Cooperative Caching in Wireless Multimedia Sensor Nets

Cooperative Diversity in Wireless Networks 文献翻译————————————————————————————————作者：————————————————————————————————日期：23 无线网络的协作分集：高效协议和中断行为 摘要：我们研究和分析了低复杂度的协作分集协议用以抵抗无线网络中多径传播引起的衰落，其底层技术是利用协作终端为其他终端转发信号而获得空间分集。

我们略述几种协同通信策略,包括固定中继方法如放大-转发，译码-转发,基于协同终端间的信道估计的选择中继方式，基于目标终端的有限反馈的增量中继方式。

我们在高SNR 条件下以中断事件、相关中断概率指标讨论了其性能特征，以估计协议对传输衰落的鲁棒性。

除固定的解码—转发协议外，所有的协同分集协议就所达到的全分集（也就是在两个终端下的二阶分集）来说是高效的，而且在某些状态下更加接近于最优（小于1。

5dB ）。

因此，当用分布式天线时，我们可以不用物理阵列而提供很好的空间分集效应，但因为采用半双工工作方式要牺牲频谱效率，也可能要增加额外接收硬件的开销。

协作分集对任何无线方式都适用，包括因空间限制而不能使用物理阵列的蜂窝移动通信和无线ad hoc 网络，这些性能分析显示使用这些协议可减少能耗.索引语——分集技术，衰落信道，中断概率,中继信道，用户协同,无线网络Ⅰ 介绍在无线网络中，多径传播引起的信号衰落是一个特别严重的信道损害问题，可以利用分集技术来减小。

II 系统模型在图1中的无线信道模型中，窄带传输会产生频率非选择性衰落和附加噪声。

我们在第四部分重点分析慢衰落，在时延限制相当于信道相干时间里，用中断概率来评价，与空间分集的优势区分.虽然我们的协同协议能自然的扩展到宽频带和高移动情况,其中面临各自的频域和时域的选择性衰落，当系统采用另一种形式的分集时对我们协议的潜在影响将相对减小。

4A 媒体接入当前的无线网络中,例如蜂窝式和无线局域网，我们将有用的带宽分成正交信道，并且分配这些信道终端，使我们的协议适用于现存的网络.这种选择产生的意外效果是，我们能够同时在I —A 处理多径（单个接收）和干扰（多个接收），相当于在信号接收机传输信号的一对中继信号.对于我们所有的协同协议，传输中的必须同时处理他们接收到的信号；但是，网络实现使终端不能实现全双工，也就是,传输和接收同时在相同的频带中实现。

5G无线通信网络中英文对照外文翻译文献(文档含英文原文和中文翻译)翻译：5G无线通信网络的蜂窝结构和关键技术摘要第四代无线通信系统已经或者即将在许多国家部署。

然而，随着无线移动设备和服务的激增，仍然有一些挑战尤其是4G所不能容纳的，例如像频谱危机和高能量消耗。

无线系统设计师们面临着满足新型无线应用对高数据速率和机动性要求的持续性增长的需求，因此他们已经开始研究被期望于2020年后就能部署的第五代无线系统。

在这篇文章里面，我们提出一个有内门和外门情景之分的潜在的蜂窝结构，并且讨论了多种可行性关于5G无线通信系统的技术，比如大量的MIMO技术，节能通信，认知的广播网络和可见光通信。

面临潜在技术的未知挑战也被讨论了。

介绍信息通信技术（ICT）创新合理的使用对世界经济的提高变得越来越重要。

无线通信网络在全球ICT战略中也许是最挑剔的元素，并且支撑着很多其他的行业，它是世界上成长最快最有活力的行业之一。

欧洲移动天文台（EMO）报道2010年移动通信业总计税收1740亿欧元,从而超过了航空航天业和制药业。

无线技术的发展大大提高了人们在商业运作和社交功能方面通信和生活的能力无线移动通信的显著成就表现在技术创新的快速步伐。

从1991年二代移动通信系统(2G)的初次登场到2001年三代系统（3G）的首次起飞，无线移动网络已经实现了从一个纯粹的技术系统到一个能承载大量多媒体内容网络的转变。

