●i．¨．畸ll卜n．．iii¨●jy叭㈨渤晦刚m㈨⋯Ⅵ¨¨Ⅲ叭”二二¨"“V．．二∽”jⅢmWl0胍耙j墓蛐一游群l●d¨Hi．¨j“㈣∥棚一哪州氇蝌∽蹦螭。啪嘲矧滞I㈨¨州¨¨州，，记一h。．：一撤¨i●●儿儿n¨¨蛐Ⅲ¨"1二=；i，引W懿¨¨Ⅱ断1：仙，¨o们一帕之越馨 基于分数阶傅立叶变换的水声信道多参数估计算法研究罗W翟⋯蜘蛳嫩：懈猁嬲：蜘黪蛔{㈤25图4—9第二种数据包发射信号波形图为便于分析，假定信道无噪声，则接收信号波形图如图4—10。-2．SL———————————L-————．————．i———————．．．．．L．．．．．．．．．．。J．．．．．．．．．．．JL．．．．．．．．．．．L．————．——_j00．5'1．522．533．5时域，s图4—10无噪声第二种数据包接收波形图我们将无噪声接收信号的Chirp信号部分进行局部放大，可得图4—11。图4一11无噪声第二种数据包接收波形局部放大图图4—12为仿真SNR=20dB的第二种数据包接收信号波形图，[羽4-13为SNR=20dB的第二种数据包接收信号的局部放大图。49]j√1_一黔，峨㈣㈣褂添卿妇。t■●■；}_．，jl●■■■l面郅班¨Ⅲm啪射H删幂二堋Hi舌蜊勘射玎硼孙酬州矧¨矾删¨¨丑"Ⅲ三二”P懿搿鳓m㈧壕Ⅲ到¨j1，¨叶●儿¨#ni■琴K．hH螬疆蚪U¨¨¨1，l●I．¨”妒r”¨KofⅫ域=：：¨鼬郴．；。啪凇Ⅲ泓q矿⋯Ii^．ji．程弘：p，i器；iiiii¨mq¨¨H钉：，”利i==懿甜i扎●，“J¨，●●H．订，}ip．"1P”卧．；¨j。I}●．●●●●●●l■■■■■^■●t}A；ilm⋯m峭⋯¨”扎Hn州㈧㈨酬川㈣Im刚豫孵％∽麟麟懈骶”2j，j0‘r14j{，nm^巡馨 基于分数阶傅立叶变换的水声信道多参数估计算法研究rll蝴盘．I羽弧揣测藩ir期{船|{{；_鬻煺姒譬‘俐弛峭铆吨潲潲，≥瀚擀惭渺图4—12SNR=20dB第二种数据包接收波形图图4—13SNR=20dB第二种数据包接收波形的局部放大图实际上，我们发射的信号由两部分组成，第一部分Chirp信号部分，第二部分为BPSK部分。接收信号的处理分三步，首先，每隔一定时间发射脉宽为0．6s的正弦信号，将其做高分辨的FFT，求出多径数及多径频偏，其次，根据Chirp信号的先验知识和估计出的多径频偏重构Chirp信号，依次与第一部分做解相关运算，即可精确的求出多径时延，最后根据估计出的频偏和时延，解调BPSK部分。因为第二种数据包是针对水况变化缓慢的情况而设计的，所以该数据包去除了正弦信号部分，提高了传输效率。4．4本章小结本章提出了两种数据包结构，第一种数据包结构适用于水况变化较快的信道，第二种数据包结构适用于水况变化缓慢的信道。第一种数据包优点是可以做到一包一估，数据传输可靠性更高，但传输效率降低。第二种数据包采用Chirp信号作为同步头，每隔一定的时间发段正弦信号估计信道频偏，优点是传输效率高，但不能一包一估，传输可靠性降低。两种数据包的信号处理都采用了FRFT的Chirp基法估计水下声信道多参数，避免了FRFT快速算法带来的误差。 基于分数阶傅立叶变换的水声信道多参数估汁算法研究5总结及展望本文采用FRFT研究了水声信道多参数的估计问题，共提出了四种新颖的估计算法。针对恒k信号模型，提出了三种基于FRFT的水声信道多参数估计算法，针对变k信号模型提出了一种基于FRFT的Chirp基特性的水声信道多参数估计算法。在变k信号模型的基础上，针对不同的水况又提出了两种基于FRFT通信系统的数据包结构设计。下面是本文的研究工作总结和结论：(1)FRFT估计法该算法的优点是可以准确的估计出多径数，并且时延估计比较准确，频偏估计也比较精确，不足在于只能估计多径频偏都相同的情况，并且需要预先精确估计出直达波的时延。(2)双Chirp信号估计法该算法的优点是能估计出多径数、多径频偏以及多径时延。不足是FRFT快速算法引入了计算误差，造成了频偏和时延估计误差较大，且计算量较大。(3)联合估计法该算法的优点是精确的估计出了多径数、多径频偏以及多径时延。不足是FRFT快速算法引入的计算误差，需要进行小范围搜索校正，信号处理算法复杂，计算量较大。(4)FRFT的Chirp基解法该算法的优点是精确的估计出了多径数、多径频偏以及多径时延。采用FRFT的Chirp基特性来估计水声信道多参数，避免了FRFT快速算法带来的计算误差，计算速度快，估计精度高，是一种可实时处理的算法。本文针对上面提出的四种算法做了大量仿真研究工作，仿真结果验证了上述的算法都是可行的。并针对不同的水况提出了两种基于FRFT通信系统的数据包结构设计。(1)第一种数据包结构，适用于水况变化较快的信道，优点是可以做到一包一估，数据传输可靠性更高，不足在于传输效率相对较低。(2)第二种数据包结构，适用于水况变化缓慢的信道，每隔一定的时间发射一定脉宽的正弦信号估计信道的多径频偏，优点是传输效率相对较高，不足在于数据传输可靠性不如第一种数据包结构。随着项目的进展，本文所提出的算法仍然要不断的完善和改进，主要体现在以下两个方面：理论方面：采用分数阶小波变换进行水声信道的多参数估计，以及提出新颖 基于分数阶傅立叶变换的水声信道多参数估计算法研究的水下探测信号。应用方面：进行大量的湖试和海试，通过实际测试来验证上述四种估计算法的有效性，推进理论算法的研究。52 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基于分数阶傅立叶变换的水声信道多参数衔计算法研究致谢本论文的研究工作是在导师黎明副教授的悉心指导下完成的，每一点成绩都与导师密不可分。黎老师洞察力敏锐、治学态度严谨、做事踏实、工作忘我，尤其是文笔凝练、隽秀、宛如行云流水，语词清新、奇异、光彩夺目。最让我心服的是黎老师的责任心、独到的思维方式、精益求精的态度、做事尽职尽责。在此衷心祝愿黎老师身体健康，工作顺利。首先，衷心感谢褚东升教授对我的科研思路指导以及对我成长、生活的关心，也衷心感谢王建国教授搭建水声组，给了我一个非常好的学习实践环境。两位导师在学术上严谨的治学精神，渊博的专业知识及高尚的道德情操令我终身难忘。衷心祝愿两位老师身体健康，一切如意。同时非常感谢张玲老师和刘兰军老师在我学习和论文写作中的热心帮助。其次，衷心感谢姜凯师兄、付东飞同学给我英语和专业上的指导，也非常感谢水声组的牛炯师兄、李可飞师兄、王有华同学、刘金龙师兄给我的帮助，还要感谢于飞伟师兄、马然师兄、刘明涛师兄等同学以及实验室的张益德师弟、梁欣师弟、时海勇师弟、范玉建师弟给予我的支持和帮助。最重要的是，衷心感谢我的父母亲人。你们亲切的叮咛、期盼的目光是我奋进中永远不竭的动力，我一定努力不辜负你们的期望。最后，非常感谢在百忙之中抽出宝贵时间对本论文进行评审的各位老师! 基于分数阶傅屯叶变换的水声信道多参数估计算法研究个人简历1981年3月28Et出生于黑龙江省鸡西市。1999年9月考入黑龙江科技学院本科自动化专业，2004年7月毕业并获得工学学士学位。2004年8月进入青岛海润自来水集团(青岛自来水公司)，职位为机关大楼中心调度员，也称一级调度员，2007年9月离职。2007年9月考入中国海洋大学工程学院控制理论与控制工程专业攻读硕士学位至今。发表的学术论文与研究成果【1】GYang,M．Li，L．Zhang，“Multi·ParameterEstimationofUnderwaterAcousticChannelBasedonFractionalFourierTransform”，IEEEWCSP2009．JEEE：11037849．El：20101012760648． Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedonFRFTOUCDISSERTATIONOceanUniversityofChinaEngineeringCollegeTsingtao，China Researchonmulti—parameterestimationalgorithmsofunderwateracousticchannelbasedonFRFTAbstractUnderwateracousticcommunicationhasbecometheresearchfocusowingtotheeconomicandmilitarysignificanceofocean．Theparametersofunderwateracousticchannelneedtobeestimatedinordertoensurethereliabilityandeffe：ctivenessofunderwateracousticcommunication．Thedata-aidedalgorithmsareadoptedinthisdissertation，andnowadaysexistingpreamblesinunderwatertelemetryarealmostexclusivelybasedonLFMsignals，alsoknownasChirpsignals．Therefore，itissignificanttoresearchthemulti—parameterestimationalgorithmsofunderwateracousticchannel．Thein．depthresearchinthisdissertationiSbasedonFI疆Talgorithms．WetreatChirpsignalsastheunderwaterdetectionsignal，andtheparametersofunderwateracousticchannelareestimatedaimingatthetwomodelsofreceivedChirpsignals(theconstant七modelandthevariablekmodel)andaccordingtotherelationofChirpsignalsandFRFT．Theworkofthisdissertationisasfollows．Firstly,threenovelalgorithmsforthemulti—parameterestimationofunderwateracousticchannelareproposedfortheconstantkmodelofChirpsignals．(1)TheFRFTbasedestimationalgorithm：TheadvantageisthatitCanestimatetheprecisemulti．．pathnumber,thedelaysandaccurateDopplershift．However,thisalgorithmisjustsuitabletothesituationwhereeachofthepathshasthesameDopplershiftandtheexactdelayestimationofdirectpathisknowninanticipation．(2)Thedouble．chirpsignalestimationalgorithm：Thestrengthisthatitcandirectlydeterminethemulti-pathnumber,theDopplershiftsandthedelaysregardlessoftheDopplershiftsbeingthesanle，similarorverydifferent．However,t11eshortcomingisthattheestimationerrorsofDopplershiftanddelayarequitelargeduetotheintroductionofthefastalgorithmofFRFTanditmakescomputationaloverload．(3)Thejointestimationalgorithm：ThevirtueiSthatitCandirectlyandaccuratelydeterminethemulti．pathnumberandthedelaysandDopplershiftsregardlessoftheDopplershiftsbeingthesame，similarorverydifferent．AnditCanalsodirectlyandaccuratelyestimatethemulti．parameterofunderwateracousticchannelnomatterhowshortorlongthedelaysofthereceivedsignalare．However,theshortcomingisthatthecalculationerrorsneedtobesearchedfinelyinsmallrange，whichresultsincomplex algorithmandcomputationaloverload．Secondly,forthevariablekmodeloftheChirpsignal，anovelmulti．parameterestimationforunderwateracousticchannelbasedontheChirp．basedcharacterofF盯Tisproposed，andthentwodesignsofpacketstructurebasedoncommunicationsystemofFRFTfordifferentwatersarealsogivenforthevariablekmodeloftheChirpsignal．(1)TheChirp-basedofFRFT：themeritisthatwecanaccuratelyandquicklyestimatetheparametersofunderwateracousticchannel．Theishighaccurateandsimple，aswellasthespeedofcalculationisveryfast．Whatisthemostimportantisthatitcailbeimplementedinreal．timeprocessing．However,theeStimationperformancewilldecreasewhentheDopplershiftsaleapproximate，andtheweakpathofthetwopathswithapproximateDopplershiftwillbeseverelyinfluenced，buttheproblemcanbesolvedbyhighresolutionandlongsinesignal．(2)Thestructuredesignofthefirstpacketsuitableforwatersoffastchange：Thestrongpointisthatitmakesthemulti-parameterestimationperpackagepossible，whichgreatlyincreasesthereliabilityofdatatransmission．However,itreducestransmissionefficiency．(3)Thestructuredesignofthesecondpacketsuitableforwatersofslowchange：Thestrengthisthatithashighertransmissionefficiency．However,itgreatlyreducesthereliability．Finally,alotofsimulationexamplesestimationalgorithms．Andthesimulationprocessed．Keywords：UnderwaterAcousticChirp—basedCharacteristicaregiventoverifytheeffectivenessoftheshowsextensivelyhowthetwopacketsareChannel，DopplerShift，Delay,FRFT, CONTENTS1．Introduction．⋯⋯⋯．．．⋯⋯⋯⋯⋯⋯．⋯．⋯⋯．⋯⋯⋯⋯⋯⋯．．⋯⋯．⋯．．⋯．⋯．⋯．．．⋯．⋯．⋯．⋯．⋯11．1Thesourceofresearchtopic．⋯．⋯⋯⋯⋯⋯．⋯⋯⋯⋯．⋯⋯．．⋯．⋯．⋯⋯．．⋯⋯．⋯．⋯⋯．11．2Researchbackgroundandsignificance．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．⋯11．3Thecharacteristicsofunderwateracousticchannelanddescriptionoftheproblem⋯⋯⋯⋯⋯⋯⋯⋯．⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯21．4Statusquoanddevelopmenttrendofresearchathomeandabroad．⋯⋯．⋯⋯．．41．5Theworkofthisdissertation⋯⋯．⋯⋯⋯⋯⋯．⋯⋯⋯．⋯⋯．．⋯．⋯⋯．⋯．⋯．．⋯⋯⋯⋯．．62．Threemulti．parameterestimationalgorithmsofunderwateracousticchannelbasedonFRFT⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯72．1Themodelofunderwateracousticchannel⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．72．2TheconstantkmodelofChirpsignal⋯⋯．⋯⋯⋯⋯⋯．．⋯⋯⋯⋯．⋯．⋯⋯⋯．．⋯⋯．82．3Rationale．⋯⋯．⋯．．．．⋯⋯⋯⋯⋯．⋯⋯．⋯⋯．⋯⋯⋯⋯．⋯⋯⋯⋯⋯⋯⋯⋯．⋯．．⋯．⋯．⋯．⋯⋯82．：；．1FRFTdefinition⋯．⋯⋯⋯．⋯⋯⋯⋯⋯．⋯⋯⋯⋯．⋯．．⋯⋯⋯．⋯．⋯．⋯⋯⋯⋯⋯．82．3．2Theanalysisformulti．parameterestimationofunderwateracousticchannelbasedonFRFT⋯．⋯．⋯．⋯⋯⋯．．⋯．⋯⋯．⋯⋯⋯⋯⋯．．⋯．．⋯⋯⋯⋯．92．4Threekindsofestimationalgorithms⋯．⋯⋯⋯⋯．⋯⋯⋯．．⋯．⋯．⋯．．．⋯．．．⋯．．．⋯⋯．．92．4．1TheFRFT-basedestimationalgorithm⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯102．4．2Thedouble-chirpsignalestimationalgorithm⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．132．4．3Theiointestimationalgorithm⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．192．5Chaptersummary⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．⋯⋯⋯⋯⋯⋯⋯⋯333．Amulti-parameterestimationalgorithmofunderwateracousticchannelbasedontheChirp．basedcharacteristicofFRFT⋯⋯⋯⋯⋯⋯⋯⋯⋯．．34：；．1ThevariablekmodelofChirpsignal．⋯．⋯⋯⋯．⋯⋯⋯．．⋯⋯．⋯⋯．⋯．．⋯．⋯⋯．．343．2Rationale⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．⋯⋯⋯．353．3nlestructureandthesignalprocessingalgorithmoftestsignal⋯⋯⋯⋯⋯⋯．353．3．1Thestructureoftestsignal⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．353．3．2111esignalprocessingalgorithmoftestsignal⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯363．4Numericalsimulation．⋯⋯．⋯⋯⋯⋯⋯⋯⋯⋯⋯．⋯⋯．⋯⋯．⋯⋯⋯．⋯⋯．．．⋯⋯⋯．．⋯．．36：；．5Chaptersummary⋯⋯⋯⋯⋯⋯⋯．⋯⋯．⋯⋯⋯．⋯⋯．⋯⋯⋯．⋯⋯⋯⋯．⋯．．．⋯．⋯．．⋯．⋯474．ThepacketstructuredesignbasedonFI强Tunderwateracousticcommunicationsystem⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．z184．1Twokindsofpacketstructure⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯484．2Theflowofthefirstpacketprocessingalgorithm⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．494．3Thesimulationofpacketsignalprocessingalgorithm⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．504．3．1Thesimulationoffirstpacket⋯⋯．⋯⋯．⋯．⋯⋯．⋯⋯⋯⋯．⋯．⋯．⋯⋯．．⋯．．504．3．2Thesimulationofsecondpacket⋯⋯⋯．⋯⋯⋯⋯⋯⋯．⋯⋯．．．⋯．⋯．．⋯．⋯524．4Chaptersummary⋯．⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯55I 5．Conclusionandfutureresearch⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯一56References⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．58 Researchonthemulti·parameterestimationalgorithmofunderwateracousticchannelbasedonFIUT1Introduction1．1ThesourceofresearchtopicInthisdissertation，thefractionalFouriertransform(FRFT)isappliedtoanalyzingthereceivedsignalforestimatingthemulti-parameterofunderwateracousticchannel，thatis，forestimatingthemulti—pathnumber,thedelaysandtheDopplershiftsofunderwateracousticchannel．Thisdissertationcomesfromtwonationalresearchprograms．(1)Thenationalhi．ghtechnologyresearchanddevelopmentprogram(863)Theresearchonthekeytechnologyoftheremoteanddeepmarineenvironmentmonitoringbasedonthesensornetworks．No．2006AA09Z15(2006．12—2009．7)(2)ThenationalnaturalsciencefoundationTheresearchonthefuzzycontrolalgorithmsoftheunderwateracousticsensornetworkscontrolsystem．No．60704023(2008．1-2010．12)Theoverallgoalofthetwonationalresearchprogramsis：weshouldproposetheoverallsolutiontotheremoteanddeepmarineenvironmentmonitoringbasedontheunderwateracousticsensornetworks(UW-ASNs)，andweshouldsolvethekeyproblemsofthehardwaredesign(architecture)ofthenodes，thephysicalaccesstechnologyofunderwateracousticcommunication，themulti—parameterestimationalgorithmsofunderwateracousticchannel，thefuzzycontrolalgorithms，communicationprotocolandenergymanagement，etc．