几种典型的混沌吸引子

关于5G通信和无线传输的相关知识5G Mobile and wirelessCommunications TechnologyEDITED BYAFIF OSSEIRANEricssonJOSE F MONSERRATUniversitat politecnica de valenciaPATRICK MARSCHCAMBRIDGEUNIVERSITY PRESSCAMBRIDGEUNIVERSITY PRESSUniversity Printing House, Cambridge CB2 8BS, United KingdomCambridge University Press is part of the University of CambridgeIt furthers the Universitys mission by disseminating knowledge in the pursuit ofeducation learning and research at the highest international levels of excellencewww.cambridge.orgInformationonthistitlewww.cambridge.org/9781107130098C Cambridge University Press 2016This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreementsno reproduction of any part may take place without the writtenpermission of Cambridge University PressFirst published 2016Printed in the United Kingdom by TJ International Ltd. Padstow Cornwalla catalogue record for this publication is available from the british libraryLibrary of Congress Cataloguing in Publication dataOsseiran. Afif editor5G mobile and wireless communications technology /[edited by] Afif Osseiran, EricssonJose F monserrat, Polytechnic University of Valencia, Patrick Marsch, Nokia NetworksNew York: Cambridge University Press, 2016LCCN2015045732|ISBN978110713009( hardback)LCSH: Global system for mobile communications. Mobile communication systems- StandardsLCC TK5103483A152016DDC62138456dc23Lcrecordavailableathttp://icCn.loc.gov/2015045732IsBN 978-1-107-13009-8 HardbackCambridge University Press has no responsibility for the persistence or accuracy ofURLS for external or third- party internet websites referred to in this publicationand does not guarantee that any content on such websites is, or will remainaccurate or appropriateTo my new born son S, my twin sons H& N, my wife L s-y for her unwaveringencouragement, and in the memory of a great lady my aunt K eA OsseiranTo my son, the proud fifth generation of the name Jose Monserrat. And with thewarmest love to my daughter and wife, for being always there.E MonserratTo my two small sons for their continuous energetic entertainment, and my dearwife for her amazing patience and support.P MarschContentsList of contributorspage xIvForewordAcknowledgmentsXIXAcronymsXXIIIntroduction1. 1 Historical background1.1.1 Industrial and technological revolution: from steam enginesto the internet1. 1.2 Mobile communications generations: from IG to 4G1.1.3 From mobile broadband ( mbb) to extreme MBB1. 1.4 IoT: relation to 5G1.2 From ICT to the whole economy6771.3 Rationale of 5G: high data volume, twenty-five billion connecteddevices and wide requirements1.3.1 Security1.4 Global initiatives1. 4.1 METIS and the 5G-PPP1. 4.2 China: 5G promotion group2241. 4.3 Korea: 5G Forum141. 4.4 Japan: ARIB 2020 and Beyond Ad Hoc1. 4.5 Other 5G initiatives14.6 Iot activities1.5 Standardization activities445551.5.1ITU-R1.5.23GPP161.5.3 EEE161.6 Scope of the book16References185G use cases and system concept212. 1 Use cases and requirements212.1.1 Use cases212. 