4G无线系统被设计出来用来满足IMT-A技术使用IP面向所有服务的需求。

在4G系统中，先进的无线接口被用于正交频分复用技术（OFDM），多输入多输出系统（MIMO）和链路自适应技术。

4G无线网络可支持数据速率可达1Gb/s的低流度，比如流动局域无线访问，还有速率高达100M/s的高流速，例如像移动访问。

LTE系统和它的延伸系统LTE-A，作为实用的4G系统已经在全球于最近期或不久的将来部署。

然而，每年仍然有戏剧性增长数量的用户支持移动宽频带系统。

The 2004 International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC2004)Hotel Taikanso, Sendai/Matsushima, Miyagi-Pref., JAPAN July 6-8, 2004 Selective Channel Scanning for Fast Handoff in Wireless LAN using NeighborGraphHye-Soo Kim,Sang-Hee Park,Chun-Su Park,Jae-Won Kim,and Sung-Jea KoDepartment of Electronics Engineering,Korea University,Anam-Dong,Sungbuk-ku,Seoul136-701,KoreaTel.:+82-2-3290-3228,Fax.:+82-2-925-5883E-mail:sjko@dali.korea.ac.krAbstract:Handoff at the link layer2(L2)consists of threephases including scanning,authentication,and reassociation.Among the three phases,scanning is dominant in terms oftime delay.Thus,in this paper,we propose an improved scan-ning mechanism to minimize the disconnected time while awireless station(STA)changes the associated access points(APs).According to IEEE802.11,an STA has to scan allchannels in scanning.In this paper,based on the neigh-bor graph(NG),we introduce a selective channel scanning method with unicast for fast handoff in which an STA scans only channels selected by the NG.Experimental results show that the proposed method reduce the scanning delay drasti-cally.1.IntroductionIn recent years,Wireless Local Area Network(WLAN)with wide bandwidth and low cost has emerged as a competitive technology to adapt the user with strong desire for mobile computing.The main issue on mobile computing is handoff management between APs.Especially,for real-time multime-dia service such as V oIP,the problem of handoff delay has to be resolved.To solve this problem,many techniques[1]-[4] have been proposed by developing new network protocols or designing new algorithms.Their approaches are broken into three distinct categories including network layer(L3),L2,and physical layer(PHY).One of the previous works that have focused on L3uses the reactive context transfer mechanism[1],[2].This mecha-nism is designed solely for access routers(ARs)and is reac-tive rather than pro-active.On the other hand,Nakhjiri[5] proposed a general purpose context transfer mechanism, called SEAMOBY,without detailing transfer triggers.In SEAMOBY,a generic framework for either reactive or pro-active context transfer is provided,though the framework does not define a method to implement either reactive or pro-active context transfer.To reduce the L2handoff delay in WLAN using IAPP[7], an algorithm on context transfer mechanism utilizing NG[6] was suggested in[7].But originally,IAPP was only reactive in nature and creats an additional delay in an handoff.Thus, this algorithm can not shorten the original L2handoff delay. One approach on PHY is the method using two transceivers.In this method,an STA has two wireless net-work interface cards(WNICs),one for keeping connection to current AP and the other for scanning channels to search alternative APs[8].In this paper,we propose a selective channel scanning(a)(b)Figure1.Type of WLAN(a)ad hoc network(b)infrastructure network.Figure2.IEEE802.11handoff procedure with IAPP.mechanism using NG to solve the L2handoff delay.In the proposed mechanism,an STA scans not all channels but chan-nels selected by NG.And on receiving a ProbeResponse mes-sage,an STA scans the next channels without waiting for the pre-defined time.Therefore,the delay incurred during scan-ning phase can be reduced.This paper is organized as follows.Section2describes the operations in IEEE802.11[9].In Section3,the proposed algorithm is presented.Finally,Section4shows the results experimented on our test platform and presents brief conclu-sion comments.2.IEEE802.11As shown in Fig.1,IEEE802.11MAC specification allows for two modes of operation:ad hoc and infrastructure modes. In ad hoc mode,two or more STAs recognize each other through beacons and establish a peer-to-peer relationship.In infrastructure mode,an AP provides network connectivity to its associated STAs to form a Basic Service Set(BSS).Mul-tiple APs form an Extended Service Set(ESS)that constructs the same wireless network.An STA might move to another because of mobility,load conditions,or degraded signal strength.The mechanism or sequence of messages between an STA and the APs is hand-off.During the handoff,physical layer connectivity is re-leased and state information is transferred from one AP to another with respect to the STA.2.1Handoff ProcedureThe complete handoff procedure can be divided into three dis-tinct logical phases:scanning,authentication,and reassocia-tion.In thefirst phase,an STA scans for APs by either send-ing ProbeRequest messages(Active Scanning)or by listening for Beacon messages(Passive Scanning).After scanning all channels,an AP is selected by the STA using the Received Signal Strength Indication(RSSI),link quality,and etc.,and the selected AP exchanges IEEE802.11authentication mes-sages with the STA.Finally,if the AP authenticates the STA, the STA sends ReassociationRequest message to the new AP. In this phase,the old AP and new AP exchanges messages de-fined in IAPP.The delay incurred during these exchanges is referred as the L2handoff delay,that consists of probe delay, authentication delay,and reassociation delay.Fig.2shows the three phases,delays,and messages exchanged in each phase.2.2Passive and Active Scanning ModesAn STA operates in either a passive scanning mode or an active scanning mode depending on the current value of the ScanMode parameter of the MLME-SCAN.request primitive. To become a member of a particular ESS using the passive scanning,an STA scans for Beacon message containing the ESS’s Service Set Identifier(SSID)whether the Beacon mes-sage comes from an Infrastructure BSS or Independent Ba-sic Service Set(IBSS).Fig.3(a)shows exchanged messages during the active scanning.To actively scan,after contend-ing to access the medium,the STA sends a ProbeRequest message with the desired SSID and broadcast BSSID,then starts a ProbeTimer.If the STA has not received a ProbeRe-sponse message before the ProbeTimer reaches MinChannel-Time,then the STA scans the next channel.Otherwise,the STA has to wait until the ProbeTimer reaches MaxChannel-Time,then scans the next channel.Upon completion of scan-ning,an MLME-SCAN.confirm is issued by the MLME indi-cating all of the BSS information received.During active scanning,the bound of scanning delay can be calculated asN×T b≤t≤N×T t,(1)STA(a)STA(b)Figure3.Active Scanning(a)full channel scanning(b)selec-tive channelscanning.ABCED(b)Figure4.Concept of neighbor graph(a)placement of APs(b) corresponding neighbor graph with channel information.where N is the total number of channels which can used in a country,T b is MinChannelTime,T t is MaxChannelTime,and t is the total measured scanning delay.Our paper focuses on the reduction of the active scanning delay time.3.Proposed Scanning MethodBefore introducing our proposed method,we briefly review the NG.The NG is an undirected graph with each edge rep-resenting a mobility path between APs.Therefore,given an edge,the neighbors of an edge represent the set of potential next APs.Fig.4shows the physical topology of a wireless network and the corresponding NG.The undirected graph representing the NG is defined as G=(V,E),V={ap1,ap2,...,ap i},e=(ap i,ap j),N(ap i)={ap ik:ap ik∈V,(ap i,ap ik)∈E},(2)where G is the data structure of NG,V is the set containing all APs,E is the set which consists of edge(e),and N is the neighbor APs of a AP.There are two methods that the NG can be automatically generated.Thefirst one uses ReassociationRequest message from an STA that contains the BSSID of the old AP.In thefirst method,the NG is created by following algorithm by usingmanagement message of IEEE802.11.(1)If an STA sends Reassociate Request to AP i with old−ap =AP j,then create new neighbors(i,j)(i.e.an entry in AP i, for j and vice versa);(2)Learns costs only one‘high latency handoff’per edge in the graph;(3)Enables mobility of APs which can be extended to wire-less networks with an ad hoc backbone infrastructure. Secondly,a receipt of a Move-Notify message from another AP via IAPP[7]also establishes the relationship.Mishra[10]showed that scanning delay is dominant among three delay.Therefore,to solve the problem of L2 handoff delay,scanning delay has to be reduced.To reduce the scanning time,we must reduce the values of T b(MinChannelTime),T t(MaxChannelTime),or N in(1). Among three values,T b and T t can not be reduced because of physical restriction.And because the frequency ranges are subject to the geographic-specific regulatory authorities,N is fixed in each country.However,the channels which are occu-pied by APs are not same in all Basic Service Areas(BSAs)or Extended Service Areas(ESAs).Thus,if we know the used channels in each site,STAs do not need to scan all channels allowed in the country.Therefore,we propose using an NG to select the channels to be scanned.The NG proposed in [6]uses the topological information on APs.But our algo-rithm needs to use not only topological information but also channels of APs.Thus,we modify the data structure of NG defined in(2)as follows:G =(V ,E),V ={v i:v i=(ap i,channel),v i∈V},e=(ap i,ap j),N(ap i)={ap ik:ap ik∈V ,(ap i,ap ik)∈E},(3)where G is the modified NG,and V is the set which consists of APs and their channels.Assumed an STA is associated to B in Fig.4,the STA scans only4channels of its neighbors(A,C,D,E)instead of all channels.Fig.3(b)shows that an STA scans the poten-tial APs selected by NG.As shown in Fig.3(a),in order to scan channels,after transmitting ProbeRequest message whose destination is all APs,STAs must wait for MinChannelTime or MaxChannel-Time because an STA does not know how many APs wouldFigure5.Experimental platform.response to ProbeRequest message.However,if using uni-cast instead of broadcast,ProbeRequest message is sent to the potential APs selected by NG.And on receiving ProbeRe-sponse message,STAs can transmit other ProbeRequest mes-sages without waiting for MaxChannelTime or MinChannel-Time.Thus,if using the proposed scanning algorithm,scan-ning delay can be expected ast=N ×rtt+α,(4)where N is the number of the potential APs,rtt is the round trip time,andαis the message processing pared with(1),we can know that the scanning delay is reduced through the proposed algorithm.4.Experimental Results and Conclusion Figure5shows our experimental platform consisting of an STA,APs,router,and Correspondent Node(CN).To ex-change the NG information,socket interface is used,and Mo-bile IPv6is applied to maintain L3connectivity while exper-imenting.The device driver of a common WNIC was modi-fied such that the STA operates as an AP.And emulated APs perform the foreign agents on our experimental platform.To simulate the operation of proposed mechanism,we developed three programs.Fig.6shows theflow charts of the developed three programs.NG Client and Monitor are deployed at an STA,and NG Server is deployed at CN in Fig.5.We defined the scanning delay as the duration taken from thefirst ProbeRequest message to the last ProbeResponse message.To capture two kinds of messages,a sniffer pro-gram,AiroPeek,was used.To evaluate the proposed algorithm,we experimented three mechanisms:basic active scanning mechanism;selec-tive scanning;and selective scanning with unicast as increas-ing the number of neighbors.As shown in Table1,the scan-ning delay by the selective scanning is shorter than the full channel active scanning.Note that the selective scanning with unicast produces a smallest delay time among the three mech-anisms.Therefore,we expect that the proposed algorithm can be an useful alternative to the existing full channel active scanning due to its reduced delay time.(a)(b)(c) Figure6.Flow charts of simulation programs(a)NG Server(b)NG Client(c)Monitor.Table1.Average probe delay of each method. Neighbors Method delay[ms]Basic active scanning322 1Selective Scanning55Selective Scanning with Unicast12Basic active scanning322 2Selective Scanning332Selective Scanning with Unicast21Basic active scanning322 3Selective Scanning145Selective Scanning with Unicast30References[1]R.Koodli,and C.Perkins,“Fast Handovers and Context Relocation in Mobile Networks,”ACM SIGCOMM Com-puter Communication Review vol.31Oct.2001.[2]R.Koodli,“Fast Handovers for Mobile IPv6,”IETF Draft,Oct.2003.[3]T.Cornall,B.Pentland,and K.Pang“Improved Han-dover Performance in wireless Mobile IPv6,”ICCS2002 vol.2pp.857-861Nov.2003.[4]S.H.Park,and Y.H.Choi,“Fast Inter-AP Handoff Us-ing Predictive Authentication Scheme in a Public Wireless LAN,”IEEE Networks ICN,Aug.2002.[5]M.Nakhjiri,C.Perkins,and R.Koodli,“Context Transfer Protocol,”Internet Draft:draft-ietf-seamoby0ctp-01.txt Mar.2003.[6]A.Mishra,M.H.Shin,and W Albaugh,“Context Caching using Neighbor Graphs for Fast Handoff in aWireless,”Computer Science Technical Report CS-TR-4477,2003.[7]IEEE“Recommended Practice for Multi-Vendor Access Point Interoperability via an Inter-Access Point Protocol Across Distribution Systems Supporting IEEE802.1Op-eration,”IEEE Standard802.11,2003.[8]M.Ohta,“Smooth Handover over IEEE802.11Wireless LAN,”Internet Draft:draft-ohta-smooth-handover-wlan-00.txt Jun.2002.[9]IEEE“Part11:Wireless LAN Medium Access Control (MAC)and Physical Layer(PHY)Specifications,”IEEE Standard802.11,1999.[10]A.Mishra,M.H.Shin,and W.Albaugh,“An Empiri-cal Analysis of the IEEE802.11MAC Layer Handoff Pro-cess,”ACM SIGCOMM Computer Communication Review vol.3pp.93-102Apr.2003.。

基于分簇加权的认知无线电协作检测算法李涛【摘要】Cooperative detection is an important part in cognitiveradio.Through the cooperation of some cognitive users,the per⁃formance of weak detection can improve in the case of channel fading and shadow effect.Traditional cooperative detection sometimes is weak because of too many detection users and individual user’s bad channel.Moreover,each user has the same proportion in the deci⁃sion of the center,and the detection performance of the single user is often ignored.A multi⁃cluster cooperative detection algorithm based on weighing is proposed.Through giving cognitive users different weights according to their SNR,the detection probability can reach the maximum.And through dividing the uses into clusters and choosing the user with the best channel characteristic to report to the decision centre,the precision of final decision can be improved effectively. Simulations show that our algorithm has a better detection perform⁃ance,increases the detection probability,and decreases the alarm probability comparing with the traditional algorithm.%协作检测是认知无线电技术（ Cognitive Radio）的重要组成部分，通过多认知用户协作可以提高信道衰落或者阴影效应而带来的低检测性能。

Telecom Power Technology144通信网络技术无线接入和有线传输之间的协同优化李鹏江（中通服咨询设计研究院有限公司，江苏无线接入和有线传输的协同优化是当前网络领域的研究热点之一。

文章详尽分析了线传输的协同优化问题，目标在于充分发挥两者的优势，以提升整体网络性能。

分析术的特性，以及协同运作中所遭遇的挑战，将网络架构优化与传输资源调度作为核心议题。

文章重点探讨协同调度、资源分配、总体延迟优化、数据缓存与预取优化以及服务质量管理等重要策略，旨在为增强5G；协同优化；网络架构；资源调度；时延优化Cooperative Optimization Between 5G Wireless Access and Wired TransmissionLI Pengjiang(China Information Cosulating and Designing Institute Co., Ltd., NanjingAbstract: The cooperative optimization of 5G wireless access and wired transmission is a current focal point in the field of network research. This study thoroughly analyzes the challenges and opportunities of cooperative optimization大规模MIMO天线大规模MIMO天线Sub-6 Ghz 5G无缝移动NOLS5 G毫米波5 G毫米波图1 大规模MIMO技术然而，5G无线接入技术尽管拥有众多优势，但仍面临一些困境，如信号传输范围有限。