SOthatweachievethereliablereal-timeacquisition，processing，transmissionandanalysisoftheoceandata．Theworkofthisdissertationistoresearchthemulti—parameterestimationalgorithmsofunderwateracousticchannelwithinthesetwOnationalresearchprograms．1．2backgroundandsignificanceWitllglobalincreasedinterestintheexplorationoftheocean，underwateracousticcommunicationwillbewidelyappliedinoceanographicdatacollection，pollutionmonitoring，offshoreexploration，disasterprevention，assistednavigation，tacticalsurveillance，naturalseabedresourceexploration，marinearcheology,maritimesearchandrescue，etc．．Theaccuratemulti-parameterestimationofunderwateracousticchannelisprerequisitetoefficientandreliablecommunicationtransmission⋯21．Therefore．theaccuratemulti．parameterestimationofunderwater1 acousticchannelisverysignificantforpracticalapplication．Wecannotdirectlytoapplytheoriesandtechnologiesofspacewirelesschanneltounderwaterchannelalthoughtheoriesofspacewirelesschannelandrelatedtechnologieshavealreadybeenmature，becauseunderwaterchannelandspacewirelesschannelareenormouslydifferent．Therefore，wemusttakeintoaccounttheconcreteconditionsofunderwaterchannelwhenwestudythedesignofunderwatercommunicationequipment．Furthermore，weshoulddevelopanddesignrelatedtheoriesandtechnologieswhicharewhollyapplicabletounderwatercommunication【3】【4】．ThecomparisonbetweenunderwaterchannelandspacewirelesschannelisshowninTab．1．1．Tab．1．1ThecomparisonbetweenunderwaterchannelandspacewirelesschannelparameterSpacewirelesschannelShallowwaterchannelCarrierfrequency824MHz～894MHz5kHz～50kHzChannelbandwidthTransmissionratePropagationdelayRelativevelocityDopplershiftDopplershifdCarrierfrequency1．25MHz1200bps～9600bps10岬100km／h92．6Hz9．26x10-610kHz1kbps500ms～1000ms10km／h20Hz2x10-3Thenumberofcarriersofasymbol90k～900k5～50AspresentedintheTab．1—1．underwaterchannelhavethecharacteristicsoflowcarrierfrequency,narrowchannelbandwidth，seriouspropagationdelay,high—impactDopplershiftandlOWtransmissionrate，etc．incomparisonwithspacewirelesschannel．Sothemulti．parameterestimationalgorithmsofspacewirelesschannelareinvalidforsolvingthemulti—parameterestimationofunderwaterchannel．Therefore，wehavetoproposemulti—parameterestimationalgorithmsthatarewhollyapplicabletounderwaterchannelinordertoguaranteee硒cientandreliabletransmissionofunderwatercommunicationt3j141．1．3ThecharacteristicsofunderwaterchanneIanddescriptionoftheproblemThechannelisactuallyaphysicalmediumanditisusedtotransmitthesignalfromlaunchingdevicetothereceivingequipment．ThechannelCanbeafreespaceinthewirelesschannelwhileitCanbeopenwire，cableandfiberinthewiredchannel．2 Researchonthemulti·parameterestimationalgorithmofunderwateracousticchannelbasedonFRFTBoththewirelesschannelandthewiredchannelhaveavarietyofphysicalmedia．Thechannelnotonlygeneratespathwayforthesignal，butalsoitcausesavarietyofinterferenceandnoiseforthesignal．Theinherentchannelcharacteristicsandtheinterferencesfromthechannelhavedirectlyeffectonthecommunicationquality【51．Wewillsummarizethecarrierandthecharacteristicsofunderwateracousticchannelinthefollowingcontentsincethemulti-parameterestimationalgorithmsofunderwateracousticchannelarethemaintopicinthisdissertation．Thepropagationperformanceoftheacousticwaveisthebestamongavarietyofformsoftheenergyradiationinunderwateracousticcommunication．Thepropagationvelocityoftheacousticwaveisabout1500m／sinwater,anditspropagationvelocityisabout340m／sintheair．Inseawater,theattenuationoftheelectromagneticandthelightwaveareverylargeandtheirpropagationdistanceisshort，SOthetwokindsofwavearefarfrommeetinghumanneeds．Thus，forthetimebeing，theacousticwaveistheonlyeffectiveradiantenergyinapplicationsofoffshoreexploration，disasterprevention，assistednavigation，etc[6]171．Theunderwateracousticchannelischaracterizedbytime-variant，space—variant，time—delayandDoppler-shift．Besides，underwateracousticcommunicationisalsoinfluencedbythepathloss，noiseandotherfactors[8q3]．Sosignalswillbedistortedduetothespace—timevarying，multi·pathandDopplershiftoftheunderwateracousticchannel，whichresultsinfuzzyofdetectionandinter-symbolinterferencewhenthesignaltraversingunderwateracousticchannel．Therefore，itisnecessarytoestimatetheparametersofunderwateracousticchanneltoimprovethedetectionperformanceandimplementchannelequalization．Wewilldescribetheproblemtobesolvedaccordingtothesystemmodelofunderwateracousticcommunicationandthebasicroadmapoftheshallowwateracousticfield．Thegoalofunderwateracousticcommunicationistransmissionofinformation．Thefunctionofunderwateracousticcommunicationsystemistosendinformationfromsourcetosink．Forexample，wetransformtheinformationintoacousticsignal，andthensendtheacousticsignaltochannelthroughthelaunchingdevice，atthesametimeweusereceivingequipmentprocessthereceivedsignalandconvertthemtotheoriginalinformationI5。．ThisprocessCanbedepictedbythesystemmodelofunderwateracousticdigitalcommunication，asisshowninFig．1-1．AspresentedintheFig．1—1，wecanclearlygetthattheworkofthisdissertationistheresearchonthemulti-parameterestimationalgorithmsofunderwateracousticchannel．3 ResearchOnthemulti·parameterestimationalgorithmofunderwatera—cous—ticchann—el—basedonF堡卫s。urceH5：：：：8H嘶rYPtHc絮1溅OUF。C。CHDecrYPtH嬲裂De-Iulat萎a习nnelwM。y咄工JoppIerlwnrk}DeIaylFig．1—1ThesystemmodelofunderwateracousticdigitalcommunicationThebasicroadmapoftheshallowwateracousticfieldisshowninFig．1-2．SourFig．1-2ThebasicroadmapoftheshallowwateracousticfieldAsshownintheFig．1—2．wecanseethattherearethreepathsfromsourcetosink．Theacousticray1isthedirectpath，theacousticray2istheseasurface，andtheacousticray3isthebottomreflection．ThedelayproblemtobesolvedinthisdissertationiSthetimeintervalbetweentheacousticray1andthestartpoint．thetimeintervalbetweentheacousticray1andtheacousticray2aswellasthetimeintervalbetweentheacousticray2andtheacousticray3．TheDopplershiftproblemtobesolvedistheDopplershiftoftheacousticray1，theDopplershiftoftheacousticray2andtheDopplershiftoftheacousticray3．。’。1．4StatusquoanddevelopmenttrendofresearchathomeandabroadAtpresent，anumberofalgorithmshavealreadybeendevelopedwithregardtothemulti—parameterestimationproblemofunderwateracousticchannel．Generallyspeaking，channelestimationalgorithmscallbedividedintoblindestimationalgorithmsanddata-aidedalgorithms．Withusingsecond．orderorhigher-orderstatistics，theblindestimationalgorithmsmainlytakeadvantageofcyclicprefix114】，virtualsub．carriers【15】andotherpriorinformationtoestimatechannelparameters．So也ealgorithmshaveverylargecomputationalcomplexity,lowefficientaswellasquiteslowconvergencerate．Bycomparison，themathematicaltheoriesofthedata—aidedalgorithmsarerelativelymatureandsimple，andthiskindofalgorithmsiSalsopractical．4 Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedOilFRFTIndata—aidedalgorithms，thepilotandtrainingsequencearemainlyusedtocarryoutchannelestimationintheimplementationcriteria，suchasLeastSquarecriteria(LS)，MinimumMeanSquareErrorcriteria(MMSE)B611171，MaximumLikehoodEstimatorcriteria(MLE)[18]119]，etc．．TheparametersofthechannelcanbeestimatedbytheMLEalgorithmwithoutknowingthesignal-to·noiseratio(SNR)andthestatisticalpropertyofthechannelbecausehisassumedtobeadeterministicbutunknownvector．Thisdissertationisbasedonthedata-aidedalgorithms，andexistingpreamblesinunderwatertelemetryarealmostexclusivelybasedonLFMsignals，alsoknownasChirpsignals120][211，thus，itissignificanttoresearchthedetectionandmulti—parameterestimationalgorithmsofunderwateracousticchannel．Forthetimebeing，therearethreecommonlyusedalgorithmsovertheparameterestimationofLFMsignals．(1)TimefrequencydistributionalgorithmsbasedontheCohenclass【221．TheadvantageoftheCohenclassisthatsuchalgorithmshavegoodtime-frequencyaggregationtothesingle-componentsignal．Thus，itiseffectiveonsignaldetectionandparameterestimation．Butitsshortcomingisseriouscrosstermsforthemulti-componentsignals．Althoughtheimprovementofnuclearfunctionhasbeenproposedtorestraincross—terms，thecostisthelossofauto—terms．(2)TheRWTalgorithms【261andtheRATalgorithms[271．ThemainideasofRadon·-Wignertransform(RWT)algorithmsandRadon··Ambiguitytransforrn(RAT)algorithmsaretotransformdetectionproblemintopeaksearch．TheiradvantageisthatRWTalgorithmandRATalgorithmareapplicabletothedetectionofmulti—componentsignals．Buttheirshortcomingisthatitisnecessarytocarryoutone-dimensionalortwo—dimensionalpeaksearch，whichhasgreatlyincreasedthecomputationalcomplexity．(3)TheFractionalFourierTransform(FRFT)algorithms【28】．TheadvantageofsuchalgorithmsisthatFRFTofLFMsignalshasastrongaggregationofenergywithoutcross—termsinterference，anditisespeciallyapplicabletothedetectionandparameterestimationofmulti—componentsignalsforlowsignal-to-noiseratio(SNR)cases．However,thecurrentapproachbasedontheFRFTneedatransformationforthetreatedsignalineachfractionaldomaininordertoscanthemaximumpeak．Apparently,therepeatedcomputationhasgreatlyincreasedthecomputationalcomplexity．Althoughliterature[29]hasimprovedtheFI强Talgorithmbyusingthepriorknowledgeofthesendingsignal，whicheffectivelydecreasesthecomputationalcomplexity,itsuffersfromthestructurecomplexitysinceittakesoneFI强T，andthenonefractionalfrequencydomaincorrelation．Moreover,itCannotprocessmulti—pathsignalsofthesimilarDopplershiftandlacksdelayestimation．5 Research011themulti·parameterestimationalgorithmofunderwateracousticchannelbasedonFR丌Thein—depthresearchinthisdissertationisbasedonthe(3)．WetreatChirpsignalsastheunderwaterdetectionsignals，andwecarryoutthemulti·parameterestimationofunderwateracousticchannelaccordingtothecharacteristicsofFRFT．1．5TheworkofthisdissertationBasedonFRFT,fournovelalgorithmsforthemulti-parameterestimationproblemofunderwateracousticchannelareproposedinthisdissertation．TwonoveldesignsofpacketstructurebasedonFIUTcommunicationsystemareproposedfordifferentchannel．ThisdissertationiSdividedintofivechapters．Inthefirstchapter,webrieflyintroducethesourceofresearchtopic．theproblemtobesolvedaswellasbackgroundandsignificance．Inthesecondchapter,threenovelmulti—parameterestimationalgorithmsofunderwateracousticchannelareproposed—theFI江T．basedestimationalgorithm，thedouble·chirpsignalestimationalgorithmandthejointestimationalgorithmfortheconstantkmodeloftheChirpsignal，andthenanalysisandcomparisonofthethreealgorithmsarecarriedout．Inthetllirdchapter,anovelmulti．parameterestimationalgorithmofunderwateracousticchannelbasedontheChirp．basedcharacteristicofFRFTiSproposedforthevariablekmodeloftheChirpsignal。andthenanalysisandsimulationaredoneforthisalgorithm．Inthefourthchapter,thetwonoveldesignsofpacketstructurebasedonFRFTcommunicationsystemareproposedfordifferentchannel．Infifnlchapter,wesummarizethefulldissertationandpredictedfutureresearchwork．6 Researchonthemulti·parameterestimationalgorithmofunderwateracousticchannelbasedOnFRFT2Threemulti—parameterestimationalgorithmsofunderwateracousticchannelbasedonFRFTThischapterbrieflyintroducesthemodelofunderwateracousticchannelandtheconstantkmodeloftheChirpsignal．