1.2 Requirements and key performance indicatorsContents2.2 5G system concept322.2.1 Concept overview322. 2.2 Extreme mobile broadband342.2.3 Massive machine-type communication362.2.4 Ultra-reliable machine-type communication382.2.5 Dynamic radio access network392.2.6 Lean system control plane432. 2. 7 Localized contents and traffic flows52.2.8 Spectrum toolbox2. 3 Conclusions48References48The 5g architecture503.1 Introduction503.1.1 NFV and SDN503.1.2 Basics about ran architecture533.2 High-level requirements for the 5G architecture563.3 Functional architecture and 5g flexibility573.3.1 Functional split criteria583.3.2 Functional split alternatives593.3.3 Functional optimization for specific applications3.3.4 Integration of lte and new air interface to fulfill 5Grequirements3.3.5 Enhanced Multi-RAT coordination features663. 4 Physical architecture and 5G deployment3.4.1 Deployment enablers673.4.2 Flexible function placement in 5G deployments713.5 Conclusions74References75Machine-type communications774.1 Introduction774.1.1 Use cases and categorization of mto774.1.2 MTC requirements804.2 Fundamental techniques for MTC834.2.1 Data and control for short packets834.2.2 Non-orthogonal access protocols854.3 Massive mtc864.3.1 Design principles864.3.2 Technology components864.3. 3 Summary of mMTC features944.4 Ultra-reliable low-latency MTC944.4. 1 Design principles944.4.2 Technology componentsContents4.4.3 Summary of uMTC features1014.5 Conclusions102References103Device-to-device(D2D)communications1075.1 D2D: from 4G to 5G1075.1.1 D2D standardization: 4G LTE D2D1095.1. 2 D2D in 5G: research challenges1125.2 Radio resource management for mobile broadband D2D1135.2.1 RRM techniques for mobile broadband d2d5.2.2 RRM and system design for D2D1145.2.3 5G D2D RRM concept: an example5.3 Multi-hop d2d communications for proximity and emergencyservices1205.3.1 National security and public safety requirements in 3GPPand Metis1215.3.2 Device discovery without and with network assistance125.3.3 Network-assisted multi-hop d2d communications1225.3.4 Radio resource management for multi-hop D2D1245.3.5 Performance of D2D communications in the proximitcommunications scenario1255. 4 Multi-operator d2d communication1275.4.1 Multi-operator D2D discovery275.4.2 Mode selection for multi-operator D2D1285.4.3 Spectrum allocation for multi-operator D2D295.5 Conclusions133References1346Millimeter wave communications1376. 1 Spectrum and regulations1376.2 Channel propagation1396.3 Hardware technologies for mm W systems1396.3.1 Device technology1396.3.2 Antennas1426.3.3 Beamforming architecture1436.4 Deployment scenarios6. 5 Architecture and mobility1466.5.1 Dual connectivit1476.5.2 Mobility1476.6 Beamforming1496.6. 1 Beamforming techniques1496.6.2 Beam finding1506.7 Physical layer techniques1526.7.1 Duplex scheme152