毫米波的传收稿日期：2024-01-15作者简介：李鹏江（1988—），男，陕西宝鸡人，本科，工程师，主要研究方向为传输、有线接入网。

Co-UWSN: Cooperative Energy-Efficient Protocol forUnderwater WSNsCo-UWSN：水下无线传感器网络协同高效节能协议摘要传感器网络特点主要体现在具有无线网络能力、有限的传输功率、受限制的资源和有限的电池能量的低消耗传感器器件。

协同路由利用无线介质的广播特性，并利用附近的传输节点作为继电器的协同传输。

这是一种很有前途的技术，利用协同通信来提高单天线传感器节点的通信质量。

在本文中，我们提出了一个水下传感器网络协同传输方案（UWSNs）以提高网络性能。

协同分级技术已被引入到抗衰落。

提出的协同水下传感器网络Co-UWSN对水下传感器网络来说是一个可靠地、高效节能的和高吞吐量的路由协议。

利用距离和信噪比计算信道条件作为成本函数来选择目的地和潜在的中继。

这有助于充分的减少在链路和数据传输中产生的路径损耗。

仿真结果表明Co-UWSN协议在端到端的延迟、能量损耗和网络寿命等方面表现得更好。

被选作比较的路由协议有：基于深度高效节能路由EEDBR、基于深度阈值优化的改进快递节点自适应迁移路由iAMCTD、水下传感器网络协同路由协议UWSN、协同路由笼的合作伙伴节点选择标准（Re和dth）。