ThentheFI强TdefinitionisintroducedandtheChirpsignalisanalyzedthroughusingFRFT．Finally,weproposedthreenovelalgorithmsforthemulti—parameterestimationofunderwateracousticchannelandsummarizetheprocessingeffectandapplicationrangeofthem．2．1ThemodelofunderwateracousticchanneIUnderwateracousticchannelcanbeseenasaslowtimevaryingcoherentmulti—pathchannel．Theacousticsignalsfromthesourcearriveatthesinkalongthedifferentacousticrays．Assumethatthedispersionphenomenonandtheabsorptionofthemediumareignored．Hereweconsiderthedirectpathasthecriterion．ThentheimpulseresponsefunctionwillbeⅣ一1M=Aod(t)+∑&d(t-ri)i=1(2一1)From(2-1)，assumethatx(f)isthesendingsignal，刀(，)isthenoise，and4(浮0⋯．，N-1)istheamplitude．Thenwegetthecorrespondingreceivedsignal．Ⅳ一l％(f)=以x(，)+∑4x(t-r，)+n(t)i=1(2—2)Assumethatthedirectpathhasdelay,andmulti—pathsignalshavethesameDopplershift．Thenthereceivedsignalwillbe11o】【111Ⅳ一lr(f)=4x(f一丁o)P72艚0‘卜f0’+∑4x(t-r,)e72啦‘卜‘’+，2(f)(2-3)f=lTheparametersinterpretationofformula(2-1)，(2-2)and(2-3)isshowninTab．2-1．(f=1，．．．，N一1)7 Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedonFRFTTab．2-1Channelparametertheeigen·raynumbertheamplitudeofdirectpaththeamplitudeoftheithpaththedelayofdirectpaththedelayoftheithpaththeDopplershiftofdirectpaththeDopplershiftoftheithpathwhiteGaussiannoise2．2TheconstantkmodeloftheChirpsignalTheinstantaneousfrequencyoftheChirpsignalchangesovertime，anditisatypicalnon-stationarysignal．Assumethat彳istheinitialfrequencyofchirpsignal，厶istheterminationfrequencyofchirpsignal，互isthelengthoftimedomain，and彳ist11eamplitudeofchirpsigllal．111ereiIlt。，七(七=百L-f,)isthechirprate．ThenthechirpsignalJ(f)Canbegivenas[301m，=Asin㈦z+纠(2—4)FortheconstantkmodelofChirpsignal，weassumethat￡iistheDopplershiftoftheithpath，0isthedelayoftheithpath，4istheamplitudeoftheithpath，foisthecenterfrequencyofChirpsignal，andNistheeigen-raynumber,thatis，themulti-pathnumber(f=0，．．．，N-1)．Thenthereceivedsignalcanbegivenas【29】2．3Rationale2．3．1FRFTdefinitionsin[2万×((石+乞)×c，一_，+兰×c，一‘，2)]c2-5，ThePth．orderFRFToff(u9isdefinedas1311‘32】8、JA靠订岛所∥4M∑瑚=、，OS 厶(“)=∽Is(“’)脚)=IIlleKp(删3f(甜t)砌’l场ere／@-)／(一“f)f，讷I口三三一IL2／e唧(／华cot口一釜肌拶口⋯口=2nn"(2—6)口=(2刀±1)万2．3．2TheanalysisforMulti—parameterestimationofunderwateracousticchannelbasedOnFRFTEmployingFRFTupon(2·3)，weget尺p(“)=4x．p@一Fosina—r0cosa)xexp(jztr02sinacosa—j2x(u—eosina)rosina)xexp(一jXe02sinacosa—j2xusoCOSg)JⅣ一l+∑4xp(z，一e',sina—TiCOSa')i=1xexp(ffcr,2sinacosa-j27r(u—tsina)r．isina)xexp(一j，rc,2sinacosa-j27ru6,cosa)+Np(甜)(2—7)Eq．(2—7)showsthatthemodulevalueofthereceivedsignalforFRFTwillfo咖aseriesofpeaksinthecorresponding材domainwhenwetakethe”best”orderp·Apparently,thedirectpathshifts岛sin口+‰cos口，andmulti。pathsignalsshiR蜀sina+rtcos口(汪O，．．．，N-1)1121．2．4ThreenovelchannelestimationalgorithmsThrou曲thepreviousanalysis，wecanseethatitisfeasibletoestimatethemulti．parameterofunderwateracousticchannelbyusingFRFT．NowthethreenoVelalgorithIllsoftheFRFT-basedestimationalgorithm，thedouble。chirpsignalestimationalgorithmandthejointestimationalgorithmareproposedtoestimatetheparametersofunderwateracousticchannelfortheconstantkmodelofChirpsigllal·9 Researchonthemulti—parameterestimationalgorithmofunderwateracousticchannelbasedonFRFT2．4．1TheFRFT-basedestimationalgorithmWelaunchaChirpsignal．Letthepulsewidthbe石，thechirpratebek，thecenterfrequencybef0，thebandwidthbeB．TheDopplershiftanddelaywillbemadewhensignaltraversesunderwateracousticchannel．AssumethateachofthepathshasthesameDopplershift，andthenwecanestimateeachDopplershiftanddelaythroughthereceivedsignal．LetthetimelengthbeAt，theDopplershiftbe占，weget[331lg尼=一At(2·8)ThetransformoutputswillbeaseriesofpeaksatthePth-orderinthecorresponding／,／domainifwecarryoutFRFTforthereceivedsignal．Assumethateachcenter行equencyofthemulti·pathsignalsshifts％．Letthepeakcoordinateoftheithpathbe4(i=0，⋯，N一1)．From(2—7)，thedelayformulaoftheadjacentpathswillbe‰印端(2-9)Atthebeginningpointofthereceivedsignal，wereconstructChirpsignal，thenwecarryoutFRFTforthereconstructedsignal，letthecoordinateofthehighestpeakbesta__peak．ThentheDopplershiftwillbe。一(哦占0一——·sta_peak)sin(a)TheflowchartoftheFRFT-basedestimationalgorithmisshowninFig．2—1．Receiredsignalr刑糯FM匝讳而仁f—季—r面■judgementIIestlmatlonDopplereStlmatlOnFig．2·1TheflowchartoftheFRFT-basedestimationalgorithm(2·10)Remark：AiscarryingoutFl婶Tforreceivedsignal；Bistakingouteachpeakcoordinatein材domain；Cisgettingthemulti—pathnumberthroughthepeaknumber；finally,wegetthedelaysthroughtheintervalofeachpeakcoordinate，atthesametimewegettheDopplershiftthroughthevariationofpeakcoordinateintervalbetweenthedirectpathandthesta__peak．TheproposedFRFT-basedestimationalgorithmincludesthefollowingsteps(1)Getthemulti-pathnumberaccordingtothepeaknumberfortheFIUTofreceivedsignal． 。、Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbased011FRFr(2)Wegetthedelayofmulti—pathsignalst+l一‘(i=O，⋯，N-1)from(2—9)．(3)WegettheDopplershift‰from(2一l0)．Wewillverifytheeffectivenessofthisalgorithminthefollowingsimulation．Example1．WelaunchaChirpsignal．Letthepulsewidthbe0．4s．andchirpratebe10kHz／s．Letthecenterfrequencybe3kHz．bandwidthbe4kHzandsampleratebe40kHz(sampling40000pointspersecond)．Letchannelparametersbeasfollows：therearethreepaths．Thedelayofdirectpathis0point．andtheamplitudeis1．Thedelayofseasurface．directpathiS120points．andtheamplitudeiS0．7．Thedelayofbottomreflection．seasurfaceis160points，andtheamplitudeis0．5．SNRis0dB．EachDopplershmofthethreepathsiS17．6Hz．Thenthethree—pathdiagramsofdirectpath．seasurfaceandbottomreflectionwithnonoiseareshowninFig．2．2．粤1星。△善．，罟’星。A岳．，∞O5D3岂0△写n502025030350．4n幅time／s00．05010．15020．为0．30．350．4n．5time／s020250303504n●5time／sFig．2-2Thethree-pathofsendingsignal仃avemingchannelThetwodiagramsofreceivedsignalwithnonoiseandSNR=0dBareshowninFig．2—3．o刁兰Q￡毋5∞口3岂O4E∞懈瓣黼黼On∞0．tn'50．20葛0．3n葛0．4o．蝤time／sFig．2-3ThetworeceivedsignalswithnonoiseandSNR=0dBInthecaseofSNR=0dB，wecarryoutFRFTforthereceivedsignal，andthe“domainfigureisshowninFig．2—4．ThebluepaneistheUdomainfigureofstandardreconstructedsignalforFRFT，andtheredStaristhe甜domainfigureofreceivedll Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedonFRFTsignalforFRFT．o℃皇△E∞Udomain／pointnumberFig．2-4The”domainofreceivedsignalwithSNR=0dBWegetFig．2—5throughthezoomofFig．2-4，forthetimebeing，wecanapparentlyseethattherearethreeredstarsandabluepane．ThepeakcoordinateofbluepaneiSthecoordinateof甜domainofstandardChirpsignal．ThepeakcoordinatesofthreeredstarsarethecoordinatesofUdomainofreceivedsignal，thatiS，thecoordinatesof材domainofdirectpath．seasurfaceandbottomreflection．Udomain／pointnumberFig．2-5Thezoomof"domainofreceivedsignalwithSNR=OdBFromFig．2-5，weCanconfirmthattherearethreepaths．From(2—9)，wegetThedelayestimationofthedirectpath-seasurfacewillbe‘一T02121．0518≈121points．Thedelayestimationoftheseasurface—thebottomreflectionwillbe吃一12158．2985≈158points．From(2—10)，eachDopplershiftestimationfromthethreepathswillbe岛217．6018Hz．Theerrorrateofchannelestimationwillbe12 Researchonthemulti—parameterestimationalgorithmofunderwateracousticchannelbasedOilFRFrTheerrorrateofdelayestimationofdirectpath—seasurfacewillbe王二鱼二!兰Q：o．833％．120Theerrorrateofdelayestimationofseasurface·bottomreflectionwillbe垒二王二!鱼Q：1．25％．160TheerrorrateofDopplershiftestimationwillbe—E'0-—17．6：O．01023％．1’7．6ThestatisticaldataiSillustratedinTab．2_2．Tab．2．2TheparameterestimationcomparisonoftheFRFT-basedestimationalgorithmThroughthepreviousanalysis，wecanseethatthestrengthofthisalgorithmisthatitCanestimatethemulti．pathnumber,thedelaysandaccurateDopplershift．However,thisalgorithmiSiuStsuitabletothesituationwhereexactdelayestimationofdirectpathiSknowninanticipationaswellaseachofthethreepathshasthesameDopplershift．Thus，thedouble—chirpsignalestimationalgorithmisproposedinordertomakeupforthelackoftheFRFT-basedestimationalgorithmandsolvethedifferentDopplershiftproblemofmulti-pathsignals．2．4．2Thedouble—chirpsignalestimationalgorithmWesendadouble—chirpsignal，whichismadeupofChirplandChirp2谢tllafixedtimeintervalT．Bothpulsewidthsare互．Bothchirpratesalek．BothbandwidthsaleB．ThecenterfrequencyofChirplisf01andthecenterfrequencyofChirp2is厶(fot≠f02)．Signaldistortionwillbemadewhensignaltraversesunderwateracousticchannel，thusthe材domainintervalofChirplandChirp2isvaried．ThisintervalvariantofeachpathismadebytheassociatedDopplershift．Throughthevariants，wemaygetDopplershifts，andthengetdelaysofmulti—pathsignalsthroughtheestimatedDopplershifts．ThestructureofthesendingsignalisdepictedinFig．2—6．13 Center，frequency^lChirp。rate0卜：u眦ls：7：一Chirpl，frequency，”Chirp，rate‘一躲uls：7：一intne”r。va]7-————_一。Ehirp2Fig．2-6ThestructureofsendingsignalAssumethatthecenterfrequencyofChirpl石lshifts岛l，andthecenterfrequencyofChirp2L2shiftsS02．LetthecenterfrequencyofChirpsignalbef0，thentheDopplershiftofthecenterfrequencyofChirpsignalwillbeSO．Lettheobjectmovementratebey．Letthecarrierratebec．ThenweCangettheformula[341兰：皂．Thereforewecani疵rcjb鱼：鱼五。石：(2—11)LetbothChirplandChirp2havenoDopplershift．IfwecarryoutFRFTforthereceivedsignal，thetransformoutputswillbeasedesofpeaksatthePth．order．From(2-7)and(2—8)，wehavethe“domainintervalbetweenthehighestpeakofChirplandthatofChirp2觚=[丁+掣]l×cos(a)j(2-12)IfeachDopplershiftofChirp1isdifferent，theneachDopplershiftofChirp2hasaccordinglyvariedfrom(2—11)．HerewecarryoutFⅪ’Tforthereceivedsignal．LettheUdomainintervaloft11eftllpathbetweenChirplandChirp2beAu2i，t11ecenterDopplershiftoftheithpathofChirplbeS01．j(i=0，．．．，N—1)．From(2．7)，(2-8)and(2—9)，aswellasthe甜domaindiagramforFRFTofreceivedsignal，thengeteachcorrespondingpeakintervaloftheUdomainofChirplandChirp2willbeFrom(2—13)，weget毗，咄‰×(1一务×掣‰2巧Au2,i--AUl×南(2—13)(2—14)LetthepeakcoordinateofChirplbeZ(i=o，⋯，N-1)．From(2-7)and(2—8)，the Researchonthemulti·parameterestimationalgorithmofunderwateracousticchannelbasedonFRFTdelayformulaoftheadjacentpathsofChirpliswheref=0，⋯，N一1．‰一蚜COS+半≯la)庀(2·15)Theflowchartofthedouble—chirpsignalestimationalgorithmisshowninFig．2-7．Fig．2-7Theflowchartofthedouble-chirpsignalestimationalgorithmRemark：AiscarryingoutFRFTforreceivedsignal；Bistakingouteachpeakcoordinateofthe甜domain；Cisgettingthe讼domainintervalbetweenthehighestpeakofChirplandthatofChirp2withoutDopplershift；DisacquiringeachcorrespondingpeakintervalbetweenChirplandChirp2inthe“domain；EisgeeingtheDopplershiftestimationofeachpath；finally,wegetthedelayestimationofmulti·pathsignals．砀eproposeddouble—chirpsignalestimationalgorithmincludesthefollowingsteps(1)Calculate△％from(2-12)，whichistheintervalbetweenthepeakofChirp1andthatofChirp2withoutDopplershiftinthe甜domain．(2)Calculate△屹Jfrom(2—13)，whichisthecorrespondingpeakintervalbetweenChirpland’Chirp2、ⅣitllDopplershiftinthe甜domain．(f=0，⋯，N一1)(3)Calculate岛lJfrom(2—14)，whichiseachDopplershiftofmulti—pathsignalsofChirpl．(扛0，．．．，N-1)(4)W色get‘+l—tfrom(2-15)，whichisthedelayoftheadjacentpathsofChirpl．(扛0，．．．，N-1)Twosimulationexamplesaregiventoverifytheeffectivenessofthedouble—chirpsignalestimationalgorithm．Example1．LetthecenterfrequencyofChirp1be3kHz，andthecenterfrequencyofChirp2be6kHz．Letbothpulsewidthsbe0．