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4G通信中的MIMO智能天线技术智能天线通常也称作自适应天线阵列，可以形成特定的天线波束，实现定向发送和接收，主要用于完成空间滤波和定位。
从本质上看，它利用了天线阵列中各单元之间的位置关系，即利用了信号的相位关系克服多址干扰及多径干扰，这是它与传统分集技术的本质区别。
MIMO系统是指在发射端和接收端同时使用多个天线的通信系统，其有效地利用随机衰落和可能存在的多径传播来成倍地提高业务传输速率。
其核心技术是空时信号处理，即利用在空间中分布的多个时间域和空间域结合进行信号处理。
因此，可以被看作是智能天线的扩展。
智能天线系统在移动通信链路的发射端/或接收端带有多根天线，根据信号处理位于通信链路的发射端还是接收端，智能天线技术被定义为多入单出（MISO，MultipleInputSingleOutput）、单入多出（SIMO，Single Input Multiple Output）和多入多出（MIMO，Multiple Input Multiple Output）等几种方式。
二、多入多出智能天线收发机结构及研究进展从图1可以看出，比特流在经过编码、调制和空时处理（波束成行或空时编码）后，映射成不同的信息符号，从多个天线同时发射出去；在接收端用多个天线接收，进行相应解调、解码及空时处理。
图1 多输入多输出智能天线收发机结构MIMO系统中的空时处理技术主要包括波束成形（beamforming）、空时编码（space-timecoding）、空间复用（spacemultiplexing）等。
波束成形是智能天线中的关键技术，通过将主要能量对准期望用户以提高信噪比。
波束成形能有效地抑制共道干扰，其关键是波束成行权值的确定。
1.MIMO系统的发射方案MIMO系统的发射方案主要分为两种类型：最大化数据率的发射方案（空间复用SDM）和最大化分集增益的发射方案（空时编码STC）。
最大化数据率发射方案主要通过在不同天线发射相互独立的信号实现空间复用。
传递英文短语怎么写传递的英文短语怎么写，你们了解过吗?下面就由店铺为大家带来关于传递的英语短语集锦，希望大家能有所收获。
关于传递的相关英语短语transmit on关于transmit on的英语例句Directional antennae, unlike the omnidirectional sort, transmit on a narrow beam.不同于全方位天线，定向天线在窄波束上传输。
An ideal video streaming mechanism should not only let user view smooth quality videos but also try to let videos transmit on the network smoothly.一个理想的视讯传输机制，应该能让使用者观看到影像品质平顺的影片，而且要设法让影片能顺利地在网路上传输。
Along with prevalence of Internet, traditional centralized applications are transformed intodistributed ones, so more data including key and confidential data transmit on-line heavy.随着因特网的普及，应用由传统的集中式向分布式转化，更多的数据包括关键的以及保密的数据大量在网上传送;It can be set to transmit on any carrier, but it cannot transmit over FM.它可以被设置为发送或载波模式，但不能通过FM传送。
However, repeaters can interfere with one another unless they are far enough apart or transmiton sufficiently separated frequencies.然而，中继器可以互相干扰，除非他们足够远或传送在充分分离的频率。
1MIMO Techniques for Wireless CommunicationsTa -Sung LeeDepartment of Communication Engineering National Chiao Tung UniversityE-mail: tslee@.twOutlinePart I: MIMO BackgroundMIMO OverviewMIMO Channel CapacityPart II: Space-Time Coding SchemesHigh Link Quality via Spatial Diversity—STBC/STTCHigh Spectral Efficiency via Spatial Multiplexing—LSTC Part III: MIMO for Future Wireless Communications 3GPPIEEE 802.11nIEEE 802.16 (-2004: WiMAX)MIMO Overview[1]-[3]Future trend for wireless communicationsFuture wireless applications create insatiability Bdemand for“high data rate”and “high link quality”wireless accessSpectrum has become a scarce and expensive resourceB bandwidth is very limitedRegulation, device and system capacity concerns Btransmit power is limitedTime and frequency domain processing are at limits, but space is not B MIMOof MIMO: Improve quality (BER) and/or dataMain history of MIMO techniques[1]-[3]“Spatial diversity”Delay diversity:Wittneben, 1991 (inspired); Seshadri &Winters, 1994 (first attempt to develop STC)STTC:Tarokh et al., 1998 (key development of STC)Alamouti scheme:Alamouti, 1998STBC:Tarokh et al., 1998“Spatial multiplexing”First results hint capacity gain of MIMO:Winters, 1987Ground breaking results:Paulraj& Kailath, 1994BLAST:Foschini, 1996MIMO capacity analysis:Telatar1995; Foschini1995 & 98Spatio-temporal vector coding for channel with multipathdelay spread:Raleigh & Cioffi, 19982122h h ⎢⎢=⎢H "()()()k k k =+y Hx v ()k y ()k x HN TXs and M RXsM RXsN TXsMIMO Channel CapacityTX 1#RX 1#TX 1RX 1 #Space-Time Coding Schemes[6]-[11]Types of space-time codeSpatial diversity perspective:ST block code (STBC)[7], [8]Provides diversity gain but no coding gainST trellis code (STTC)[6]Provides both diversity and coding gainOriginates from transmit diversity conceptSpatial multiplexing perspective:Layered ST code (LSTC)[10], [11]Provides some coding gain and diversity gain (depending oncode structure)Provides bandwidth efficiencyST Block Code (STBC) / ST Trellis Code (STTC)Layered STC (LSTC)Potential MIMO ApplicationsMIMO applications in future wireless standards 3GPP[12]-[17]: MIMO-CDMASpatial diversitySpatial multiplexingIEEE 802.11n[18]-[19]: MIMO-OFDMBeamformingSpatial diversitySpatial multiplexingIEEE 802.16 (-2004: WMAX)[20]-[21]: MIMO-OFDM BeamformingSpatial diversitySpatial multiplexing3GPP[12]-[17]MIMO Techniques in 3G CDMA SystemsOpen loopTime-switched transmit diversity (TSTD)[12]: adopted in3GPPOrthogonal transmit diversity (OTD)[13]: adopted in 3GPPSpace-time transmit diversity (STTD)[7]: adopted in 3GPP Space-time spreading (STS)[14]: adopted in 3GPP2IST-METRA (HSDPA)[15]: adopted in 3GPPCDMA-BLAST (HSDPA)[16]: adopted in 3GPPClosed loopSwitched transmit diversity (STD): adopted in 3GPP[17]Transmit adaptive array (TXAA): adopted in 3GPP[17]IEEE 802.11nKey Features in IEEE 802.11nEnhancements to OFDM PHYEnables 2 x 2 MIMO operation in 20 MHz to achieve100 Mbps throughputUp to 4 x 4 MIMO to achieve 500+ MbpsPackage of enhancements carries over to all antenna configurations and bandwidthsBandwidth extension optionEmployees channel doubling (40 MHz) to furtherincrease data rateIEEE 802.16 (-2004: WMAX)Full MobilityAny IP ServiceNomadicityPortability with Simple MobilityStationary BroadbandAccess:Laptops, PDA Wherever you arePedestrian SpeedMobility Boot for latency Tolerant servicesAccessResidential/SMB Broadband AccessReferences[1] A. J. Paulraj, R. Nabar and D. Gore, Introduction to space-time wirelesscommunications, Cambridge University Press, 2003.[2] H. Bocskei and A. J. Paulraj, Multiple-input multiple-output (MIMO) wirelesssystems, Cambridge University Press, 2003.[3] D. Gesbert, M. Shafi, D. Shiu, P. J. Smith and A. Naguib, “From theory topractice: An overview of MIMO space-time coded wireless systems,”IEEE J. Select. Areas Commun., vol. 21, no. 3, pp. 281-302, April 2003.