1、介绍UWSN形成了一个新兴的技术，有望实现或增强海洋研究中的几个关键应用。

这些措施包括数据采集，污染监测，战术侦察和灾害防治。

不像传统的地面传感器节点，大量水下移动传感器节点的被降到兴趣集中处以形成配水生（SEA）的传感器群。

每个传感器配有一个低带宽的声学调制解调器和一个单天线。

它可以通过一个鱼形膀胱装置和一个压力计控制其深度。

该群是由水槽汇护送的，汇既是在海面上配备了声音和无线电通信装备的声呐浮标。

在一个配水生传感器群架构下SEA，每个传感器监视本地水下活动以及利用声音多次反射将关键时刻数据报告到在海水表面的任意水槽汇。

本文的主要焦点设计一个高效的路由协议，能够通过一个移动的传感器向海面上任意的一个水槽汇可靠地传输数据。

Consensus and Cooperation in Networked Multi-Agent SystemsAlgorithms that provide rapid agreement and teamwork between all participants allow effective task performance by self-organizing networked systems.By Reza Olfati-Saber,Member IEEE,J.Alex Fax,and Richard M.Murray,Fellow IEEEABSTRACT|This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow,robustness to changes in network topology due to link/node failures,time-delays,and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided.Our analysis frame-work is based on tools from matrix theory,algebraic graph theory,and control theory.We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators,flocking,formation control,fast consensus in small-world networks,Markov processes and gossip-based algo-rithms,load balancing in networks,rendezvous in space, distributed sensor fusion in sensor networks,and belief propagation.We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms.A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions.Simu-lation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations.KEYWORDS|Consensus algorithms;cooperative control; flocking;graph Laplacians;information fusion;multi-agent systems;networked control systems;synchronization of cou-pled oscillators I.INTRODUCTIONConsensus problems have a long history in computer science and form the foundation of the field of distributed computing[1].Formal study of consensus problems in groups of experts originated in management science and statistics in1960s(see DeGroot[2]and references therein). The ideas of statistical consensus theory by DeGroot re-appeared two decades later in aggregation of information with uncertainty obtained from multiple sensors1[3]and medical experts[4].Distributed computation over networks has a tradition in systems and control theory starting with the pioneering work of Borkar and Varaiya[5]and Tsitsiklis[6]and Tsitsiklis,Bertsekas,and Athans[7]on asynchronous asymptotic agreement problem for distributed decision-making systems and parallel computing[8].In networks of agents(or dynamic systems),B con-sensus[means to reach an agreement regarding a certain quantity of interest that depends on the state of all agents.A B consensus algorithm[(or protocol)is an interaction rule that specifies the information exchange between an agent and all of its neighbors on the network.2 The theoretical framework for posing and solving consensus problems for networked dynamic systems was introduced by Olfati-Saber and Murray in[9]and[10] building on the earlier work of Fax and Murray[11],[12]. The study of the alignment problem involving reaching an agreement V without computing any objective functions V appeared in the work of Jadbabaie et al.[13].Further theoretical extensions of this work were presented in[14] and[15]with a look toward treatment of directed infor-mation flow in networks as shown in Fig.1(a).Manuscript received August8,2005;revised September7,2006.This work was supported in part by the Army Research Office(ARO)under Grant W911NF-04-1-0316. R.Olfati-Saber is with Dartmouth College,Thayer School of Engineering,Hanover,NH03755USA(e-mail:olfati@).J.A.Fax is with Northrop Grumman Corp.,Woodland Hills,CA91367USA(e-mail:alex.fax@).R.M.Murray is with the California Institute of Technology,Control and Dynamical Systems,Pasadena,CA91125USA(e-mail:murray@).Digital Object Identifier:10.1109/JPROC.2006.8872931This is known as sensor fusion and is an important application of modern consensus algorithms that will be discussed later.2The term B nearest neighbors[is more commonly used in physics than B neighbors[when applied to particle/spin interactions over a lattice (e.g.,Ising model).Vol.95,No.1,January2007|Proceedings of the IEEE2150018-9219/$25.00Ó2007IEEEThe common motivation behind the work in [5],[6],and [10]is the rich history of consensus protocols in com-puter science [1],whereas Jadbabaie et al.[13]attempted to provide a formal analysis of emergence of alignment in the simplified model of flocking by Vicsek et al.[16].The setup in [10]was originally created with the vision of de-signing agent-based amorphous computers [17],[18]for collaborative information processing in ter,[10]was used in development of flocking algorithms with guaranteed convergence and the capability to deal with obstacles and adversarial agents [19].Graph Laplacians and their spectral properties [20]–[23]are important graph-related matrices that play a crucial role in convergence analysis of consensus and alignment algo-rithms.Graph Laplacians are an important point of focus of this paper.It is worth mentioning that the second smallest eigenvalue of graph Laplacians called algebraic connectivity quantifies the speed of convergence of consensus algo-rithms.The notion of algebraic connectivity of graphs has appeared in a variety of other areas including low-density parity-check codes (LDPC)in information theory and com-munications [24],Ramanujan graphs [25]in number theory and quantum chaos,and combinatorial optimization prob-lems such as the max-cut problem [21].More recently,there has been a tremendous surge of interest V among researchers from various disciplines of engineering and science V in problems related to multia-gent networked systems with close ties to consensus prob-lems.This includes subjects such as consensus [26]–[32],collective behavior of flocks and swarms [19],[33]–[37],sensor fusion [38]–[40],random networks [41],[42],syn-chronization of coupled oscillators [42]–[46],algebraic connectivity 3of complex networks [47]–[49],asynchro-nous distributed algorithms [30],[50],formation control for multirobot systems [51]–[59],optimization-based co-operative control [60]–[63],dynamic graphs [64]–[67],complexity of coordinated tasks [68]–[71],and consensus-based belief propagation in Bayesian networks [72],[73].A detailed discussion of selected applications will be pre-sented shortly.In this paper,we focus on the work described in five key papers V namely,Jadbabaie,Lin,and Morse [13],Olfati-Saber and Murray [10],Fax and Murray [12],Moreau [14],and Ren and Beard [15]V that have been instrumental in paving the way for more recent advances in study of self-organizing networked systems ,or swarms .These networked systems are comprised of locally interacting mobile/static agents equipped with dedicated sensing,computing,and communication devices.As a result,we now have a better understanding of complex phenomena such as flocking [19],or design of novel information fusion algorithms for sensor networks that are robust to node and link failures [38],[72]–[76].Gossip-based algorithms such as the push-sum protocol [77]are important alternatives in computer science to Laplacian-based consensus algorithms in this paper.Markov processes establish an interesting connection between the information propagation speed in these two categories of algorithms proposed by computer scientists and control theorists [78].The contribution of this paper is to present a cohesive overview of the key results on theory and applications of consensus problems in networked systems in a unified framework.This includes basic notions in information consensus and control theoretic methods for convergence and performance analysis of consensus protocols that heavily rely on matrix theory and spectral graph theory.A byproduct of this framework is to demonstrate that seem-ingly different consensus algorithms in the literature [10],[12]–[15]are closely related.Applications of consensus problems in areas of interest to researchers in computer science,physics,biology,mathematics,robotics,and con-trol theory are discussed in this introduction.A.Consensus in NetworksThe interaction topology of a network of agents is rep-resented using a directed graph G ¼ðV ;E Þwith the set of nodes V ¼f 1;2;...;n g and edges E V ÂV .TheFig.1.Two equivalent forms of consensus algorithms:(a)a networkof integrator agents in which agent i receives the state x j of its neighbor,agent j ,if there is a link ði ;j Þconnecting the two nodes;and (b)the block diagram for a network of interconnecteddynamic systems all with identical transfer functions P ðs Þ¼1=s .The collective networked system has a diagonal transfer function and is a multiple-input multiple-output (MIMO)linear system.3To be defined in Section II-A.Olfati-Saber et al.:Consensus and Cooperation in Networked Multi-Agent Systems216Proceedings of the IEEE |Vol.95,No.1,January 2007neighbors of agent i are denoted by N i ¼f j 2V :ði ;j Þ2E g .According to [10],a simple consensus algorithm to reach an agreement regarding the state of n integrator agents with dynamics _x i ¼u i can be expressed as an n th-order linear system on a graph_x i ðt Þ¼X j 2N ix j ðt ÞÀx i ðt ÞÀÁþb i ðt Þ;x i ð0Þ¼z i2R ;b i ðt Þ¼0:(1)The collective dynamics of the group of agents following protocol (1)can be written as_x ¼ÀLx(2)where L ¼½l ij is the graph Laplacian of the network and itselements are defined as follows:l ij ¼À1;j 2N i j N i j ;j ¼i :&(3)Here,j N i j denotes the number of neighbors of node i (or out-degree of node i ).Fig.1shows two equivalent forms of the consensus algorithm in (1)and (2)for agents with a scalar state.The role of the input bias b in Fig.1(b)is defined later.According to the definition of graph Laplacian in (3),all row-sums of L are zero because of P j l ij ¼0.Therefore,L always has a zero eigenvalue 1¼0.This zero eigenvalues corresponds to the eigenvector 1¼ð1;...;1ÞT because 1belongs to the null-space of L ðL 1¼0Þ.In other words,an equilibrium of system (2)is a state in the form x üð ;...; ÞT ¼ 1where all nodes agree.Based on ana-lytical tools from algebraic graph theory [23],we later show that x Ãis a unique equilibrium of (2)(up to a constant multiplicative factor)for connected graphs.One can show that for a connected network,the equilibrium x üð ;...; ÞT is globally exponentially stable.Moreover,the consensus value is ¼1=n P i z i that is equal to the average of the initial values.This im-plies that irrespective of the initial value of the state of each agent,all agents reach an asymptotic consensus regarding the value of the function f ðz Þ¼1=n P i z i .While the calculation of f ðz Þis simple for small net-works,its implications for very large networks is more interesting.For example,if a network has n ¼106nodes and each node can only talk to log 10ðn Þ¼6neighbors,finding the average value of the initial conditions of the nodes is more complicated.The role of protocol (1)is to provide a systematic consensus mechanism in such a largenetwork to compute the average.There are a variety of functions that can be computed in a similar fashion using synchronous or asynchronous distributed algorithms (see [10],[28],[30],[73],and [76]).B.The f -Consensus Problem and Meaning of CooperationTo understand the role of cooperation in performing coordinated tasks,we need to distinguish between un-constrained and constrained consensus problems.An unconstrained consensus problem is simply the alignment problem in which it suffices that the state of all agents asymptotically be the same.In contrast,in distributed computation of a function f ðz Þ,the state of all agents has to asymptotically become equal to f ðz Þ,meaning that the consensus problem is constrained.We refer to this con-strained consensus problem as the f -consensus problem .Solving the f -consensus problem is a cooperative task and requires willing participation of all the agents.To demonstrate this fact,suppose a single agent decides not to cooperate with the rest of the agents and keep its state unchanged.Then,the overall task cannot be performed despite the fact that the rest of the agents reach an agree-ment.Furthermore,there could be scenarios in which multiple agents that form a coalition do not cooperate with the rest and removal of this coalition of agents and their links might render the network disconnected.In a dis-connected network,it is impossible for all nodes to reach an agreement (unless all nodes initially agree which is a trivial case).From the above discussion,cooperation can be infor-mally interpreted as B giving consent to providing one’s state and following a common protocol that serves the group objective.