4s，andbothsampleratesbe40kHz(sampling40000pointspersecond)．Letbothbandwidthsbe4kHz．LetthetimeintervalbetweenChirplandChirp2bels．Letchannelparametersbeasfollows：therearethreepaths．Thedelayofdirectpathis30points，andtheamplitudeis1．Thedelayofseasurface—directpathis160points，andtheamplitudeis0．7．nedelayofsea15 ResearchONthemulti—parameterestimationalgorithmofunderwateracougicchannelbasedOnFlU可surface-bottomreflectionis180points，andtheamplitudeis0．5．SNRis0dB．TheDopplershiftofdirectpathis19．595Hz．TheDopplershiftofseasurfaceis12．67Hz．TheDopplershiftofbottomreflectionis-18．333Hz．ThenthereceivedsignalisshowninFig．2-8．Fig．2-8Thereceiveddouble—chirpsignalwithSNR=0dBTherefore，the甜domaindiagramofreceivedsignalforFRFTisshowninFig．2—9．oD岂nEmI’一}一一．．一I一一一量⋯．Io30。口暑20△暑10O．．．～。瑚L⋯上⋯上j174517517551781765177Udomain／pointnumberx10'Fig．2-9The甜domainofreceivedsignalandthezoomoftheChirplpartAsshowninFig．2-9，wecanconfirmthattherearethreepaths．Theresultshowsthatthedouble--chirpestimationalgorithmiseffectivetoconfirmmulti--pathnumber．16 Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedOnFRFTFig．2-10The口domainzoomdiagramofreceivedsignalFromFig．2—10．wecanseethez，domainintervalofeachpathbetweenChirplandChirp2afterthesendingsignaltraversingtheunderwateracousticchannel．From(2-12)，(2·13)，(2-14)and(2—15)，wecanestimatetheDopplershiftsanddelaysofmulti—pathsignals．ThestatisticaldataisillustratedinTab．2—3．Tab．2—3Theparameterestimationcomparisonofthedouble—chirpalgorithmExample2．Thesendingsignalisthesameasabove．Letchannelparametersbeasfollows．TheDopplershiftofdirectpathiSmadebyrelativemotionof0m／s．10rn／s．andtheamplitudeis1．TheDopplershiRofseasurfaceis12．67Hz．andtheamplitudeiS0．7．TheDopplershiftofboRomreflectioniS—l8．333Hz．andtheamplitudeis0．5．Thedelayofseasurface—directpathis160points．ThedelayofboRomreflection．seasurfaceisl80points．SNRiS0dB．Accordingtothesechannelparameters．thesimulationresultsareshowninFig．2-11，Fig．2—12andFig．2—13．Fig．2-1listheDopplershiftestimationofdirectpath．Fig．2—12istheDopplershiftestimationofseasurfaceandbottomreflection．Fig．2．13iSthedelayestimationofseasurface．directpathandbottomreflection—seasurface．17 Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedonFRFTVelocitym／sFig．2-11TheDopplershiftestimationofdirectpathRemark：Blackpointistherealchannelvalue．Redstaristheestimatedvalue．Velocitym／sFig．2—12TheDopplershiftestimationofseasurfaceandbottomreflectionRemark：Blackpointistherealchannelvalue．BluetriangleistheestimationvalueofDopplershiftofseasurface．CarminepaneistheestimationvalueofDopplershiftofbottomreflection．旦．EOeX童oD日—q、B——旧—_电、I，Ⅱ／‘色日f△／·A／．：／一。一一—一一1、．／。j‘Velocitym／sFig．2·13Thedelayestimationofseasurface-directpathandbottomreflection·seasurfaceRemark：Blackpointistherealchannelvalue．Bluetriangleisthedelayestimationvalueofseasurface—directpath．Carminepaneisthedelayestimationofbottomreflection·seasurface．TheFig．2·11，Fig．2—12andFig．2—13showthattheseestimationvalueshavealwaysbeenneartotherealchannelparameters．Theestimationdeviationvaluedoesn’tincreasewiththeDopplershiftanddelayincreasing．Fig．2—11andFig．2—1218N工，J∞一Q△o凸N工，JofdQoo Research011themulti-parameterestimationalgorithmofunderwateracousticchannelbasedonFRFTshowthattheDopplershiftdeviationvalueofdirectpathandseasurfaceisonly0．913Hzat6m／s，butthealgorithmstillestimatestheirchannelparametersrespectively．Theresultshowsthatthealgorithmcandistinguishmulti—pathsignalsofsimilarDopplershift．Fig．2—14showsthattheestimationdiagramofDopplershiftsofdirectpathfordifferentSNRunderthesameconditions．Velocit,／rn／sFig．2-14TheDopplershiftsestimationofdirectpathfordifferentSNRRemark：Blackpointistherealchannelvalue．BluetriangleIStheestimationvaluewithSNR-l0dB．CarminepaneistheestimationvaluewithSNR-5dB．RedstaristheestimationvaluewithSNR0dB．Fig．2—14showsthatestimationvaluefluctuatesneartherealchannelparameterswithSNR0dBand-5dB．AfewpointsfluctuateslightlylargerwithSNR一10dBthanSNR0dBand一5dB．Inconclusion，FIUThasagoodanti-noisecharacteristicattheaspectofestimatingunderwateracousticchannelparameters，anditsestimationperformanceisstillstable、^，iththenoiseincreasing．Throughthepreviousanalysis，weCanseethatthestrongpointofthedouble-chirpsignalestimationalgorithmisthatitCandirectlydeterminethemulti·-pathnumberandthedelaysandDopplershiftsofmulti-·pathsignalsofsimilarDopplershift．However,theshortcomingisthatitisloosetoestimatetheparametersofunderwateracousticchannelduetousingthefastalgorithmofFRFT．Thejointestimationalgorithmisproposedinordertomakeupforthelackofthedouble·chirpsignalestimationalgorithm，thatis，solvetheproblemoftheaccurateestimation．2．4．3ThejointestimationalgorithmWesendaChirpsignalandasinesignal、析t11afixedtimeintervalT．LetthepulsewidthofChirpsignalbe石，chirpratebek，thecenterfrequencybef0，bandwidthbeB．Letthecarrierfrequencyofsinesignalbef0，andthepulsewidthbe疋．BecausetheDopplershiftanddelaywillbemadewhensignaltraverses19 underwateracousticchannel．SowereconstructtheChirpsignalatthestartpointofreceivedsignalaccordingtothepriorknowledge，andletthelengthofreconstructedsignalandthelengthofreceivedsignalbethesame．WelisttwoequationsaccordingtoFI心Tanddecorrelation，andthenwegettherelationtableofDopplershiftanddelay．WeextracttheestimatedDopplershiftanddelayfromtherelationtablethroughthesinesignalgettingtheDopplershiftfromeachpath．ThestructureofthesendingsignalisdepictedinFig．2—15．Centel"，frequencyJoChirp}rate“一Pulse_r——-idth1lChirp．Time，T1ntervaJ—Carriertrequency五J口一Pulse7=一-idth2SineFig．2—15ThestructureofsendingsignalAssumethatthecenterfrequencyofreceivedChirpsignalf0shifts60，thenthecartierfrequencyofsinesignalalsoshifts％．LettheUdomainintervalbetweenthepeakofreconstructedsignalandthepeaksofreceivedChirpsignalintheUdomainbeU“(扛0，．．．，N一1)．LetthetimedomainintervalofthepeaksafterthedecorrelationbetweenreconstructedsignalandreceivedChirpsignalaswellasthepeakaftertheautocorrelationofreconstructedsignalbetc．，(i=0，．．．，N一1)．Letthedelaypointsofthemulti-pathsignalsbetaJ(i=0，．．．，N-1)．LettheDopplershiftofmulti—pathsignalsbee0．j(i=0⋯．，N一1)．LetthebestangleofreceivedChirpsignalforFRFTbe口．Thenthetwo1istedequationswillbe2，c』=td，jXcos(a)+So。f×sin(a)From(2-16)and(2-17)，wegettci=lad+s托oj×z‰2石uc,,-面to,,xc丽os(a)乙，，=。一百(uc,丽-to丽,,xc面os(a))xf,(2—16)(2—17)(2-18)(2—19)WeneedtocarryoutfinesearchingofsmallrangebecauseitisloosetoestimatetheparametersofacousticchannelthroughusingthefastalgorithmofFI强T．ThenwegettheestimationtableofDopplershiftanddelay．AccordingtotheDoppler20 Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedOnFR阿shiftsestimationofsinesignal，wecanextractthebestDopplershiftsanddelays．TheflowchartofthejointestimationalgorithmisshowninFig．2—16．Fig．2-16TheflowchartofthejointestimationalgorithmRemark：AiscarryingoutFIU叮forreceivedsignal；Bisconductingdecorrelationwiththereconductedsignalforreceivedsignal；CisexecutingfinesearchofsmallrangeandlisttheparameterestimationtableaccordingtotheSimultaneousEquationsoftheAandtheB；DisgettingDopplershiftfromeachpathaccordingtosinesignal；finally,weextracttheestimatedchannelparametersaccordingtotheestimationvalueofeachDopplershift．Theproposedjointestimationalgorithmincludesthefollowingsteps(1)Welist(2·16)throughthe甜domaindiagramofChirpsignal．(2)Weget(2-17)throughthedecorrelationdiagramofChirpsignal．(3)WeacquiretheDopplershiftanddelaythrough(2—18)and(2—19)，andcarryingoutfinesearchofsmallrange，wecangettherelationtableofDopplershiftanddelayofmulti-pathsignals．(4)WeCanextractthechannelparametersfromtherelationtablethroughtheDopplershiftsestimationofsinesignal．Threesimulationexamplesaregiventoverifytheeriectivenessoftheiointestimationalgorithm．WithSNIt=0dB．wesimulaterespectivelythethreesituationswhicharethatthedelayofmulti．pathsignalsiSshortandtheDopplershiftofmulti—pathsignalsisverydifferent，thatthedelayofmulti-pathsignalsisshortandtheDopplershiftofmulti-pathsignalsisapproximate，andthatthedelayofmulti—pathsignalsislongandtheDopplershiftofmulti-pathsignalsisapproximate．W色verifytheeffectivenessofthejointestimationalgorithmthroughthethreesimulations．Example1．WesendaChirpsignalandasinesignalwithafixedtimeintervalls．LetthepulsewidthofChirpsignalbeO．5s，chirpratebe2kHz／s，thecenterfrequencybe300Hz，andbandwidthbe400Hz．Letthecarderfrequencyofsinesignalbe300Hz，andletthepulsewidthbeO．6s．Letbothsampleratesbe4000Hz(4000pointspersecond)．Letchannelparametersbeasfollows：therearethreepaths．Thedelayofdirectpathis120points，andtheamplitudeis1．Thedelayofseasurface—directpathiSl60points．andtheamplitudeiS0．7．Thedelayofseasurface—bottomreflectioniS180points，andtheamplitudeis0．5．SNRis0dB．TheDopplershiftofdirectpathis21 Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedonFlU可8．333Hz．TheDopplershiftofseasurfaceis15．777Hz．TheDopplershiftofbottomreflectionis-10．777Hz．Thethree-pathdiagramofreceivedsignalwithoutnoiseisshowninFig．2-17．粤’星。Ca．暑．，罢1星o△量．，害0．5星oQ暑舶O010203040506n7time／sO乱，n20．30．●O．5n60．7time／sFig．2-17Thethree-pathofreceivedsignalwithoutnoiseThereceivedsignaldiagramwithoutnoiseandwithSNR=0dBisshowninFig．2-18． ————————’———1’——’。’—1。。—1。。’————————————————————————’。’——’’———。’——1’——1。’——。。’—’。’——’。。1。’’。。1’。。。’。’’。’。—。。。’’’’。1。’。’’。。。1。。’。。。。。。1。’。’。。’。’。。。。。。。。。。’。’。。’—’。。—1。。。’。。’。。’。’。1。。。。。。。。。。。’’。。’—’。。—1TheFig．2-19isenlarged，asisshowninFig．2·20．20∞2100220023(3024002500timedomain／pointnumberFig．2—20TheenlargeddecorrelationofreceivedsignalFromFig．2—20，wecangettO,0103points；乞．12248points；tc,2=482points．HerewecarryoutFl珂Tforthereceivedsignal，asisshowninFig．2-21．Udomain／pointnumberFig．2—21The甜domainofreceivedsignallTheFig．2—21isenlarged，asisshowninFig．2—22．∞D三△E毋Fig．2—22TheenlargedⅣdomainofreceivedsignalm口rq¨dEmo口nl=Q￡∞ FromFig．2—22，weget"f．o=：一31poims；“。。l2：·75points；材f，22=-146points；sin(a1=．0．9524；cos(a)2-0．3048．Accordingto(2．18)and(2．19)，wecangettheDopplershiftanddelayofmulti．pathsignals，thenwecarryoutfinesearchofsmallrangeandgettherelmiontableofDopplershiftanddelayofdirectpath，asisshowninTab·2-4·Wec锄directlyextractthechannelestimationvaluefromtheTab．2—4becauseitiseasyt0gettheestimationvalueofDopplershiftthroughthesinesignal·Thatis‰．o28．3324Hz；b，o≈120points·Tab．2．4TheDopplershift—delayestimationofdirectpath一一————————————————————————————————————一I2345678910pointS123．4032123．1696122．9359122．7023122．4687122．235122．0014121．7677121·534112l·3004Hz10．201610．08489．9689．85129．73439．61759．50079．38399．2679-1502111213141516．17181920points121．0668120．8331120．5995120．3658120．1322119．8985119．6649119．4312119·1976l18·964Hz9,03348．91668．79978．68298．56618．44938．33248．21568．09887．982———————————————————————————————————————一21222324252627282930points118．7303118．4967i18．263118．0294117．7957117．5621117．3284i16．861I116·6275116·3938Hz7,86527．74837．63157．51477．39797．2817．16426．93066．81376．6969W色conductfinesearchofsmallrange，thenacquiretherelationtableofDopplershiftanddelayofseasurface，asisshowninTab．2-5．Tab．2．5TheDopplershift-delayestimationofseasurface一一——————————————————————————————————————————一i2345678910一—————————————————————————————————————————————一points280．