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研究了在工程中如何通过算法来实现利用 Hilbert 变换提取信号的瞬时特征。深入地分析了如何利用数值微分法提高提取瞬时频率特征的精度。最后,给出了一种可行的算法,并通过实验验证了这种方法可以在工程中有效地提取信号的瞬时频率特征。84微机发展第13卷①H(x)=y;H(x)=y;(i=0,1,…n)(j=0,1(11)②在每个小区间/x1,x1+17i=0,1,…,n-1)上由相关定理知:当划分的小区间的长度趋于零时H(x)是三次多项式。s(x)及其一至三阶导数分别一致收敛到f(x)及其一至可以写出分段三次 Hermite插值函数的分段表达式:三阶导数。所以用三次样条插值函数去近似表达用离散值(x)=(1+2x-x过+)2v;+表示的原函数,具有较高的可靠性。3)两种插值的比较挨尔米特 Hermite插值较三次样I-i,1+2条插值具有较好的稳定性与收敛性,但它只能休让各段曲线在连接点上的连续性,而不能保证整条曲线在这些点上y+1Ditl的光滑性。而有时不仅要求曲线连续,而且要求曲线的曲X/(i=0,18)率也连续即要求分段插值函数具有连续的一阶导数,埃H(x)的导数为尔米特 Hermite插值此时就不能满足上述要求6次样条插值较埃尔米特 Hermite插值具有较好的H(x光滑程度,用三次样条插值函数求数值导数比用埃尔米特+2(x-x2(xHermite插值可靠性大,但计算比较复杂,二者的区别见图h2yV+17, h(i-0,12)三次样条插值。已知函数y=f(x)在区间/a,b上的n+1个节点上的值y=f(x;)(i=0,1,…m),求插值函数s(x),使(i=0,1图4 Hermite插值与三次样条插值的比较图2在每个小区间x,x+1(=0.1.…n-1)上利用埃尔米特 Hermite插值得到的2FSK信号的瞬时s(x是三次多项式,记为s(x频率见图5,利用二次样条插值得到的该信号的瞬时频率③3(x)在la,b/上二阶连续可徵。见图6。数s(x)称为f(x)的三次样条插值函数可以利用节点处的二阶导数值为参数,也可以利用节点处的导数值为参数求三次样条插值涵数的表达式。若利用节点处的一阶导数值为参数,求得的三次样条插值函数的表达式为(x)=M-1x-x-)36 h6 hMihi5 DEMeN5a亩pai66hx∈[x;,x+17,b-x+1-x,S"(x)=M图5由 Hermite插值提取图6由三次样条插值提取(j=0,1的2FSK信号的瞬时频率的2FSK信号的瞬时频率对s(x)进行求导,利用S(x)在节点处一阶导数连从图5、图6可以看出利用三次样条插值得到的瞬时续的性质结合边界条件求解出参数M,把求得的参数代频率可以准确反映出信号具有的的摒时频率特征而利用入公式(10),即得三次样条插值函数的s(x)分段表示式。埃尔米特 Hermite插值得到的瞬时频率与信号具有的瞬s;(x)的导数为时频率特征不符。这是因为利用数值微分法求瞬时频率插值以后喫进行求导。三次样条插值函数具有连续的二阶M2 hiM; 2 hj导数,因而具有较好的光滑程度,符合求导条件,所以可以J+1-h(M2+1-M/)准确求出信号的瞬时频率;而埃尔米特 Hernite插值.不够光滑,虽能保证插值多项式收敛于原函数,但不能保证插x Elx,x;+1 h,=xi+I-x, S(xj )=M;值多顷式的导数收敛于原函数的导数,所以求得的值与信o1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreservedhttp://www.cnki.net第6期刘慧婷等:利用 Hilbert变提取信号瞵时特征的算法实现号实际的瞬时频率值不符。实验结果和理论分析结果是(1) Hilbert变换只能近似应用于窄带信号,即形如纹的(t)=a(1)cosu+6(1)),其中>>B(B为信号带2.3.3结论宽)的信号。但实际应用中,存在许多非窄带信号, Hilbcrt利用数值微分法求瞬时频率ω(t)的步骤可以归纳变换对这些信号无能为力为:首先通过三次样条插值得到分段多项式p(1),(2)对于任意给定时刻,通过 Hilbert变换运算后的结pp(抄);然后分别对分段多项式p(t),Pp()关于变量t果只能存在一个频率值,即只能处理任何时刻为单一频率进行求导,得到pd(,ppd(t);最后求出每一时刻t所对的信号。这显然不合理,因为在实东中同一信号会含有多应的导数值,即求得t(t,u(t)。再把求得的值代入公种频率成分式(6)就完成了提取瞬时频率ω(1)的过程。求解结果见(3)对信号进行 Hilbert变换时,信号的两端会出现严图7重的端点效应。提取某些信号瞬时特征所得的瞬时频率在局部出现了负数,端点效应是造成负频率的一个原因而端点效应可以通过利用特征波对原有数据序列进行延拓的方法来解决,具体解决办法将在今后讨论。尽管目前出现了EMD担论4,其目的是将不满足Hibt变换的信号进行分解得到若干个IMF( intrinsic mode function),然后进行 Hilbert运算,达到提取信号瞬时特征的目的。该理论开辟了信号处理的新空间。但它还不够成熟还需喫进一步的完善和研究图7利用数值微分法提取信号的瞬时频率特征参考文献从图7可以看出,以三次烊条指值进行的数值微分可[]黄长蓉. Hilbert变换及其应用[J].成都气象学院学报以准确岀提取岀信号的瞬时频率特征。199,14(3):273-276.[2]杨小牛,楼A义,徐建良.软件无线电原理与应用[M].北3结束语京:电子工业出版社,2001在工程中, Hilbert变换使得我们对短信号和复杂信号[3]丁丽妤.数值计算方法[M].北京:北京理工大学出版社,的摒时特征的提取成为可能特别是对瞬时频率特征提1997取,在工程中具有十公重要的意义。文中讨论的利用三次[4] Huang N e. The empirical mode decomposition and the hilbert样条插值进行数值徵分以提取瞬时特征的方法是可行的,spectrum for nonlinear and nor stationary time series anal ysis但还存在着如下问题。[].Proc.R.soc.Lond.A,1998,454:903-995(上接第81页)218994。例22(x)=(1-2siny=223101075一般的(A算法计算了120代,求到的最大值为454176.219。154370083改进的α算法计算了34代,求到的最大值为1048575.875。改进后的αA算法收敛速度(指迭代次数)比一般GA算法几乎快了一个数量级,精度也提高了不少,特别是例2的最大值提高一倍多,速度提高这么快是未曾料到的y=74958参考文献+4X Axl Thla[1]陈国良.遗传算法及其应用[M]·北京:人民邮电出版社,图2函数2的图像1996一般GA算法计算了20代,求到的最大值为[2]袁亚湘,孙文瑜.最优化理沦与方法[M]北京:科学出版社,19991.218983[3]张铃,张钹·遗传算法杋理的硏究[J]·软件学报,改进(A算法计算了5代,求到的最大值为2000,11(7):945952o1994-2010ChinaacAdemicJournalElectronicPublishingHouse.Allrightsreservedhttp://www.cnki.net

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