[One might think that solving the alignment problem is not a cooperative task.The justification is that if a single agent (called a leader)leaves its value unchanged,all others will asymptotically agree with the leader according to the consensus protocol and an alignment is reached.However,if there are multiple leaders where two of whom are in disagreement,then no consensus can be asymptot-ically reached.Therefore,alignment is in general a coop-erative task as well.Formal analysis of the behavior of systems that involve more than one type of agent is more complicated,partic-ularly,in presence of adversarial agents in noncooperative games [79],[80].The focus of this paper is on cooperative multi-agent systems.C.Iterative Consensus and Markov ChainsIn Section II,we show how an iterative consensus algorithm that corresponds to the discrete-time version of system (1)is a Markov chainðk þ1Þ¼ ðk ÞP(4)Olfati-Saber et al.:Consensus and Cooperation in Networked Multi-Agent SystemsVol.95,No.1,January 2007|Proceedings of the IEEE217with P ¼I À L and a small 90.Here,the i th element of the row vector ðk Þdenotes the probability of being in state i at iteration k .It turns out that for any arbitrary graph G with Laplacian L and a sufficiently small ,the matrix P satisfies the property Pj p ij ¼1with p ij !0;8i ;j .Hence,P is a valid transition probability matrix for the Markov chain in (4).The reason matrix theory [81]is so widely used in analysis of consensus algorithms [10],[12]–[15],[64]is primarily due to the structure of P in (4)and its connection to graphs.4There are interesting connections between this Markov chain and the speed of information diffusion in gossip-based averaging algorithms [77],[78].One of the early applications of consensus problems was dynamic load balancing [82]for parallel processors with the same structure as system (4).To this date,load balancing in networks proves to be an active area of research in computer science.D.ApplicationsMany seemingly different problems that involve inter-connection of dynamic systems in various areas of science and engineering happen to be closely related to consensus problems for multi-agent systems.In this section,we pro-vide an account of the existing connections.1)Synchronization of Coupled Oscillators:The problem of synchronization of coupled oscillators has attracted numer-ous scientists from diverse fields including physics,biology,neuroscience,and mathematics [83]–[86].This is partly due to the emergence of synchronous oscillations in coupled neural oscillators.Let us consider the generalized Kuramoto model of coupled oscillators on a graph with dynamics_i ¼ Xj 2N isin ð j À i Þþ!i (5)where i and !i are the phase and frequency of the i thoscillator.This model is the natural nonlinear extension of the consensus algorithm in (1)and its linearization around the aligned state 1¼...¼ n is identical to system (2)plus a nonzero input bias b i ¼ð!i À"!Þ= with "!¼1=n P i !i after a change of variables x i ¼ð i À"!t Þ= .In [43],Sepulchre et al.show that if is sufficiently large,then for a network with all-to-all links,synchroni-zation to the aligned state is globally achieved for all ini-tial states.Recently,synchronization of networked oscillators under variable time-delays was studied in [45].We believe that the use of convergence analysis methods that utilize the spectral properties of graph Laplacians willshed light on performance and convergence analysis of self-synchrony in oscillator networks [42].2)Flocking Theory:Flocks of mobile agents equipped with sensing and communication devices can serve as mobile sensor networks for massive distributed sensing in an environment [87].A theoretical framework for design and analysis of flocking algorithms for mobile agents with obstacle-avoidance capabilities is developed by Olfati-Saber [19].The role of consensus algorithms in particle-based flocking is for an agent to achieve velocity matching with respect to its neighbors.In [19],it is demonstrated that flocks are networks of dynamic systems with a dynamic topology.This topology is a proximity graph that depends on the state of all agents and is determined locally for each agent,i.e.,the topology of flocks is a state-dependent graph.The notion of state-dependent graphs was introduced by Mesbahi [64]in a context that is independent of flocking.3)Fast Consensus in Small-Worlds:In recent years,network design problems for achieving faster consensus algorithms has attracted considerable attention from a number of researchers.In Xiao and Boyd [88],design of the weights of a network is considered and solved using semi-definite convex programming.This leads to a slight increase in algebraic connectivity of a network that is a measure of speed of convergence of consensus algorithms.An alternative approach is to keep the weights fixed and design the topology of the network to achieve a relatively high algebraic connectivity.A randomized algorithm for network design is proposed by Olfati-Saber [47]based on random rewiring idea of Watts and Strogatz [89]that led to creation of their celebrated small-world model .The random rewiring of existing links of a network gives rise to considerably faster consensus algorithms.This is due to multiple orders of magnitude increase in algebraic connectivity of the network in comparison to a lattice-type nearest-neighbort graph.4)Rendezvous in Space:Another common form of consensus problems is rendezvous in space [90],[91].This is equivalent to reaching a consensus in position by a num-ber of agents with an interaction topology that is position induced (i.e.,a proximity graph).We refer the reader to [92]and references therein for a detailed discussion.This type of rendezvous is an unconstrained consensus problem that becomes challenging under variations in the network topology.Flocking is somewhat more challenging than rendezvous in space because it requires both interagent and agent-to-obstacle collision avoidance.5)Distributed Sensor Fusion in Sensor Networks:The most recent application of consensus problems is distrib-uted sensor fusion in sensor networks.This is done by posing various distributed averaging problems require to4In honor of the pioneering contributions of Oscar Perron (1907)to the theory of nonnegative matrices,were refer to P as the Perron Matrix of graph G (See Section II-C for details).Olfati-Saber et al.:Consensus and Cooperation in Networked Multi-Agent Systems218Proceedings of the IEEE |Vol.95,No.1,January 2007implement a Kalman filter [38],[39],approximate Kalman filter [74],or linear least-squares estimator [75]as average-consensus problems .Novel low-pass and high-pass consensus filters are also developed that dynamically calculate the average of their inputs in sensor networks [39],[93].6)Distributed Formation Control:Multivehicle systems are an important category of networked systems due to their commercial and military applications.There are two broad approaches to distributed formation control:i)rep-resentation of formations as rigid structures [53],[94]and the use of gradient-based controls obtained from their structural potentials [52]and ii)representation of form-ations using the vectors of relative positions of neighboring vehicles and the use of consensus-based controllers with input bias.We discuss the later approach here.A theoretical framework for design and analysis of distributed controllers for multivehicle formations of type ii)was developed by Fax and Murray [12].Moving in formation is a cooperative task and requires consent and collaboration of every agent in the formation.In [12],graph Laplacians and matrix theory were extensively used which makes one wonder whether relative-position-based formation control is a consensus problem.The answer is yes.To see this,consider a network of self-interested agents whose individual desire is to minimize their local cost U i ðx Þ¼Pj 2N i k x j Àx i Àr ij k 2via a distributed algorithm (x i is the position of vehicle i with dynamics _x i ¼u i and r ij is a desired intervehicle relative-position vector).Instead,if the agents use gradient-descent algorithm on the collective cost P n i ¼1U i ðx Þusing the following protocol:_x i ¼Xj 2N iðx j Àx i Àr ij Þ¼Xj 2N iðx j Àx i Þþb i (6)with input bias b i ¼Pj 2N i r ji [see Fig.1(b)],the objective of every agent will be achieved.This is the same as the consensus algorithm in (1)up to the nonzero bias terms b i .This nonzero bias plays no role in stability analysis of sys-tem (6).Thus,distributed formation control for integrator agents is a consensus problem.The main contribution of the work by Fax and Murray is to extend this scenario to the case where all agents are multiinput multioutput linear systems _x i ¼Ax i þBu i .Stability analysis of relative-position-based formation control for multivehicle systems is extensively covered in Section IV.E.OutlineThe outline of the paper is as follows.Basic concepts and theoretical results in information consensus are presented in Section II.Convergence and performance analysis of consensus on networks with switching topology are given in Section III.A theoretical framework for cooperative control of formations of networked multi-vehicle systems is provided in Section IV.Some simulationresults related to consensus in complex networks including small-worlds are presented in Section V.Finally,some concluding remarks are stated in Section VI.RMATION CONSENSUSConsider a network of decision-making agents with dynamics _x i ¼u i interested in reaching a consensus via local communication with their neighbors on a graph G ¼ðV ;E Þ.By reaching a consensus,we mean asymptot-ically converging to a one-dimensional agreement space characterized by the following equation:x 1¼x 2¼...¼x n :This agreement space can be expressed as x ¼ 1where 1¼ð1;...;1ÞT and 2R is the collective decision of the group of agents.Let A ¼½a ij be the adjacency matrix of graph G .The set of neighbors of a agent i is N i and defined byN i ¼f j 2V :a ij ¼0g ;V ¼f 1;...;n g :Agent i communicates with agent j if j is a neighbor of i (or a ij ¼0).The set of all nodes and their neighbors defines the edge set of the graph as E ¼fði ;j Þ2V ÂV :a ij ¼0g .A dynamic graph G ðt Þ¼ðV ;E ðt ÞÞis a graph in which the set of edges E ðt Þand the adjacency matrix A ðt Þare time-varying.Clearly,the set of neighbors N i ðt Þof every agent in a dynamic graph is a time-varying set as well.Dynamic graphs are useful for describing the network topology of mobile sensor networks and flocks [19].It is shown in [10]that the linear system_x i ðt Þ¼Xj 2N ia ij x j ðt ÞÀx i ðt ÞÀÁ(7)is a distributed consensus algorithm ,i.e.,guarantees con-vergence to a collective decision via local interagent interactions.Assuming that the graph is undirected (a ij ¼a ji for all i ;j ),it follows that the sum of the state of all nodes is an invariant quantity,or P i _xi ¼0.In particular,applying this condition twice at times t ¼0and t ¼1gives the following result¼1n Xix i ð0Þ:In other words,if a consensus is asymptotically reached,then necessarily the collective decision is equal to theOlfati-Saber et al.:Consensus and Cooperation in Networked Multi-Agent SystemsVol.95,No.1,January 2007|Proceedings of the IEEE219average of the initial state of all nodes.A consensus algo-rithm with this specific invariance property is called an average-consensus algorithm [9]and has broad applications in distributed computing on networks (e.g.,sensor fusion in sensor networks).The dynamics of system (7)can be expressed in a compact form as_x ¼ÀLx(8)where L is known as the graph Laplacian of G .The graph Laplacian is defined asL ¼D ÀA(9)where D ¼diag ðd 1;...;d n Þis the degree matrix of G with elements d i ¼Pj ¼i a ij and zero off-diagonal elements.By definition,L has a right eigenvector of 1associated with the zero eigenvalue 5because of the identity L 1¼0.For the case of undirected graphs,graph Laplacian satisfies the following sum-of-squares (SOS)property:x T Lx ¼12Xði ;j Þ2Ea ij ðx j Àx i Þ2:(10)By defining a quadratic disagreement function as’ðx Þ¼12x T Lx(11)it becomes apparent that algorithm (7)is the same as_x ¼Àr ’ðx Þor the gradient-descent algorithm.This algorithm globallyasymptotically converges to the agreement space provided that two conditions hold:1)L is a positive semidefinite matrix;2)the only equilibrium of (7)is 1for some .Both of these conditions hold for a connected graph and follow from the SOS property of graph Laplacian in (10).Therefore,an average-consensus is asymptotically reached for all initial states.This fact is summarized in the following lemma.Lemma 1:Let G be a connected undirected graph.Then,the algorithm in (7)asymptotically solves an average-consensus problem for all initial states.A.Algebraic Connectivity and Spectral Propertiesof GraphsSpectral properties of Laplacian matrix are instrumen-tal in analysis of convergence of the class of linear consensus algorithms in (7).According to Gershgorin theorem [81],all eigenvalues of L in the complex plane are located in a closed disk centered at Áþ0j with a radius of Á¼max i d i ,i.e.,the maximum degree of a graph.For undirected graphs,L is a symmetric matrix with real eigenvalues and,therefore,the set of eigenvalues of L can be ordered sequentially in an ascending order as0¼ 1 2 ÁÁÁ n 2Á:(12)The zero eigenvalue is known as the trivial eigenvalue of L .For a connected graph G , 290(i.e.,the zero eigenvalue is isolated).The second smallest eigenvalue of Laplacian 2is called algebraic connectivity of a graph [20].Algebraic connectivity of the network topology is a measure of performance/speed of consensus algorithms [10].Example 1:Fig.2shows two examples of networks of integrator agents with different topologies.Both graphs are undirected and have 0–1weights.Every node of the graph in Fig.2(a)is connected to its 4nearest neighbors on a ring.The other graph is a proximity graph of points that are distributed uniformly at random in a square.Every node is connected to all of its spatial neighbors within a closed ball of radius r 90.Here are the important degree information and Laplacian eigenvalues of these graphsa Þ 1¼0; 2¼0:48; n ¼6:24;Á¼4b Þ 1¼0; 2¼0:25; n ¼9:37;Á¼8:(13)In both cases, i G 2Áfor all i .B.Convergence Analysis for Directed Networks The convergence analysis of the consensus algorithm in (7)is equivalent to proving that the agreement space characterized by x ¼ 1; 2R is an asymptotically stable equilibrium of system (7).The stability properties of system (7)is completely determined by the location of the Laplacian eigenvalues of the network.The eigenvalues of the adjacency matrix are irrelevant to the stability analysis of system (7),unless the network is k -regular (all of its nodes have the same degree k ).The following lemma combines a well-known rank property of graph Laplacians with Gershgorin theorem to provide spectral characterization of Laplacian of a fixed directed network G .Before stating the lemma,we need to define the notion of strong connectivity of graphs.A graph5These properties were discussed earlier in the introduction for graphs with 0–1weights.Olfati-Saber et al.:Consensus and Cooperation in Networked Multi-Agent Systems220Proceedings of the IEEE |Vol.95,No.1,January 2007。