092280．0622280．0324280．0026279．9728279．943279．9132279．8834279·8537279·8239Hz16．04616．031116．016216．001315．986415．971515．956615．941715．926815·9119112131415161718,1920Doints279．7941279．7643279．7345279．7047279．6749279．6451279．6153279．5855279·5558279·526points279．4962279．4664279．4366279．4068279．377279·3472279·3l74279·2876279，2579279．228lHz15．74815．733215．718315．703415．688515．673615．658715．643815·628915614一l—————————————————————————————————一24 Researchonthemulti-parameterestimationalgorithmofunderwateracousticchanneIbasedOnFRFTTheextractioniSthesanleasabove．SO氏，1215．7779Hz；td，l—td，o≈160points．Wecarryonfinesearchofsmallrange，andthengettherelationtableofDopplershiftanddelayofbottomreflection，asisshowninTab．2—6．Theextractionisthesameasabove，thatis岛，22-10．775Hz；ta，2一乞，l≈180points．Tab．2-6TheDopplershift—delayestimationofbottomreflectioni2345678910points461．2678461．2094461．151461．0925461．0341460．9757460．9173460．8589460．8005460．7421Hz一10．3661·10．3953-10．4245-10．4537·10．4829—10．5121．10．5413．10．5705．10．5998．10．6291Ii21314．151617181920points460．6837460．6253460．5668460．5084460．45460．3916460．3332460．2748460．2164460．158Hz-10．6582一10．6874-10．7166-10．7458．10．775．10．8042．10．8334．10．8626．10．8918．10．9212l222324252627282930points460．0996460．0411459．9827459．9243459．8659459．8075459．7491459．6907459．6323459．5738Hz-10．9502—10．9794·1I．0086-11．0378-1I．067．1I．0963．11．1255．11．1547．11．1839．11．2131ThestatisticaldataofdelayestimationbasedonthejointestimationalgorithmarelistedinTab．2．7．Tab．2—7ThedelayestimationofthejointestimationalgorithmDirectdelayDirect—surfacedelaySurface—bottomdelayRealchannel120pointsEstimation120points160points160points180points180pointsErrorrate0WejustresearchthedelayestimationofreceivedsignalsforthisalgorithmbecausetheDopplershiftestimationwillberesearchedindetailinthethirdchapter．Weseethattheerrorratesofthedelaysofthemulti—pathsignalsare0，whichverifytheeffectivenessofthisalgorithminthesituationwherethedelaysofmulti—pathsignalsareshortandtheDopplershiftsareverydifferentwithSNR=0dB．Example2．ThesendingsignalisthesalTleasabove．Letchannelparametersbeasfollows：therearethreepaths．Thedelayofdirectpathis120points，andtheamplitudeis1．Thedelayofseasurface—directpathis160points，andtheamplitude Researchonthemulti·parameterestimationalgorithmofunderwateracousticchannelbasedonFRFTis0．7．Thedelayofseasurface—bottomreflectionis180points，andtheamplitudeis0．5．SNRis0dB．TheDopplershiftofdirectpathis8．333Hz．TheDopplershiftofseasurfaceis9．777Hz．TheDopplershiftofbottomreflectionis-8．777Hz．Thethree-pathdiagramofreceivedsignalwithoutnoiseisshowninFig．2-23．O030405O鼻O．7time／sOntn20．30．40．5nO覆7time／sOtime／sFig．2-23Thethree—pathofreceivedsignalwithoutnoiseThereceivedsignaldiagramwithoutnoiseandwitllSNR=OdBisshowninFig．2-24．∞口三△E西mD三△E哪Fig．2-24ThereceivedsignalwithoutnoiseandwithSNR=0dBHerewecarryoutdecorrelationforthereceivedsignal，asisshowninFig．2—25．m口兰△E西∞"10三e-tE毋timedomain／po=ntnumber【】IL一～L⋯一一上[Ⅱh．ddEk～垂timedoma=n／pointnumberFig．2·25Thedecorrelationandtheenlargeddecorrelationofreceivedsignal，O1，O，5OS。D暑盖E∞∞D暑=nE毋。口nl盖E” ～—————————————————————————————————————一—』型业唑型尘竺坠墅坐韭竺塑垡塑!竺幽竺堕型堕!!里￡垦旦FromFig．2-25，weget，c，。2103points；t。l--261points；fc．2=478points．HerewecaqOtltFRFTforthereceivedsignal，asisshowninFig．2．26．m口兰QE西m口三△EmFig．2-26The甜domainandtheenlarged材doraainofreceivedsignalFromFig．2-26，weget材c，o2·31points；“。，12—79points；％．2=-145points；sin(a)=·0．9525；cos(a)=．0．3045．．-A∞ordmg的(2-18)and(2—19)，wecangettheDopplershiftanddelayofm_17-path．Signals·Thenweconductfinesearchofsmallrangeandacquiretherelatlon‘aDleofDopplershiftanddelayofdirectpath，aSisshowninTab．2．8jTab·2_8TheDopplershift-delayestimationofdirectpath————■————————————————————～一12345678■—i■———===i了了■—————————————————～-．vpoints122‘83⋯22_觚3122·3734122．1404121．9075121．6745121．4416121．20ii磊再；i云iHz9·91969．80319．68679．57029．45379．33739．22089．10438．98798．8714—————————————————————————一111213"141516171819了——————i====■—■■——————————————～points120．5099娩n2769120肼4119．811119．5781119．3452i19．1122118．879五ii矗磊iHz8·75498·63858．5228．40558．2898．17268．05617．93967．82327．7067————————————————————————一．2122232425262728j—了———ii===■—————————————————————一-．vpoints¨8J805I17．9475117·7146117．4817117．2487117．0158116．7828116．5499l磊丁面Hz7·59027·47387·35737．24087．12447．00796．89146．77496．65856．542—————————————————————————一Theextractionisthesameasabove，SOe0，o28．4055Hz；乞o≈120points．Jll|fffffJJJJJJIIIIfIIIIIIIIllIIIIJl ResearchOnthemulti—parameterestimationalgorithmofunderwateracousticchannelbasedOnFRFTWemakefinesearchofsmallrange，thenobtaintherelationtableofDopplershiftanddelayofseasurface，asisshowninTab．2-9．Tab．2-9TheDopplershift-delayestimationofseasurface245689points281．0292280．9995280．9698280．9402280．9105280．8808280．8511280．8214280．7917280．762Hz10．01469．99989．98499．97019．95529．94049．92559．91079．89589．88114"17points280．7323280．7026280．6729280．6432280．6135280．5838280．5541280．5244280．4947280．465Hz9．86619．85139．83649．82169．80679．79199．7779．76229．74739．7325222324252627282930points280．4353280．4056280．3759280．3462280．3165280．2868280．2571280．2274280．1977280．168Hz9．71769．70289．68799．673l9．65829．64349．62859．61379．59889．584TheextractioniSthesameasabove，t11atise-0，l29．777Hz；ta，】一td，o≈161points．Weconductfinesearchofsmallrange，thenacquiretherelationtableofDopplershiftanddelayofbottomreflection，asisshowninTab．2·10．Tab．2-10TheDopplershift-delayestimationofbottomreflectionpoints460．624460．5658460．5076460．4493460．3911460．3329460．2746460．2164460．1582460．0999Hz．8．688．8．7171．8．7462．8．7753．8．8044-8．8336·8．8627-8．8918-8．9209—8．95TheextractioniSthesameasabove，thatis，CO,2=-8．7753Hz；岛，2_二纭，l簧179points．28 Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedonFRFTThestatisticaldatasofdelayestimationbasedonthejointestimationalgorithmarelistedinTab．2．11．Tab．2-11ThedelayestimationofthejointestimationalgorithmObviously,thedelayerrorratesarelittle．whichverifyitseffectivenessinthesituationoftheshortdelaysandtheapproximateDopplershiftswitllSNRiodB．Example3．ThesendingsignaliSthesameasabove．Letchannelparametersbeasfollows：therearethreepaths．ThedelayofdirectpathiS1200points．andtheamplitudeis1．Thedelayofseasurface．directpathis1600points．andtheamplitudeisO．7．Thedelayofseasurface—bottomreflectioniS180points．andtheamplitudeiS0．5．SNRisOdB．TheDopplershiftofdirectpathis8．333Hz．TheDopplershiftofseasurfaceiS9．777Hz．TheDopplershiftofbottomreflectioniS．8．777Hz．Thethree．pathdiagramofreceivedsignalwithoutnoiseisshowninFig．2．27．罢1星。△毫．，罢’星o△暑．，罢n5星oQ暑舶0乱2040608''．2'．4’．6'．Blime／sOn2n●n80811．2'．●'．e1．11time／sFig．2—27Thethree—pathofreceivedsignalwithoutnoiseThereceivedsignaldiagramisshowninFig．2—28withoutnoiseandSNR=0dB． ResearchOilthemulti-parameterestimationalgorithmofunderwateracouSticchannelbasedonFRFT2r”—‘——，—————，—‘。‘—‘’’—。—。，’——‘——r——’。—t‘——‘。，’’———，————1暑1星o△§．，-2m-o三△E母Fig．2·28ThereceivedsignalwithoutnoiseandSNR=0dBHerewecarryoutdecorrelationforthereceivedsignal，asisshowninFig．2—29．FromFig．2—29，wegetBraedomain／pointnumberFig．2—29Thedecorrelationofreceivedsignalt，o2183points；tc。l22781points；乞，224618points．HereweconductFRFTforthereceivedsignal，asisshowninFig．2—30．FromFig．2—22，weget∞"10三△EmFig．2—30TheⅣdomainofreceivedsignal Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedonFRFTUc，o2·759points；U。,I一----1785points；％．22-2964points；sin(a)2·0．7667；COS(O!)=-0．642．Accordingto(2—18)and(2—19)，weCallacquiretheDopplershiftsanddelaysofmulti—pathsignals．ThenwecarryonfinesearchofsmallrangeandgettherelationtableofDopplershiftanddelayofdirectpath，asisshowninTab．2．12．Theextractionisthesanleasabove，thatis氏，o28．312Hz；ta。o≈1200points．Tab．2-12TheDopplershift-delayestimationofdirectpath12345678910points1197．304I197．459I197．614I197．768I197．9231198．0781198．2321198．3871198．5411198．696Hz7．15227．22957．30687．38417．46147．53887．61617．69347．77077．8481112131415"1617181920points1198．8511199．0051199．161199．3151199．4691199．6241199．7791199．9331200．0881200．243Hz7．92548．00278．088．15738．23468．312’8．38938．46668．54398．62122l222324252627282930points1200．3971200．5521200．7061200．8611201．0161201．171201．3251201．481201．6341201．789Hz8．69868．77598．85328．93059．00789．08529．16259．23989．31719．3944Wecarryonfinesearchofsmallrange，andthenobtaintherelationtableofDopplershiftanddelayofseasurface，asisshowninTab．2．13．Tab．2-13TheDopplershift—delayestimationofseasurface12345678910points2800．2832800．3032800．3222800．3422800．3622800．3822800．4012800．4212800．4412800．461Hz9．64159．65149．66129．67119．68099．69089．70079．71059．72049．73021121314"151617181920points2800．482800．52800．522800．5392800．5592800．5792800．5992800．6182800．6382800．658Hz9．74019．74999．75989．76979．77959．78949．79929．80919．8199．82882l222324252627282930points2800．6772800．6972800．7172800．7372800．7562800．7762800．7962800．8152800．8352800．855Hz9．83879．84859．85849．86829．87819．8889．89789．90779．91759．9274 Theextractionisthesameasabove，thatis氏，l29·7795Hz；‰一乞．o≈160Ipoints．Weimplementfinesearchofsmallrange，thengettherelationtableofDopplershiftanddelayofbottomreflection，asisshowninTab．2．14．extractionisthesameasabove，thatis‰，22—8·777Hz；乞，2一乞．】≈1799points．Tab·2-14Dopplershift·delayestimationofbottomreflection———————————————————————————————一一123456789IO—■————————————————————————————————一pomtS4599·8664599·9054599．9444599．9824600．0214600．0594600．0984600．1374600．1754600．214Hz-9·0669-9·0476-9．0283-9．0089·8．9896．8．9703．8．9509．8．9316．8．9123．8．893——————————————————————————————一ll12131415"1617181920—■————————————————————————————————一一一p0Ints4600-2534600·2914600．334600。3694600．4074600．4464600．4854600．5234600．5624600．60lHz-8·8736-8．8543-8．835·8．8156-8．7963-8．777．8．7576．8．7383．8．719．8．6997——————————————————————————————一-21222324252627282930—■—————————————————————————————————一points4600·6394600·6784600．7174600．7554600．7944600．8334600．8714600．914600．9494600．987Hz-8·6803-8．661-8．6417—8．6223—8．603—8．5837．8．5643．8．545．8．5257．8．5064——————————————————————————————一．ThestatiS廿caldataSofdelayestimationbasedonthejointestimationalgorithmarelistedinTab．2—15．Tab·2-15delayestimationofthejointestimationalgorithmEstimation1200points1601points1799pointsErrorrate00．0625％0．0556％————————————————————————————一一Accordingtothissimulation，weseethattheerrorratesofthedelaysofmulti-pathsignalsareverylittle，whichverifytheeffectivenessofthisalgo棚瑚inthesituationwherethedelaysofmulti-pathsignalsarelongandtheDopplershiftsofmulti—pathsignalsareapproximatewithSNR=0dB．Throughthepreviousanalysis，wecallseethattheadvantageofthejointestimationalgorithmisthatitcandirectlyandaccuratelyestimatethemulti—pathnulnber，thedelaysandDopplershiftsofmulti—pathsignalsregardlessoftheDoppler32 Researchonthemulti—parameterestimationalgorithmofunderwateracousticchannelbasedonFRFTshiftsbeingthesame，similarorverydifferent．Alsoitcandirectlyandaccuratelyestimatesthemulti-parameterofunderwateracousticchannelnomatterhowshortorlongthedelaysofmulti-pathsignalsare．However,theshortcomingisthatitliststwoequationsandneedtosearchfinelyinsmallrange，whichresultsincomplexalgorithmandcomputationaloverload．2．