论文集锦We ig h t e d Ha r d Co m b in a t io n fo rCo o p e r a t ive S p e c t r u m S e n s in g in Co g n it ive R a d io Ne t w o r k sLi Jia jun1,2,Tan Zhe nhui1,2,Ai Bo1,Y ang Shan11State Key Laboratory of Rail Traf c Contro l and Safety,Beijing Jiaotong Univers ity,Beijing100044,P.R.China2Research Institute of Broadband Wireles s Mobile Co mmun ications,Beijing Jiaotong Univers ity,Beijing100044, P.R.ChinaAbstr act:Weighted one bit hard combination for cooperative spectrum sensing is proposed in this paper.Two thresholds are adopted to divide the possible energy value into three weighted regions. If the energy value falls into the corresponding region,it will be judged as“1”,no information or“0”.When the pr obability of false alar m is constrained to be constant,the objective is to maximize the probability of detection.The optimization problem is simplified by separating th e weight of the mid dle region into sever al intervals.Simulation results show that the sensing perfor mance of the proposed scheme is much better than that of the traditional one bit har d combination scheme and almost the same as that of the equal gain combination(EGC)scheme. Moreover,compared with the traditional one bit hard combination,fewer average sensing bits are required to transmit to the data fusion center with the proposed method.Key wor ds:cognitive radio;cooperative spectrum sensing;har d combination;the pr obability of detection I.INTRODUCTIONCognitive radio(CR)is a promising technique to improve the spectral efficiency of the wireless netwo rks[1].As one of the mo st impor tant com ponents of CR,spectrum sensing enables the secondary users to adapt to the environment by detecting the spectrum holes without causing interference to the primary network.C oo per ativ e sp ectr um s ensin g h as been proposed as a solution to combat the multipath fading or shadowing effects[2-4].Information from the cooperative secondary users is combined in the fusion centre to make the final decision. Traditional one-bit hard decision for cooperative spectrum sensing has been investigated in[3-5], in which secondary users exchange only one-bit decisions rather than the sensing statistics.Soft combination in cooperative spectrum sensing has been proposed in[6-7],which outperforms one-bit hard decision.However,the soft combination scheme requires much more overhead,e.g.the perf ect channel state inf ormation between theprimary users and secondary users are required for the maximum ratio combination(MRC).Double-threshold energy detection has been studied in [9-11].In[9],only the secondary uses with enough information send their local1-bit decisions to the data fusion centre.As a result,the average sen sing bits decr eases at the expense of the sensing performance loss.Re-detection is needed when the energy detection value falls into the middle region[10].Therefore the sensing period will last a long time to achieve a good detection performance.In[11],only the secondar y user with the highest energy detection value makes the decision using the conventional energy detection method if all the cooperative secondary detection values fall into the middle region.Otherwise,the sensing process is the same as[9].However,it is not realistic to assume that the data fusion centre knows the highest energy detection value and the sensing performance is almost the same as that of the traditional one-bit hard combination when the probability of false alarm is larger than0.001.I n this pap er,the weig hted on e bit har d combination scheme f or cooperative spectrum sensing is proposed.Two thresholds are adopted to divide the observation energy value into three weighted regions:“1”and“0”or no information. The corresponding weights of each region and the thresholds are joined optimized to maximum the probability of detection in the fusion centre. The weight of the middle region is separated into several in tervals to simplify the optimization pr ob lem.Sim ulation r es ults sho w that ou r proposed scheme has much better performance than that of the traditional one-bit hard scheme. Meanwhile the average sensing bit of our proposed method is the same as that of[9]with the same double thr esholds.And the prop osed scheme exhibits almost the same performance as the EGC scheme.The rest of this paper is organized as follows:In Section II.the weighted one bit hard combination scheme is proposed and system perf ormance is evaluated analytically.Numerical results are presented and compared with the traditional one bit hard combination and EGC schemes in Section III.Finally,Section IV concludes the paper.II.SYSTEM MODELA.Local Spectr um Sensin gThe binary hypothesis test for spectrum sensing at the nth time instant is formulated as:1:()():()()()H r n w nH r n x n w n==+(1) where r(n)is the signal to be detected,x(n)is theprimary signal with powerσx2,and()w n is the complex additive white Gaussian noise(AWGN)with zero-mean and varianceσn2.Without loss of generality,it is assumed that all the powers of thelocal noise are the same andσn2is normalized to be1.Hand H1denote the hypotheses corresponding to the absence and presence of the primary signal respectively.The local decision statistic is given by21|()|MnS r n==∑(2) where M is the number of samples.When there is only noise present,21|()|MnS w n==∑(3) Then the prob ability of f alse alarm can be expressed as[8](,)22()()2fMP P SMλΓλΓ=>=(4) where(,)Γis the incomplete gamma function,()Γis the gamma f unction andλis the final threshold of the local detector to decide whether there is a primary user present.When there is primary signal present,211|()()|MnS x n w n===+∑(5)The probability of detection can be expressed as [12,Eq.2.1-124]论文集锦12()(2,)d M P P S Q M λγλ=>=(6)where 222/2/2x n xγσσσ==denotes th e signal to no is e r atio (SNR ),221()/2(,)(/)m x a m bQ a b x x a e ∞+=∫1()d m I ax x is the generalized Marcum ’s Q function and 1()m I denotes the modi ed Bessel function of the rst kind.In a fading channel,we have()()d d d P P f γγγγ′=∫(7)where ()f γis the probability density function(PDF)of SNR.B.Cooper ative Spectr um Sensin gSuppose there are N secondary users to perform cooperative spectrum sensing.As shown in Figure 1,two thresholds (12,λλ)are designed for one-bit hard combination of the proposed cooperative spectrum sensing,which divides the whole range of the decision statistic of the local spectrum sensing into three regions.The following weights are adopted in our proposed scheme:ω0=0,ω1,ω2=1.In the fusion centre,if the energy value falls into the corresponding region,it will be judged as "1",no information or "0".And the decision rule adopted is given by211110N N D other wiseω+= (8)where 1N is the number of local detectors the energies of which are greater than 1λand less than 2λ,2N is the number of local detectors the energies of which are greater than 2λ.Obviously,1ωshould be more than 11/N and less than 1.1λ2λ1ω12=ω00=ωFig.1the structure of the weighted cooperativespectrum sensing with two thresholdsLet 2f Q be the probability that one or mor e observation local energy values are greater than 2λand 1f Q be the probability that more th an 111/N ω=%observation local energy values ar e greater than 1λand less than 2λ.Here,x is the largest integer that is no more than x .W e have22021(0|)1(1)Nf f Q P N H P ===(9)111201012212(0|)(|)()(1)(1)Nf j N jNf f Nf j N Njf f Q P N H P Nj H NP P j P P P ======+∑∑%%(10)where f n P is the probability that the local energyvalue is greater than n λand according to (4)0(,)22()()2n fn n M P P S M λΓλ=>=ΓΓ(11)We have12(,())22n fn M MP λΓ=Γ(12)where Γ-1(,)denotes the inverse of the incompletegamma function.Then the probability of false alarm in the fusion centre can be expressed as12f f f Q Q Q =+(13)Suppose all the channels between the primaryu ser and s eco nd ary user s are ind epen dent identically distributed.The probability of detection in the fusion centre can be expressed as12212121(1)(1)()(1)N Nd d d Nj Njd d d d j N Q P P N P P P P j==++∑%(14)where dn P is the probability that the local energyvalue is greater than n λwhen there is primary present according to (6)and (7).Therefore,the objective of the sensing problem is to find the optimal ω1,λ1and λ2to maximize d Q .In CR systems,the probability of false alarmQ f is designed to be constant.So the optimization problem can be formulated as121,,121{(,,)}max d Q λλωλλω(15)Subject to12f f f Q Q Q +=(16)11/1N ω≤<≤(17)2101f f P P <<<(18)As described above,when the number of the cooperative users N is fixed,1ωcan be divided into N-1intervals,each interval optimization problem can be written as,max 12max{(,)},2,,di di i i Q Q i N λλ==L (19)Subject to12f i f i f Q Q Q +=(20)11/1/(1)ii ω<(21)1N i =%(22)2101f i f i P P <<<(23)According to (9)-(13)and (20),1i λcan be written as a function of 2i λ,i.e.12()i i f λλ=.Then thereis only one variable to maximize 12(,)d i i i Q λλ.Although it is hard to get the analytical form of 2()i f λespecially when N is very large,1i λcan be obtained by finding the root of (20)for a given 2i λ.Therefore the optimal threshold and weight are derived by searching,which can be done of ine in practice.If the thresholds are selected r andomly,the probability of detection of the proposed scheme may be even worse than the traditional one-bit hard combination.The optimal thresholds of each interval are searched as follows:1)Choose initial 2()f i Q k =,k=1.2)Calculate 2()i k λaccording to (9),(11)and (12).3)Calculate 1()i k λaccording to (10)-(13).4)Ob tain ()di Q k accord ing to (14)or thesimulation.5)Let 22(1)()f i f i Q k Q k +=+.If 2(1)f i Q k +<f Q ,k=k+1,go to step 2.Else,nd ,max di Q .After getting each local maximum ,max di Q ,i =2,…,N,the global optimum of the probability of detection ismax 2,max ,max max{,,}d d dN D Q D =L (24)Let 00{}P P H =and 11{}P P H =.The average number of the sensing bits can be calculated as:100110111111(()|)(1(()|))(()|)(1(()|))l Navg l Nll Nl NlNlP N N l H K P lP N N l H NlP N N l H P lP N N l H ======+=∑∑(25)Consequently,the normalized average numberof sensing bit is010********{|}{|}avgK K P P S H NP P S H λλλλ==<<<<(26)where 1λand 2λare the optimal thresholds of ourproposed scheme.III.SIMULA TION RESULTSI n or der to illustr ate our theoretical r esults,computer simulations are carried out.The number of cooperative secondary users and the number of samples adopted are N=4and M=100.“OR ”rule is employed for the traditional one-bit hard combination.The equal gain combination (EGC)[7]is employed for the soft combination.It is assumed that the fading coef cient of the primary signal keeps constant during the energy detection progress.Figure 2and Figure 3show the probability of missed detection vs.average SNR over Rayleigh channels for the proposed weighted one-bit hard combination,traditional one-bit hard combination and EGC schemes when the probability of false alarm Q f is equal to 0.01and 0.05respectively.论文集锦Th e o ptimal thr esho lds and weigh t 1ωare obtain ed numerically as descr ibed in Section II,which can be done offline in practice.It is shown that o ur pr opo sed scheme has m uch better performance than the traditional one-bit hard combination scheme and approaches to the EGC scheme.When Q f is constrained higher,the performance of the proposed method is closer to the EGC scheme.Table I Optimal thresholds under Rayleigh channelsSNR(dB)-15-10-50Q f =0.05λ1120.440120.911120.496120.849Q f =0.05λ2140.123138.991139.971139.123Q f =0.01λ1127.558127.675127.920127.125Q f =0.01λ2149.173148.917148.437150.327Table I lists the optimal thresholds and 1N %of ourproposed scheme over Rayleigh channels.Then the theoretical probability of false alarm Q f can be obtained from (9),(10)and (12).Fig.4presents the-15-12-9-6-3010-310-210-110Averag e SNR (dB)th e p r o b o b i l i t y o f m i s s e d d e t e c t i o n 1-Q dWeighte d 1-bitTraditiona l1-b it EGCFig.2Q m Vs.average SNR under Rayleighchannels when Q f =0.01-15-12-9-6-3010-410-310-210-110Averag e SNR (dB)th e p r o b o b i l i t y o f m i s s e d d e t e c t i o n 1-Q dWeighted 1-bitTrad itio nal 1-bit E GCFig.3Q m Vs.average SNR under Rayleighchannelswhen Q f =0.05-15-10-500.010.020.030.040.050.06S N R(dB)Q fthe or y Q f =0.05sim ula tion Q f =0.05the or y Q f =0.01sim ula tion Q f =0.01Fig.4Theoretical and simulated Q f with the optimalthresholds over Rayleigh channels-15-12-9-6-3010-410-310-210-110Ave ra ge SNR (dB)t h e p r o b o b i l i t y o f m i s s e d d e t e c t i o n 1-Q dFixed Weighte d 1-bit Q f =0.05fixe d We ighte d 1-bit Q f =0.01Optim al Weighte d 1-bit Q f =0.05Optim al Weighte d 1-bit Q f =0.01Fig.5Q m Vs.average SNR with xedand optimal thresholds-15-10-500.70.750.80.850.90.9511.051.1A vera ge SNR (dB)N o r m a l i z e d a v e r a g e s e n s i n g b i t Traditona l1-bitWeighte d 1-bit A WGN Weighte d 1-bit R ayle ighFig.6Normalized average sensing bit Vs.averageSNR when Q f =0.05-15-10-500.70.750.80.850.90.9511.051.1A vera ge SNR (dB)No r ma l i z e da v e r a g e s e n s i n gb i t Tradit ona l 1-bitWeighte d 1-bit A WGN Weighte d 1-bit Ra yleighFig.7Normalized average sensing bit Vs.averageSNR when Q f =0.01theo r etical an d sim u lated Q f with t he list parameters.It is clear that our proposed scheme described in Section 2is pr acticab le and Q f remains constant after the optimization.Figure 5plots the performance of the proposed scheme with the optimal thresholds and fixed thresholds.The xed thresholds and weight for the proposed is set to be 11/21ω≤<,1λ=127.6747,2λ=148.9174when Q f =0.01and 11/21ω≤<,1λ=120.849,2λ=139.123when Q f =0.05.It can be seen that the proposed method with the fixed thr esh olds an d weight alm ost h as the same performance with that with the optimal thresholds and weight.This indicates that the proposed method is also applicable in the case that the channel conditions between the primary user and secondary user are different.Figure 6and Figure 7show the normalized sensing bits for our proposed method and the traditional 1-bit hard combination method.The thresholds used are the optimal thresholds over Rayleigh fading channels.It can be observed that fewer average sensing bits are needed to transmit to the data fusion centre compared with traditional 1-bit hard combination method.Because there is no bit transmitted to the data fusion centre when the energy value falls into the middle region,the average sensing bits are the same as [9]with the same thresholds.IV .CONCLUSIONSW eighted one-bit hard combination for cooperativespectr um sensing has been pr opo sed in this paper.Three regions with two thresholds,which are allocated with weights,have been adopted to m aximize the probability of detection.The weight of the middle region has been separated into several intervals to simplify the optimization problem.Simulation results have demonstrated that the probability of detection of the proposed scheme improves much more than that of the conventional one-bit hard combination.It also has shown thatthe probability of detection of the proposed scheme approaches to that of the EGC scheme,while fewer average sensing bits are transmitted to the data fusion centre compared to the conventional one bit hard combination method.Acknowledg ementsThis work is supported in part by the Hi-tech research and development program of China (2009AA011805),National Natural Science Fou ndation of China (61032002),the Important National Science and Technology Speci c Projects of China (2009ZX03003-007)and the Joint State Key Program of the National Natural Science Foundation of China and the National Railway Ministry of China (60830001).References[1]HAYKIN S.Cognitive Radio:Brain-empowered WirelessCommunications,Selected Areas in Communications [J].IEEE Journal on,2005,23(2):201–220.[2]GANESAN G,LI Ye.Cooperative Spectrum Sensing inCognitive Radio Networks[C]//Proceedings of DySPAN 2005.Baltimore,Maryland USA:IEEE Press,2005:137–143.[3]GHASEMI A,SOUSA E S.Collaborative SpectrumSensing for OpportunisticAccess in Fading Environments [C]//Proceedings of DySPAN 2005.Baltimore,Maryland USA:IEEE Press,2005:131–136.[4]RENZO M Di,GRAZIOSI F,SANYUCCI F.CooperativeSpectrum Sensing in Cognitive Radio Networks over Correlated Log-Normal Shadowing [C]//Proceedings of VTC 2009-Spring.Barcelona,Spain:IEEE Press,2009:1–5.[5]MISH RA S M,SAH AI A ,BROD ERSE N R W.Cooperative Sensing among Cognitive Radios [C]//Proceedings of ICC ’06.Istanbul,Turkey:IEEE Press,2006:1658–1663.[6]YUAN Y,ANXIN L,KAY AMA H.Study on Soft DecisionBased Cooperative Sensing in Cognitive Radio Network [C]//Proceedings of VTC 2009-Fall.Anchorage,Alaska USA:IEEE Press,2009:1–5.[7]MA Jun,ZHAO Guodong,LI Ye.Soft Combination andDetection for Cooperative Spectrum Sensing in Cognitive Radio Networks [J].Wireless Communications,IEEE论文集锦Transactions on,2008,17(11):4502–4507.[8]DIGHAN F F,ALOUINI M S,and SIMON M K.Onthe Energy Detection of Unknown Signals over Fading Channels[C]//Proceedings of ICC’03,Anchorage,Alaska USA:IEEE Press,2003:3575–3579.[9]SUN Chunhua,ZHANG Wei,Letaief K B.CooperativeSpectrum Sensing for Cognitive Radios under Bandwidth Constraints[C]//Proceedings of WCNC2007.Hong Kong:IEEE Press,2007:1–5.[10]WU Jinbo,LUO Tao,YUE Guangxin.An EnergyDetection Algorithm Based on Double-Threshold in Cognitive Radio Systems[C]//Proceedings of ICISE’09, Nanjing,China:IEEE Press,2009:493–496.[11]DUAN Lili,ZHANG Lei,CHU Yujun,et al.CooperativeSpectrum Sensing with Double Threshold Detection Based on Reputation in Cognitive Radio[C]//Proceedings of WiCom’09.Beijing,China:IEEE Press,2009:1–4. [12]PRAOKIS J G.Digital Communications[M].4th ed.New Y ork,McGraw-Hill,2001.Bio grap hiesLi J iaju n,received his B.S.degree in communication engineering from Beijing Jiaotong University in2007.He is currently working toward the Ph.D degree in communication and information system in Beijing Jiaotong University.His current research interests include cognitive radio networks and cooperative networks.Email:jiajunlisun@Tan Zh enh u i,received his PhD degree in Communi-cation and Information System from Nanjing Institute of Engineering(present Southeast University)in1987.He is now working in Beijing Jiaotong University as a professor. He is member of the state863Hi-Tech Project’s Specialists Committee for three consecutive tenures,member of the evaluation group of the Commission for Academic Degree Affairs of the State Council,member of the Commission for Academic Degree Affairs of Beijing,fellow of China Association of Communications,deputy director of the Committee for Automation of China Association of Railways,member of Committee for Academic Exchanges of China Association of Railways,and member of the editorial boards of both Chinese Journal of Electronics,Journal of the China Railways Society,Transprotation System Engineering and Information,Chinese Railways,and Research on Metropolitan Rail Transportation.His research interest is mainly in communication and information systems,including digital mobile communications,spread spectrum communications, adaptive ltering algorithms,and applications of digital signal processing(DSP)in communications,etc.Email:zhhtan@ Ai Bo,received a B.S.Degree from Engineering College of Armed Police Force in1997,a Master and Dr.degree from Xidian University in2002and2004in China,respectively. From2005to2007,he worked as a Post Dr.research fellow in Dept.of E\&E,state key lab.on microwave and digital communications in Tsinghua University in China and graduated with great honors of Excellent Postdoctoral Research Fellow in T singhua University.He is now working in Beijing Jiaotong University as an associate professor.He is an editorial committee member of journal of Wireless Personal Communications,Recent Patents on Electrical Engineering, Compu ter Si mulati ons,In format ion an d El ect ro nic Engineering,an IEEE Senior member and a senior member of Electronics Institute of China(CIE).His current interests are the research and applications of OFDM techniques with emphasis on synchronization,HPA linearization techniques, radio propagation and channel modeling,GSMRailway systems.Email:boai@Y a ng Sh an,re ceive d his B.S.degre e in comm unic ation engineering from Jilin University in2005,the M.S degree in communication and information system from Beijing Jiaotong University in2008.He is currently working toward the Ph.D degree in communication and information system in Beijing Jiaotong University.His current research interests include resource management in heterogeneous wireless network. Email:06120210@。