5Chaptersummary131Jschaptermainlyintroducesthreenovelalgorithmsformulti—parameterestimationofunderwateracousticchannel．ThefirstalgorithmisFRFTobasedestimationalgorithmwhoseadvantageisthesimplestructureofsendingsignal．WeonlyneedaChirpsignaltoestimatetheparametersofunderwateracouaicchannel．ItsshortcomingisthatweneedtheaccuratedelayestimationofdirectpathandthesameDopplershifts．Thedouble-chirpsignalestimationalgorithmcomessecond．Itsstrengthisthatwecanestimatetheparametersofunderwateracousticchannelwhateverthedelaysofmulti-pathsignalsareshortorlong，alsotheDopplershiftsarethesame，similarorverydifferent．Itsshortcomingisthattherelativelycomplicatedstructureofsendingsignal，whichconsistsoftwoChirpsignals，alsoitmakesrelativelylargeestimationerrorsandcalculationoverloadandduetothefastalgorithmofFRFT．Thet11irdalgorithmisthejointestimationalgorithm．Itsstrongpointisthatwecanaccuratelyestimatetheparametersofunderwateracousticchannelnomatterhowshortorlongthedelaysofmulti—pathsignalsare，moreover，regardlessoftheDopplershiftsbeingthesame，similarorverydifferent．However，itsshortcomingisthatthestructureofsendingsignalisrelativelycomplicated，whichconsistsofaChirpsignalandasinesignal，furthermore，itliststwoequationsandneedtosearchfinelyinsmallrange，whichresultsincalculationoverloadandcomplexalgorithm．33 Research0nthemulti—parameterestimationalgorithmofunderwateracousticchannelbasedonFRFT3Amulti-parameterestimationalgorithmofunderwateracousticchannelbasedontheChirp—basedCharaCter．StiCofFRFTThepreviouschapteradoptedthefastalgorithmofFl强T，whichresultsinrelativelylargecalculationerrorandcalculationoverload．ThenweCaH'youtfinesearchingofsmallrangefortheaccurateestimation，whichcausescomplexalgorithmandlargecalculationoverload．Inthischapter,thechirp—basedcharacteristicofFRFTisappliedtoanalyzingandprocessingtheChirppartofreceivedsignalforthevariablekmodelofChirpsignal，whichavoidtheusingofthefastalgorithmofFIⅫTandgreatlyimprovethealgorithmefficiency．Besides，thealgorithmCanrealizethereal—timeprocessingofreceivedsignalunderthesameaccurateparameterestimation．Finallythesimulationresultswillconfirmthevalidityofthisalgorithm．3．1ThevariablekmodeloftheChirpsignalWeassumethats(f)isthesendingsignal，andr2(t)isthereceived’signalwithoutmulti-path，and△istheDopplercoefficient，whichequalstotheratioofobjectmovementrateandcarrierrate．LetAjbeDopplercoefficientoftheithpath．LettibethedelayoftheithpathandAlbetheamplitudeoftheithpath(i=O⋯．，N一1)．Let石betheinitialfrequencyofChirpsignal，and厶betheterminationfrequencyofChirpsignal．Let互bethelengthoftimedomain，andNbetheeigen-raynumber,thatis，themulti-pathnumber(i=0⋯．，N-1)．Thesendingsignaltraversestheunderwateracousticchannel．Thenthereceivedsignalwillbe{81‘(f)=s((1+△)，)(3-1)Letco．bethecarder行equencywithoutmulti—path．Thenthefrequencyofreceivedsignalwillbe【8】q’=co．(1+△)(3—2)From(2—4)and(3一1)，thereceivedsignalforthevariablekmodelofChirpsignalwillbe【8】【30】：啪，=扣H(1+A,)xfx(t-ri)+f22-，iflx(t-r,)2]]B3， Researchonthemulti—parameterestimationalgorithmofunderwateracousticchannelbasedonFRFT3．2RationaleWecanseethatthex。(甜)ofFRFTofChirpsignalCanbeinterpretedtotheexpansionofthefunctionspacebasedontheinversetransformationnuclear—K。O，甜)ofxO)accordingtotheinversetransformationformulaofFRFTx(，)2LXp(“)挺p(f，u)du·WeknowthatthenuclearisagroupoforthogonalChirp-basedinthe甜domain．ThatisanalogoustotheprincipleofFourierbecausetheyonlyhavedifferentbasement．ThebasementofFI强TisagroupoforthogonalChirp-basedintheUdomain，thatis，theChirp—baseddecompositioncharacteristicofFRFT02]【321．Thus，apeakwillbemanifestedwhenaChirpsignalisattheappropriate甜domain．Thatis，theenergyofChirpsignalwillgatheratacertainorderforagivenChirpsignal(thechirprateiscertain)，SOwecallitthe“best'’orderforthechirprate．Theoretically,thecorrespondingrelationofthechirprateandthe‘'best’’orderPis[121⋯。t(等)(3-4)WeCanclearlyseethatthereisacorrespondingorderPforanychirprate．Conversely,thereisacorrespondingchirprateforanyorderP．Thatistosay,FRFTcontainsChirpsignalofanychirprate．ThereasonwhyusingaChirpsignalestimatedelayinsteadofasinesignalisthatthechirpratesofsinesignalwithDopplershiftsareconstant，butthechirpratesofChirpsignalwithDopplershiftsarevariable．SoweadoptthedifferentvariationcharacteristicbetweenthechirprateofsinesignalandthatofChirpsignaltoestimatethedelaysofmulti—pathsignals．Thestructureandthesignalprocessingalgorithmoftestsignal．3．3Thestructureandthesignalprocessingalgorithmoftestsignal3．3．1Thestructureoftestsignal硼他parametersofsendingsignalarethesameasthatin2．4．3．andthestructureofsendingsignalisdepictedinFig．2—15．TheDopplershiftsanddelayswillbemadewhensignaltraversesunderwateracousticchannel．W色carryouttlleFFTofhi211resolutioninordertodeterminethemulti．pathnumberandestimatetheDopplershifisofmulti—pathsignals．AccordingtOtheestimatedDopplershiftsandpriorsignalknowledge。wereconstructtheChirpsignalsj肥decorrelatethereconstructedsignals35 Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedonFRFTwiththereceivedsignalaccordingtothearrivaltimeorderofmulti—pathsignals，thenwecanaccuratelyandquicklyestimatethedelaysthroughthedifferencesofpeakcoordinates．3．3．2ThesignalprocessingalgorithmoftestsignalW色carryouttheFFTofhighresolutiononthesinepartofreceivedsignal．thenwecandeterminetheaccuratemulti．pathnumber,aswellasestimateaccuratelyandquicklytheDopplershiftsofmulti·pathsignals．Bytakingadvantageofthechirp—basedcharacteristicofFRFTinsteadofthefastalgorithmofFRFZwecanaccuratelyandquicklyestimatethedelaysofthereceivedsignalaccordingtothedifferencesofthepeakcoordinatesanddifferentchirprate．Theflowchartofestimationalgorithmofthechirp．basedcharacteristiciSshowninFig．3．2．=：：l—_=]口n面研CFig．3-2Theflowchartofestimationalgorithmofthecharacteristicofchirp—basedRemark：Aistakingoutthechirppartofreceivedsignal；Bisinterceptingthesinepartofreceivedsignal；CisestimatingtheDopplershiftsofmulti—pathsignals；finally,wegetthedelaysofmulti-pathsignalsthroughthedecorrelationsofAandthereconstructedsignalsbasedonC．Theproposedestimationalgorithmofchirp—basedcharacteristicincludesthefollowingsteps(1)Weestimatethemulti-pathnumberandDopplershiftsofreceivedsignalthroughtheFFTofhighresolutiononthesinepartofreceivedsignal．(2)Weaccuratelyandquicklyestimatethedelaysofreceivedsignalthroughdifferentchirprateandthedifferencesofthepeakcoordinates．3．4NumericaIsimulationThreesimulationexamplesaregiventoverifytheeffectivenessoftheestimationalgorithmofchirp—basedcharacteristic．WitllSNRjodB，wesimulaterespectivelythethreesituationswherethedelaysofmulti-pathsignalsareshortandtheDopplershiftsofmulti-pathsignalsareverydifferent，thedelaysofmulti—pathsignalsareshortandtheDopplershiftsofmulti··pathsignalsaresimilar,aswellasthedelaysofmulti--pathsignalsarelongandtheDopplershiftsofmulti-pathsignalsissimilar．Weverifytheeffectivenessoftheestimationalgorithmofthechirp·basedcharacteristicthroughthreeexamples．36 Researchonthemulti-parameterestimarionalgorithmofunderwateracousticchannelbasedonFRFTExample1．WesendaChirpsignalandasinesignalwithafixedtimeintervallS．LetthepulsewidthofChirpsignalbe0．01S，thebandwidthbe800Hz，thecenterfrequencybelkHz．LetthecarrierfrequencyofsinesignalbelkHz，andletthepulsewidthbe0．6s．Letbothsampleratesbe12kHz(12000pointspersecond)．Letchannelparametersbeasfollows：therearethreepaths．Thedelayofdirectpathis120points，andtheamplitudeiS1．Thedelayofseasurface．directpathis133points．andtheamplitudeiS0．7．Thedelayofseasurface．bottomreflectioniSl8lpoints．andtheamplitudeiS0．5．SNRiS0dB．TheDopplershiftofdirectpathiS3．777Hz．TheDopplershiftofseasurfaceiS100．777Hz．TheDopplershiftofbottomreflectioniS-100．777Hz．Thethree-pathdiagramofthesinesignalpartofreceivedsignalwithoutnoiseandthesinesignalpartdiagramofreceivedsignalwithSNR予0dBareshowninFig．3—3．o羔：}-，：∞三△E∞0405080．700time／s0010203040S0．00．70．●timeIs0010203O4050B070．0time／s040．50．8n7n0time／sFig．3-3Thethree-pathofthesinesignalpartofreceivedsignalwithoutnoiseandthesinesignalpartofreceivedsignalwithSNR=0dBThethree—pathdiagramofChirpsignalpartofreceivedsignalwithoutnoiseandtheChirpsignalpartdiagramofreceivedsignalwithSNR=0dBareshowninFig．3—4．罢．善jEj鳓E三三三三三]暑00．01n∞n03n“o·皓0．06∞血me，s善．oE二=二逊幽蛀二==j磊on们乱蛇o∞n∽o∞o．∞otJmels嚣E三三三三三皿旺三]苎。卜————————————————J⋯㈣M圳8卜_一{言舢卜1扩1矿、矿心掣‰一詈：P塑0．01巡O．幽m业0．03竺0．0坚4警q毫‘oo．皓o．∞Fig．34Thethree-pathofChirpsignalpartofreceivedsignalwithoutnoiseandtheChirpsignalpartofreceivedsignalwithSNR=0dBWithSNR=0dB，weearlyouttheFFTofhighresolutiononthesinesignalpartofreceivedsignal，asisshowninFig．3—5．37，oo帖。帖口星dⅢmm口jⅦdF Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedonFR丌o-o．兰△E∞0．8●O．7O．00．S0．●O．3乱20．1Oh●Ill：li一．．‘．L一-川川一．●⋯J--．-‘0。uC540000000洲frequency／HzFig．3·5TheFFTofhighresolutiononthesinepartofreceivedsignalwithSNR=0dBWegetFig．3-6throughthezoomofFig．3-5．O．8O．7O．8粤0．5△0●E∞n302n'}S_fl}一m口r●“It-k-L▲．●L．一▲jL～A一二ObO10501'001150Fig．3-6ThezoommapofFFTdiagramofhighresolutionofthesinepartwithSNR=0dBWecanapparentlyseetheDopplershiftsofthreepathsfromFig．3—6，asisshowninTab．3．1．Tab．3-1TheDopplershiftestimationoftheChirp·basedalgorithmFromTab．3-1，theestimationperformanceofDopplershiftsisverygoodwhenthedelaysofmulti·pathsignalsareshortandtheDopplershiftsaleverydifferent、析tllSNR=OdB．AccordingtotheestimatedDopplershiftsandpriorsignalknowledge，werespectivelyreconstructtheChirpsignals，andthenwedecorrelatethereconstructedsignalswiththereceivedsignalaccordingtothearrivaltimeorderofmulti—path38 signals．WegetFig．3—7，Fig．3—8andFig．3—9．∞刁j△E∞蔓产i■—_0100200300400500600700800timedomain／pointnumberFig．3—7Thedecollrelationofthereconstructedsignalofdirectpathandthereceivedsignal0100200300400500600700800timedomain／pointnumberFig．3-8ThedecorrelationofthereconstructedsignalofseasurfaceandthereceivedsignalO·9O．。n706∞暑o．5拿0．4mn30．2010：。2麓：==_．1『．1．|l；烈淡薹-黛蒯撼‰捌O00290300400500600700a00timedomain／pointnumberFig．3—9ThedecorrelationofthereconstructedsignalofbottomreflectionandthereceivedsignalThedelayofdirectpathisthedifferencebetweenthefirstpeakfromFig．3—7andZ×石．Thedelayofseasurface—directpathisthedifferencebetweenthesecondpeakfromFig．3-8andthefirstpeakfromFig．3—7．Thedelayofseasurface-bottomreflectionisthedifferencebetweenthesecondpeakfromFig．3—8andthethirdpeak39¨盯¨”¨ooD3嚣一△Em Researchonthemulti-parameterestimationalgorithmofunderwateracouSticchanneIbasedonFRFTfromFig．3-9．ThestatisticaldatasofthedelayestimationbasedontheChirp-basedalgorithmarelistedinTab．3．2．Tab．3-2ThedelayestimationoftheChirp—basedalgorithmDirectdelayDirect--surfacedelaySurface··bottomdelayFromTab．3-2，thedelayestimationisveryaccuratewhenthedelaysofmulti-pathsignalsareshortandtheDopplershiftsareverydifferentwithSNR=0dB．Example2．ThesendingsignaliSthesameasabove．Letchannelparametersbeasfollows：therearethreepaths．ThedelayofdirectpathiS120points．andtheamplitudeiS1．Thedelayofseasurface—directpathiS133points．andtheamplitudeiS0．7．Thedelayofseasurface—bottomreflectioniS181points．andtheamplitudeiS0．5．SNRiS0dB．TheDopplershiftofdirectpathiS33．333Hz．TheDopplershiftofseasurfaceis35．777Hz．TheDopplershiftofbottomreflectionis．33．373Hz．Thethree-pathdiagramofthesinesignalpartofreceivedsignalwithoutnoiseandthesinesignalpartdiagramofreceivedsignalwitllSNR=OdBareshowninFig．3．10．∞薹：詈．，∞刁昌‘五E毋O01020304050．8O．70．8time／sO．50_0．S∞刁兰△E∞O01020304time，sO0．102O3O4O5O．6O．7n●time／sFig．3-10Thethree—pathofsinesignalpartofreceivedsignalwithoutnoiseandthesinesignalpartofreceivedsignalwithSNR=0dBThethree-pathdiagramoftheChirpsignalpartofreceivedsignalwithoutnoiseandtheChirpsignalpartdiagramofreceivedsignal、舫tllSNR=0dBareshowninFig．3-11．o口32一△E∞ jEj赋E三三三三j00,010020030．04005O．∞fime／s：F二二孤一iL——————————————————o03n04o．皓006otime／s嚣oE三三三三j盈曰．羔}⋯⋯——一⋯J|f∽【：ⅧmL—一J争s卜1矿、矿、矿世胖≮一∞time／s詈j臣巫孥哑亚巫妇0．060．010．030．040．05毫‘o仉陀一一。Fig．3-1lThethree-pathoftheChirpsignalpartofreceivedsignalwithoutnoiseandtheChirpsignalpartofreceivedsignalwithSNR=OdBWithSNR=OdB，wecarryouttheFFTofhighresolutiononthesinesignalpartofreceivedsignal，asisshowninFig．3-12．●L—⋯．一～-～“h⋯．．01000fmqtmncy／Hz50006嘲Fig．3—12TheFFTofhiighresolutiononthesinepartofreceivedsignalwithSNR=0dBWegetFig．3—13throughthezoomofFig．3·12．∞口皇QE∞frequency／HzFig．3-13ThezoomOfFFTofhighresolutiononthesinepartwithSNR=0dBWecanapparentlyseetheDopplershiftsofthreepathsaccordingtoFig．3—13，asisshowninTab．3．3．4l∞口暑=QE∞∞o)兰QEm们"¨：詈¨"¨o∞Dnl¨aE∞ Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedonFRFTTab．3-3TheDopplershiftestimationofChirp-basedalgorithmFromTab．3-3，whenthedelayofmulti-pathsignalsareshortandtheDopplershiftsareverydifferent谢thSNR=0dB，theestimationperformanceofDopplershiftisstillverygood．ButtheestimationperformanceisalittledecreasedwhentheDopplershiftsaresimilar,andtheweakoneoftwopathswithsimilarDopplershiftisseverelyinfluenced．Fortunately,theproblemcanbesolvedbyhighresolutionandlongsinesignal．AccordingtotheestimatedDopplershiftsandpriorsignalknowledge，werespectivelyreconstructtheChirpsignals，andthenwedecorrelatethereconstructedsignalswiththereceivedsignalaccordingtothearrivaltimeorderofmulti—pathsignals．WegetFig．3-14，Fig．3—15andFig．3—16．O．口n。n7n6o弓05．羔拿o．4毋03n201O燃幽!l1幽鳐戡0100200300400500600700鲫timedomain／pointnumberFig．3—14Thedecorrelationofthereconstructedsignalofdirectpathandthereceivedsignal09n8n70．8∞弓0．5兰譬¨∞n3n2010·●j撼娥l{燃：燃■型0100200300400500600700800timedomain／pointnumberFig．3-15Thedecorrelationofthereconstructedsignalofseasurfaceandthereceivedsignal42 Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedOBFRFT[山；划。I}{f1剿0'00200300400500600700咖timedomnWpointnumberFig．3-16ThedecorrelationofthebottomreconstructedsignalandthereceivedsignalThedelayofdirectpathisthedifferencebetweenthefirstpeakfromFig．3·14andZX巧．Thedelayofseasurface—directpathisthedifferencebetweenthesecondpeakfromFig．3—15andthefirstpeakfromFig．3-14．Thedelayofseasurface-bottomreflectionisthedifferencebetweenthesecondpeakfromFig．3-15andthethirdpeakfromFig．3—16．ThestatisticaldatasofthedelayestimationbasedontheChirp-basedalgorithmarelistedinTab．3．4．Tab．3_4ThedelayestimationoftheChirp—basedalgorithmFromTab．3-4．wecanseethatthedelaysestimationareveryaccuratewhenthedelaysofmulti—pathsignalsareshortandtheDopplershiftsaresimilarwithSNR=0dB．Example3．ThesendingsignaliSthesameasabove．Letchannelparametersbeasfollows：therearethreepaths．Thedelayofdirectpathisl200points．andtheamplitudeis1．111edelayofseasurface·directpathis1330points，andtheamplitudeiS0．7．Thedelayofseasurface—bottomreflectioniS1810points．andtheamplitudeiS0．5．SNRiSOdB．TheDopplershiftofdirectpathis33．333Hz．TheDopplershiftofseasurfaceiS35．777Hz．TheDopplershiftofbottomreflectionis．33．373Hz．Thethree-pathdiagramofthesinesignalpartofreceivedsignalwithoutnoiseandthesinesignalpartdiagramofreceivedsignal晰t}lSNR=0dBareshowninFig．3-17．43¨"¨帖¨他"o∞口三¨aEm Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbased011FRFTmD3兰QEm0204060．0time／s020406O8'12time／s1●00．2O608time／sOo．20．40．60．8''．2'．4tJme／sFig．3-17Thethree—pathofthesinesignalpartofreceivedsignalwithoutnoiseandthesinesignalpartdiagramofreceivedsignalwithSNR=OdBThethree-pathdiagramoftheChirpsignalpartofreceivedsignalwithoutnoiseandtheChirpsignalpartdiagramofreceivedsignalwithSNR=0dBareshowninFig．3—18．罟．善jE三j三三三三三三j磊。o0．060．10．15020．250．30．350．4∞time／s主：F二二二二二f二二习拿．，1．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．。．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．!!!1．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．_JI∞-’00．060．10．150．20．250．30．350．4d，timels00∞010．15020250．30350．4lime／sFig．3·18Thethree—pathoftheChirpsignalpartofreceivedsignalwithoutnoiseandtheChirpsignalpartofreceivedsignalwithSNR=0dBWithSNR=0dB，wecarryouttheFFTofhighresolutiononthesinesignalpartofreceivedsignal，asisshowninFig．3-19．∞"10量QE母I●～⋯jL·～一～⋯■．-～～一～0frequency／Hz4000500060∞Fig．3-19TheFFTofhighresolutionofthesinepartofreceivedsignalwithSNR50dB44，O，50505。口nlI|△E时啦口三盖}m∞D暑IIaE¨o¨：o五口星}西∞曼Id§ Researchonthemulti—parameterestimationalgorithmofunderwateracousticchannelbasedonFRFrWegetFig．3-20throughthezoomofFig．3-19．∞口三△E∞●『≥L^．-。．^．。-矗一ll。‰9∞97098099010001010102010301040frequency／HzFig．3·20ThezoomofFFTofhighresolutionofthesinepartofreceivedsignalwithSNR=0dBWecanapparentlyseetheDopplershiftsofthreepathsaccordingtoFig．3-20．asisshowninTab．3．5．Tab．3—5TheDopplershiftestimationoftheChirp-basedalgorithmFromTab．3—5，whenthedelaysofmulti—pathsignalsarelongandtheDopplershiftsaresimilarwitllSNR=0dB，theestimationperformanceofDopplershiftsisstillverygood．However,theestimationperformanceisalittledecreasedwhentheDopplershiftsaresimilar,andtheeffectisseverefortheweakoneoftwopathsofsimilarDopplershift．Luckily，theproblemCanbesolvedbyhighresolutionandlongsinesignal．AccordingtotheestimatedDopplershiftsandpriorsignalknowledge，werespectivelyreconstructtheChirpsignals，andthenwedecorrelatethereconstructedsignalswiththereceivedsignalaccordingtothearrivaltimeorderofmulti—pathsignals．WegetFig．3—21，Fig．3—22andFig．3-23．45帖懈¨嘴¨惜啦吣¨哺 Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedonFRFTo刁兰△Emtimedomain／pointnumberFig．3-21Thedecorrelationofthereconstructedsignalofdirectpathandthereceivedsignaltimedomain／pointnumberFig．3—22ThedecorrelationofthereconstructedsignalofseasurfaceandthereceivedsignalFig．3—23ThedecorrelationofreconstructedsignalofbottomreflectionandthereceivedsignalThedelayofdirectpathisthedifferencebetweenthefirstpeakfromFig．3-21andZ×互．Thedelayofseasurface—directpathisthedifferencebetweenthesecondpeakfromFig．3-22andthefirstpeakfromFig．3-21．Thedelayofseasurface—bottomreflectionisthedifferencebetweenthesecondpeakfromFig．3—22andthethirdpeakfromFig．3-23．ThestatisticaldatasofdelayestimationbasedontheChirp—basedalgorithmare46 listedinTab．3．6．Tab．3·6ThedelayestimationoftheChirp—basedalgorithmDirectdelayDirect-·surfacedelaySurface··bottomdelayRealchannel1200points1330points18lOpointsEstimation1200points1330pointsI810pointsErrorrate0’0FromTab．3．6，thedelayestimationisstillveryprecisewhenthedelaysofmulti—pathsignalsarelongandtheDopplershiftsaresimilarwithSNR=0dB．3．5ChaptersummaryThischaptertakesadvantageofthechirp—basedcharacteristictoestimatetheparametersofunderwateracousticchannel，SOweavoidthecalculationerrorcausedthefastalgorithmofFRFT．nlreesimulationexamplesalegiventoverifytheeffectivenessofthechirp．basedcharacteristicalgorithm．WithSNIPOdB，wesimulaterespectivelythethreesituationswherethedelaysofmulti-pathsignalsareshortandtheDopplershiftsareverydifferent，thedelaysofmulti—pathsignalsareshortandtheDopplershiftsaresimilar,andthedelaysofmulti—pathsignalsalelongandtheDopplershiftsaresimilar．Inthesesituations，weallCanaccuratelyandquicklyestimatet11eparametersofunderwateracousticchannel．However,theestimationperformanceiSalittledecreasedwhentheDopplershiftsaresimilar,andtheweakoneoftwopathsofsimilarDopplershiftisseverelyinfluenced．Fortunately,theproblemCallbesolvedbyhighresolutionandlongsinesignal．ThesimulationresultsshowthatthealgorithmCanaccuratelyandquicklyestimatetheparametersofunderwateracousticchannel．Furthermore，thisalgorithmishighaccurateandsimple，andthespeedofcalculationiSveryfast．WhatiSthemostimportant，wecaneffectivelyconductreal—timeprocessingfortheunderwateracousticsignalthroughthisalgorithm．47 4ThepacketstructuredesignbasedonFRFTunderwateracousticcommunicationsystemThecharmeliSoneindispensablepartofthecommunicationsystem，anditisalsoakeyissuetobeconsideredinthepacketstructuredesignofcommunicationsystem．Therearedifferentdesignsaccordingtodifferentchannelcharacteristics．ThischapterproposestwopacketstructuredesignsbasedontheFRFTcommunicationsystemfordifferentchannel．Wedesignonepacketstructureforthechanneloffastchange，andthenwedesignanotherpacketstructureforthechannelofslowchange．4．1TwokindsofpacketstructureThischapterproposestwopacketstructuredesignsbasedonFRFTcommunicationsystemfordifferentchannel，whichareshowninFig．4—1andFig．4-2，respectively．Chirp：uidtls：写intervalAtSine黼uls：瓦Fig．4—1ThefirstpacketstructureThefirstpacketstructurewasdesignedfort11echanneloffastchange，whichconsistsofChirpsignal，sinesignalandBPSK．ThepulsewidthofChirpsignalis互，anditisusedastheheadofthefirstpacket．Thepulsewidthofsinesignalis正，whichisusedtoestimatetheDopplershiftsandthemulti—pathnumber．ThedataadoptBPSK，withpulsewidth瓦．Inordertopreventtheinterferencebetweensignals，lettheintervalbetweenChirpsignalandsinesignalbe．Atl，andtheintervalbetweensinesignalandBPSKbeAt2．Theadvantageofthiskindofpacketisthatwecanestimatetheparametersofunderwateracousticchannelperpacket，whichgreatlyincreasethereliabilityofdatatransmission．However,itreducestransmissionefficiency．Chirp：uidtls：7；intervalAtBPSK：uidtlshe五Fig．4-2ThesecondpacketstructureThesecondpacketstructureWasdesignedforthechannelofslowchange，whichconsistsofChirpsignalandBPSK。ThepulsewidthofChirpsignalis正，anditisusedastheheadofthesecondpacket．ThedatastilladoptBPSK，withpulsewidth五．Welaunchsinesignalto—e．stima．tetheDopplershiftsandthemulti。pathnumberevery4R Researchonthemulti—parameterestimationalgorithmofunderwateracousticchannelbasedOilFRFTcertaintimeinterval，withpulsewidth兀．Inordertopreventtheinterferencebetweensignals，theintervalbetweenChirpsignalandBPSKisAt．ThestrongpointofthiskindofpacketiSthatwecanestimatetheparametersofunderwateracousticchannel，andthisstructuregreatlyincreasestransmissionefficiency．However,itcan’testimatetheDopplershiftofunderwateracousticchannelperpacket．whichenormouslyreducesthereliabilityofdatatransmission．4．2TheflowofthefirstpacketprocessingalgorithmWeCalTyouttheFFTofhighresolutiononthesinepartofreceivedsignal，thenwecandeterminetheprecisemulti。pathnumber,atthesametimewecanaccuratelyandquicklyestimatetheDopplershiftsofmulti—pathsignals．AccordingtotheestimatedDopplershiftsandpriorsignalknowledge，wecanreconstructtheChirpsignals．Thenwedecorrelatethereconstructedsignalswiththereceivedsignalaccordingtothearrivaltimeorderofmulti-pathsignals．Bytakingadvantageofthechirp—basedcharacteristicofFRFTinsteadofthefastalgorithmofFRFT,wecanaccuratelyandquicklyestimatetheparametersofunderwateracousticchannelthroughthedifferencesofthedecorrelatedpeakcoordinatesanddifferentchirprate．Accordingtotheestimatedparametersofunderwateracousticchannel，wecandemodulatetheBPSK．