无线网络的协作分集:高效协议和中断行为摘要:我们研究和分析了低复杂度的协作分集协议用以抵抗无线网络中多径传播引起的衰落,其底层技术是利用协作终端为其他终端转发信号而获得空间分集。

我们略述几种协同通信策略,包括固定中继方法如放大－转发,译码－转发，基于协同终端间的信道估计的选择中继方式,基于目标终端的有限反馈的增量中继方式。

我们在高SＮR条件下以中断事件、相关中断概率指标讨论了其性能特征，以估计协议对传输衰落的鲁棒性。

除固定的解码-转发协议外,所有的协同分集协议就所达到的全分集(也就是在两个终端下的二阶分集）来说是高效的,而且在某些状态下更加接近于最优（小于 1.5d Ｂ)。

因此，当用分布式天线时,我们可以不用物理阵列而提供很好的空间分集效应，但因为采用半双工工作方式要牺牲频谱效率，也可能要增加额外接收硬件的开销。

协作分集对任何无线方式都适用，包括因空间限制而不能使用物理阵列的蜂窝移动通信和无线ad hoc网络，这些性能分析显示使用这些协议可减少能耗。

索引语——分集技术,衰落信道,中断概率，中继信道，用户协同,无线网络Ⅰ介绍在无线网络中,多径传播引起的信号衰落是一个特别严重的信道损害问题,可以利用分集技术来减小。