TheflowchartofsignalprocessingalgorithmofthefirstpacketstructureiSshowninFig．4-3．Fig．4-3111eflowofsignalprocessingalgorithmofthefirstpacketstructureRemark：Aistakingoutthechirppartofreceivedsignal；Bisinterceptingthesinepartofreceivedsignal；CistakingouttheBPSKpartofreceivedsignal；DisestimatingtheDopplershiftsofmulti—pathsignals；EisgettingthedelaysthroughthedecorrelationbetweenAandthereconstructedsignalsforD．Finally,weextractthetransmitteddataaccordingtoC，DandETheproposedestimationalgorithmbasedonthechirp—basedcharacteristicincludesthefollowingsteps(1)Weestimatethemulti—pathnumberandDopplershiftsofreceivedsignalthroughtheFFTofhighresolutiononthesinepartofreceivedsignal．(2)Weaccuratelyandquicklyestimatethedelaysofreceivedsignalthrough49 ResearchOnthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedorlFRFTdifferentchirprateandthedifferencesofpeakcoordinates．(3)WeCandemodulatetheBPSKthroughtheestimatedparametersofunderwateracousticchannel．4．3Thesimulationofpacketsignalprocessingalgorithm4．3．1lhesimulationoffirstpacketExample1．WesendaChirpsignalandasinesignalwithafixedtimeinterval0．05s，andlettheintervalbetweensinesignalandBPSKbe0．66s．LetthepulsewidthofChirpsignalbeO．Ols，thebandwidthbe800Hz，thecenterfrequencybelkHz．LetthecarrierfrequencyofsinesignalbelkHz，andletthepulsewidthbe0．6s．LetthecartierfrequencyofBPSKbelkHz．andletthepulsewidthbe2．789s．Letallsampleratesbe12kHz(12000pointspersecond)．Letchannelparametersbeasfollows：therearethreepaths．Thedelayofdirectpathis120points，andtheamplitudeis1．Thedelayofseasurface-directpathis160points，andtheamplitudeis0．7．Thedelayofseasurface—bottomreflectionis180points，andtheamplitudeis0．5．SNRis20dB．TheDopplershiftofdirectpathis3．777Hz．TheDopplershiftofseasurfaceis10．777Hz．TheDopplershiftofbottomreflectioniS．10．777Hz．Thesendingsignalstructureoffirstpacketconsistsofachirpsignal，asinesignalandBPSK，asisshowninFig．4-4．4：=Il赋瓣05152535●bm眺Fig．4—4ThesendingsignalstructureoffirstpacketTheDopplershiftanddelaywillbemadewhensignaltraversesunderwateracousticchannel．Forsimpleanalysis，assumethatthechannelhasnonoise，thenthereceivedsignalisshowninFig．4-5．●l～J，E；．，●l{；}，i!；+●-{，¨们。舭引那m4o口nl=QE毋 Research011themulti-parameterestimationalgorithmofunderwateracousticchannelbasedOnFRFTI：I燃烬燃蜮燃卜}2幽剐固，嘲嘲雕黜渺溯．{节懒糊删惝删；00．5'，．522533．5●tJme／sFig．4-5ThereceivedsignalforthefirstpacketwithoutnoiseWegetFig．4—6throughthezoomofchirpsignalpartandsinesignalpartofFig．4-5．Ih斜叫利!翟随酗濑{{《缈；i泸；副渺1n'0．20．30．40．50．60．700Fig．4-6ThezoomofchirpsignalpartandsinesignalpartofreceivedsignalwithoutnoiseThereceivedsignaldiagramforthefirstpacketwit}lSNR=20dBisshowninFig．4—7．军幽峨|I瓿Il{涮f；l黼{||j[差f|；：!}捧O0．5'1．522533．54time／sFig．4—7ThereceivedsignalforthefirstpacketwithSNR=20dBThezoomdiagramofchirpsignalpartandsinesignalpartofreceivedsignalwitllSNR=20dBisshowninFig．4-8．拍2侣，¨o帕一¨{：搴∞口暑IIaE叮2伤，：詈。∞。帕童由寸nl=QEm拍2协，¨。帕。¨之舶。口nI=QE∞ ResearchOnthemulti·parameterestimationalgorithmofunderwateracousticchannelbasedonFRFTFig．4-8ThezoomofchirpsignalpartandsinesignalpartofreceivedsignalwithSNR=20dBInfact，thesendingsignalconsistsofthethreeparts—·Chirpsignal，sinesignalandBPSK．Theprocessingofreceivedsignalincludesthreesteps．Firstly,wecarryouttheFFTofhighresolutionforthesinepartofreceivedsignal，thenwecandeterminetheaccuratemulti—pathnumberandestimateaccuratelyandquicklytheDopplershiftsofmulti—pathsignals．Secondly，wereconstructtheChirpsignalsaccordingtotheestimatedDopplershiftsandpriorsignalknowledge．Thirdly,wedecorrelatethereconstructedsignalswiththereceivedsignalaccordingtothearrivaltimeorderofmulti—pathsignals，andthenwecanaccuratelyandquicklyestimatethedelaysthroughthedifferenceofthedecorrelatedpeakcoordinatesanddifferentchirprate．Finally,wecandemodulatetheBPSKaccordingtOtheestimatedparameters．4．3．2ThesimulationofsecondpacketExample2．WresendChirpsignalandBPSKwithafixedtimeinterval0．05s．LetthepulsewidthofChirpsignalbe0．01s，thebandwidthbe800Hz，thecenterfrequencybelkHz．LetthecartierfrequencyofBPSKbelkHz，withthepulsewidth2．789s．Letbothsampleratesbe12kHz(12000pointspersecond)．Letchannelparametersbeasfollows：therearethreepaths．Thedelayofdirectpathis120points，andtheamplitudeis1．nledelayofseasurface-directpathis160points．andtheamplitudeiS0．7．Thedelayofseasurface．bottomreflectioniS180points．andtheamplitudeis0．5．SNRis20dB．TheDopplershiftofdirectpathis3．777Hz．TheDopplershiftofseasurfaceiS10．777Hz．TheDopplershiftofbottomreflectioniS．10．777Hz．ThesendingsignalstructureofthesecondpacketconsistsofChirpsignalandBPSK．asiSshowninFig．4．9．52：侣，¨。舶J帕之∞Dnl=QEm 。：+：童。：fK0-山·●：．0．6l。o．8l05S2time，s33．5Fig．4．9ThesendingsignalstructureofthesecondpacketTheDopplershiftanddelaywillbemadechannel．Forsimpleanalysis，assumethatsignalisshowninFig．4-l0．m口盏nE∞whensignaltraversesunderwateracousticthechannelhasnonoise，SOthereceivedFig．4—10ThereceivedsignalforthesecondpacketwithoutnoiseWegetFig．4—11throughthezoomofChirpsignalpartofFig·4一l0-∞D兰QE仍Fig．4．1lTheZOOlllofChirpsignalpartofreceiVedsignalwithoutnoiseThereceivedsignaldiagramforthesecondpacketwithSNR=20dBisshowninFig．4—12．53 Researchonthemulti-parameterestimationalgorithmofunderwateracous—ti—c—ch—a—n—ne—l—ba—sedonFRFTOO．5'．522．533．5lJme．JsFig．4—12ThereceivedsignaldiagramforthesecondpacketwithSNR=20dBThezoomdiagramofChirpsignalpartandsinesignalpartofreceivedsignalwitllSNR=20dBisshowninFig．4—13．∞口三△E∞Fig．4-13ThezoomofChirpsignalpartofreceivedsignalwithSNR=20dBInfact，thesendingsignalconsistsofthetwoparts—ChirpsignalandBPSK，andtheprocessingofreceivedsignalincludesthreesteps．Firstly,wesendasinesignaleverycertaintime，thenwecarryouttheFFTofhighresolutionforthesinepartofreceivedsignalSOthatwecandeterminetheaccuratemulti—pathnumberandaccuratelyandquicklyestimatetheDopplershiftsofmulti·pathsignals．Secondly,wereconstructtheChirpsignalsaccordingtotheestimatedDopplershiftsandpriorsignalknowledge，thenwedecorrelaterespectivelythereconstructedsignalswiththereceivedsignalaccordingtothearrivaltimeorderofmulti-pathsignals，andwecanaccuratelyandquicklyestimatethedelaysthroughthedifferencesofthedecorrelatedpeakcoordinatesanddifferentchirprate．Finally,wedemodulatetheBPSKaccordingtotheestimatedparameters．Thisstructurewasdesignedforthechannelofslowchange，SOthesinesignalpartisremoved，whichresultsinhighefficiency,however,atthesametimewhichenormouslyreducesthereliabilityofdatatransmission．=s：协，¨。：；一们{∞m口rqlloE西 Researchonthemulti-parameterestimationalgorithmofunderwateracousticchannelbasedonFRFT4．4ChaptersummaryThischapterproposestwopacketstructuredesignsbasedonFRFTcommunicationsystemfordifferentchannel．Wedesignthefirstpacketstructureforthechanneloffastchange．ThestrongpointofthispacketiSthatwecanestimatetheparametersofunderwateracousticchannelperpacket．whichgreatlyincreasethereliabilityofdatatransmission．HoweveLitreducestransmissione街ciency．W色designthesecondpacketstructureforthechannelofslowchange．Thestrengthofthispacketisthatwecangreatlyincreasetransmissionefficiency．However,itCan’testimatetheDopplershiftsofunderwateracousticchannelperpacket，whichgreatlyreducethereliabilityofdatatransmission．Inconclusion，thechirp—basedcharacteristicofFRFTisappliedtoanalyzingandprocessingtheChirpsignalpartofthemixedsignalforbothtwopackets，whichavoidstheusingofthefastalgorithmofFI珂Tandgreatlyimprovethealgorithmefficient．Besides，bothtwopacketsCanberealizedforreal—timeprocessingundertheaccurateparameterestimation．55 5ConclusionandfutureresearchInthisdissertation，fournovelalgorithmsforthemulti．parameterestimationproblemofunderwateracousticchannelareproposed．nlreenovelalgorithmsforthemulti-parameterestimationofunderwateracousticchannelareproposedfortheconstantkmodeloftheChirpsignal．andthenanovelmulti．parameterestimationalgorithmofunderwateracousticchannelbasedontheChirp．basedcharacteristicofFRFTforthevariablekmodeloftheChirpsignaliSalSOproposed．ForthevariablekmodeloftheChirpsignal，twodesignsofpacketstructurebasedonthecommunicationsystemofFRFTfordifferentchannelareproposed．Thesummarizationofthisdissertationisasfollows(1)TheFRFT-basedestimationalgorithmTheadvanmgeoftheFRFT-basedestimationalgorithmisthatitCanestimatetheaccuratemulti—pathnumber,thedelayandaccurateDopplershift．However,thisalgorithmisjustsuitableforthesituationwhereeachofthepathshasthesameDopplershiftandtheexactdelayestimationofdirectpathisavailable．(2)Thedouble-chirpsignalestimationalgorithmThesuperiorityofthedouble—chirpsignalestimationalgorithmisthatitCandirectlyestimatethemulti-pathnumber,thedelaysandtheDopplershiftsregardlessoftheDopplershiftsbeingthesame，similarorverydifferent．However,theshortcomingisthattheparametersestimationofunderwateracousticchannelislooseandithascomputationaloverloadduetousingthefastalgorithmofFRFT．(3)Thejointestimationalgorithm·Thestrongpointofthejointestimationalgorithmisthatitcandirectlyandaccuratelyestimatethemulti—pathnumber,thedelaysandDopplershiftsofmulti—pathsignalsofthesame，similarordifferentDopplershift，anditcanalsodirectlyandaccuratelyestimatetheparametersofunderwateracousticchannelnomatterhowshortorlongthedelaysofmulti-pathsignalsare．However,theweakpointisthatitneedtosearchfinelyinsmallrange，whichresultsincomplexalgorithmandagreatdealofcalculation．(4)TheChirp-basedalgorithmofFIUTThemeritoftheChirp—basedalgorithmofFI心Tisthatwecanaccuratelyandquicklyestimatetheparametersofunderwateracousticchannel．Thealgorithmishighaccuratewhiletheprocessingprocedureissimplewitllfastcalculation．Ⅵmatisthemostimportantisthatwecaneffectivelytakereal—timeprocessingfortheunderwateracousticsignal．However,theestimationperformancedecreaseslightlyandtheweakoneoftwopathsisseverelyinfluencedwhenthedifferenceofDopplershiftsisapproximate．Fortunately,theproblemCanbesolvedbyhighresolutionandlongsine56 signal．Alotofsimulationexamplesaregiventoverifytheeffectivenessofthefourestimationalgorithms．AndthetwodesignsofpacketstructurebasedonthecommunicationsystemofFRFTfordifferentchannelareproposedforthevariablekmodeloftheChirpsignal．．(1)Thestructuredesignofthefirstpacket．Itiseffectivetomaketheparameterestimationperpacketpossibleinchanneloffastchange，whichgreatlyincreasethereliabilityofdatatransmission．However,itreducestransmissionefficiency．(2)Thestructuredesignofthesecondpacket．Itiseffectivetoestimatetheparametersinchannelofslowchange．Althoughtransmissionefficiencyisincreased，thereliabilityofdatatransmissioniSreduced．Withthedevelopmentofthetwonationalresearchprograms，thealgorithmspresentedinthisdissertationwillbecontinuallyrefinedandimproved，asrealizedinthefollowingtwoaspects．Theoreticalaspect：ThefractionalwaveletstransfcItinwillbeusedtoestimatethemulti—parameterofunderwateracousticchannel．Furthermore，anovelunderwaterdetectionsignalwillbeproposed．Applicationaspect：alotofseatrialsandlaketrialswillbecarriedout，andwecanverifytheeffectivenessofthefouralgorithmsandthetwopacketsthroughthesetrialsSOthatwecancontinuallypromotetheresearchontheparametersestimationofunderwateracousticchannel．57 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