IＩ系统模型在图1中的无线信道模型中,窄带传输会产生频率非选择性衰落和附加噪声。

我们在第四部分重点分析慢衰落,在时延限制相当于信道相干时间里，用中断概率来评价，与空间分集的优势区分。

虽然我们的协同协议能自然的扩展到宽频带和高移动情况，其中面临各自的频域和时域的选择性衰落,当系统采用另一种形式的分集时对我们协议的潜在影响将相对减小。

Ａ媒体接入当前的无线网络中，例如蜂窝式和无线局域网,我们将有用的带宽分成正交信道，并且分配这些信道终端,使我们的协议适用于现存的网络。

这种选择产生的意外效果是,我们能够同时在I-A处理多径(单个接收）和干扰(多个接收），相当于在信号接收机传输信号的一对中继信号。

对于我们所有的协同协议，传输中的必须同时处理他们接收到的信号；但是,网络实现使终端不能实现全双工，也就是,传输和接收同时在相同的频带中实现。

I NTRODUCTIONMultiple-input multiple-output (MIMO) is an advanced technology that can effectively exploit the spatial domain of mobile fading channels to bring significant performance improvements to wireless communication systems. Conventional MIMO systems, known as point-to-point MIMO or collocated MIMO, require both the transmit-ter and receiver of a communication link to be equipped with multiple antennas. In practice,however, many wireless devices may not be able to support multiple antennas due to size, cost,and/or hardware limitations. Cooperative MIMO [1], also known as virtual or distributed MIMO,aims to utilize distributed antennas on multiple radio devices to achieve some benefits similar to those provided by conventional MIMO systems.The basic idea of cooperative MIMO is to group multiple devices into virtual antenna arrays(VAAs) to emulate MIMO communications. A cooperative MIMO transmission involves multi-ple point-to-point radio links, including links within a VAA and links between possibly differ-ent VAAs. For relay-based cooperative MIMO communications, there are three main coopera-tive strategies: amplify-and-forward, decode-and-forward, and compress-and-forward techniques.Previous theoretical studies have revealed the pros and cons of cooperative MIMO compared to point-to-point MIMO systems [1]. The disad-vantages of cooperative MIMO come from the increased system complexity and the large signal-ing overhead required for supporting device cooperation. The advantages of cooperative MIMO, on the other hand, are due to its capa-bility to improve the capacity, cell edge through-put, coverage, and group mobility of a wireless network in a cost-effective manner. These advan-tages hinge on the usage of distributed antennas,which can increase the system capacity by de-correlating the MIMO channels and allow thesystem to exploit the benefits of macro-diversity in addition to micro-diversity. In many practical applications, such as cellular mobile and wireless ad hoc networks, the advantages of deploying cooperative MIMO technology usually outweigh the disadvantages [2, 3]. Over recent years,cooperative MIMO technologies have been gradually adopted into the mainstream of wire-less communication standards.In this article we focus on cooperative MIMO in the context of cellular mobile systems. Three types of cooperative MIMO schemes have been proposed for cellular systems: coordinated multi-point transmission (CoMP) [2], fixed relay [3],and mobile relay [3]. Simple illustrations of these cooperative MIMO schemes are shown in Fig.1a–c. As the most mature cooperative MIMO technology, fixed relays have been incorporated into the IEEE 802.16j WiMAX standard. Mean-while, the Third Generation Partnership Project (3GPP) is currently evaluating cooperative MIMO technologies for its fourth-generation (4G) cellular communication standard, Long Term Evolution-Advanced (LTE-Advanced).A BSTRACTCooperative multiple-input multiple-output technology allows a wireless network to coordi-nate among distributed antennas and achieve considerable performance gains similar to those provided by conventional MIMO systems. It promises significant improvements in spectral efficiency and network coverage and is a major candidate technology in various standard pro-posals for the fourth-generation wireless com-munication systems. For the design and accurate performance assessment of cooperative MIMO systems, realistic cooperative MIMO channel models are indispensable. This article provides an overview of the state of the art in cooperative MIMO channel modeling. We show that although the existing standardized point-to-point MIMO channel models can be applied to a cer-tain extent to model cooperative MIMO chan-nels, many new challenges remain in cooperative MIMO channel modeling, such as how to model mobile-to-mobile channels, and how to charac-terize the heterogeneity and correlation of multi-ple links at the system level appropriately.Cheng-Xiang Wang and Xuemin Hong, Heriot-Watt University Xiaohu Ge, Huazhong University of Science and Technology Xiang Cheng, Heriot-Watt UniversityGong Zhang, Huawei Technologies Company Ltd.John Thompson, The University of EdinburghCooperative MIMO Channel Models:A SurveyM OBILE R ELAYSMobile relays differ from fixed relays in the sense that the RSs are mobile and are not deployed as the infrastructure of a network. Mobile relays are therefore more flexible in accommodating vary-ing traffic patterns and adapting to different propagation environments. For example, when a target MS temporarily suffers from bad channel conditions or requires relatively high-rate service, its neighboring MSs can help to provide multihop coverage or increase the data rate by relaying information to the target MS. Moreover, mobile relays enable faster and lower-cost network roll-out. Similar to fixed relays, mobile relays can enlarge the coverage area, reduce the overall transmit power, and/or increase the capacity at cell edges. On the other hand, due to their oppor-tunistic nature, mobile relays are less reliable than fixed relays since the network topology is highly dynamic and unstable.As shown in Fig. 1c, two types of mobile relay systems can be distinguished: moving networks and mobile user relays. The moving network employs dedicated RSs on moving vehicles (e.g., trains) to receive data from the BS and forward to the userMSs onboard, and vice versa. The purpose of themoving network is to improve coverage on thevehicle. The mobile user relay enables distributedMSs to self-organize into a wireless ad hoc net-work, which complements the cellular networkinfrastructure using multihop transmissions. Theo-retical studies have shown that mobile user relayshave a fundamental advantage in that the total net-work capacity, measured as the sum of the through-puts of the users, can scale linearly with the numberof users given sufficient infrastructure supports.Mobile user relays are therefore a desirableenhancement to future cellular systems. However,mobile user relays also face huge challenges inrouting, radio resource management, and interfer-ence management. The major disadvantage ofmobile user relays is that MS batteries can be usedup by relay transmissions even if the user does notuse them. Mobile user relays also complicate thebilling problem (i.e., who shall pay the bill when auser helps other users as a relay).Currently, moving networks are supported bythe IEEE 802.16j WiMAX standard. A numberof advanced mobile relays concepts are beingevaluated for the 4G standard. Moving networksinvolve the BS-MS, BS-RS, and RS-MS links,where the BS-MS and BS-RS channels are F2Mchannels, while the RS-MS channels are F2F orF2M channels. Mobile user relays involve BS-MS and MS-MS links, where the BS-MS chan-nels are F2M channels, while the MS-MSchannels are M2M channels.C OOPERATIVE MIMOC HANNEL M ODELSTo allow accurate assessments and fair compar-isons of different cooperative MIMO technolo-gies, realistic cooperative MIMO channel modelsare indispensable. Although a standardized coop-erative MIMO channel model is not yet available,it can be constructed with reasonable accuracybased on the existing standardized point-to-pointMIMO channel models and recently developedmodels for some scenarios (e.g., M2M models).This section aims to review the existing standard-ized MIMO channel models, compare their prosand cons, and discuss how they can be extendedand applied to cooperative MIMO systems.Standardized channel models are developedfor different purposes, based on which we canclassify them into two types: system simulationmodels and calibration models. System simula-tion models are intended for accurate perfor-mance assessments of different algorithms andsystems. They seek to represent the real-worldchannels as realistically as possible, with reason-able computational complexity. Calibrationchannel models, on the other hand, are simpli-fied channel models developed for conformancetesting of different products and technologies.Conformance testing specifies a required level ofsystem performance when using the calibrationchannel model and indicates whether a testedsystem fulfills this requirement. In this article weconcentrate on system simulation models.Prominent standardized MIMO channel mod-els include the COST 259/273 channel model,the 3GPP SCM, the SCM-Extended model, theWINNER II channel model, the IEEE 802.11nchannel model, the Stanford University interim(SUI) channel model, and the IEEE 802.16channel model [7]. Although these models aredeveloped by different research bodies and pro-jects, they are closely related. In the followingwe focus on the three most representativeMIMO channel models:•The SCM [4], which is a cellular MIMOchannel model developed by the 3GPP in2003 for the evaluation of different MIMOschemes in high-speed downlink PacketAccess (HSDPA) systems. The SCM sup-ports a center frequency of 2 GHz and asystem bandwidth of 5 MHz.•The WINNER II model [5], which wasdeveloped by the IST-WINNER II projectin 2007 and represents the state of the artin wireless channel modeling. It supports acenter frequency range from 2 to 6 GHzand a system bandwidth up to 100 MHz.•The IEEE 802.16j channel model [6], whichis based on the SUI model and was extend-ed in 2007 to cover relay scenarios in IEEE802.16j WiMAX systems. It supports a cen-ter frequency of 5 GHz and a maximumsystem bandwidth of 20 MHz.G ENERAL F EATURESAll three models employ a tapped-delay-linestructure to construct the wideband channelimpulse response, with each tap representing aresolvable path or a cluster of scatterers with adifferent delay. The numbers of taps used by theSCM and IEEE 802.16j channel model are fixedto 6 and 3, respectively, while the numbers oftaps in the WINNER II channel model can varybetween 4 and 24. Intracluster delay spread isfurther introduced in the WINNER II channelmodel to account for better delay resolution andconsequently broader bandwidths.Based on the modeling methodology, standard-ized MIMO channel models can be roughly classi-fied into geometry-based stochastic models2050 0 100 150 200 250 300 350 400 450 500 4060 80 100 120 140160180。