[4] G. J. Foschini and M. J. Gans, “On limits of wireless communications in afading environment using multiple antennas,”Wireless Personal Commun., vol. 6, no. 3, pp. 311-355, 1998.[5] A. F. Naguib and A. R. Calderbank, “Space-time coding and signalprocessing for high data rate wireless communications,”Wireless Commun.and Mob. Comput., vol. 1, pp. 13-43, 2001.[6] V. Tarokh, N. Seshadri and A. R. Calderbank, “Space-time codes for highdata rate wireless communication: Performance analysis and codeconstruction,”IEEE Trans. Inform. Theory, vol. 44, no. 2, pp. 744-765, March 1998.[7] S. M. Alamouti, “A simple transmit diversity technique for wirelesscommunications,”IEEE JSAC, vol. 16, no. 8, pp. 1451-1458, Oct. 1998.[8] V. Tarokh, H. Jafarkhani and A. R. Calderband, “Space-time block codesfrom orthogonal designs,”IEEE Trans. Inform. Theory, vol. 45, no. 5, pp.1456-1467, July 1999.[9] B. Vucetic and J. Yuan, Space Time Coding, W. Sussex, England: JohnWiley & Sons, 2003.[10] G. J. Foschini, “Layered space-time architecture for wirelesscommunication in a fading environment when using multiple antennas,”Bell Labs Syst. Tech. J., vol. 1, pp. 41-59, Autumn 1996.[11] P. W. Wolniansky, G. J. Foschini, G. D. Golden, and R. A. Valenzuela,“V-BLAST: An architecture for realizing very high data rates over the rich-scattering wireless channel,”Proc. ISSSE VTC’91, pp. 259-300, Apr.1998.[12] A. Hiroike, F. Adachi, and N. Nakajima, “Combined effects of phasesweeping transmitter diversity and channel coding,”IEEE Trans. Veh.Tehnol., vol. 41, no. 2, pp. 170-176, May 1992.[13] TIA/EIA IS-2000 Physical layer specification of CDMA spread spectrumcommunication system, June 2000.[14] B. Hochwald, T. L. Marzetta and C. B. Papadias, “A transmitter diversityscheme for wideband CDMA systems based on space-time spreading,”IEEE JSAC, vol. 19, no. 1, pp. 48-60, Jun. 2001.[15] IST METRA, “METRA public Deliverables”http://kom.auc.dk/~schum/MIMO/index.html, 2002.[16] H. Huang, H. Viswanathan and G. J. Foschini, “Achieve high data ratesin CDMA systems using BLAST techniques,”Proc. Glovecom’99, pp.2316-2320, 1999.[17] High speed downlink packet access (HSDPA), 3GPP TR 25.855, V5.0.0(Release 5), Sept. 2001.[18] Airgo Networks, Bermai, Broadcom,Conexant, ST Microelectronics,Texas Instruments, “WWiSE IEEE 802.11n Proposal WWiSE IEEE802.11n Proposal Technical Technical Summary ,“, WWiSE group, Aug.2004.[19] F.Petré, B.V.Poucke,A.Bourdoux, and L.V.Perre, “MIMO-OFDM forHigh-Speed WLANs,”IMEC, Jan. 2004.[20] Intel Corp. “WiMAX,”Intel technology journal, vol. 8, no. 3, pp. 173-258,Aug. 2004.[21] IEEE Std. 802.16-2004.。
空时编码技术空时编码STC (Space-Time Coding) 技术在无线通信领域引起了广泛关注,空时编码的概念是基于Winters 在20世纪80年代中期所做的关于天线分集对于无线通信容量的重要性的开创性工作。
空时编码是一种能获取更高数据传输率的信号编码技术，是空间传输信号和时间传输信号的结合，实质上就是空间和时间二维的处理相结合的方法。
在新一代移动通信系统中，空间上采用多发多收天线的空间分集来提高无线通信系统的容量和信息率；在时间上把不同信号在不同时隙内使用同一个天线发射，使接收端可以分集接收。
用这样的方法可以获得分集和编码增益，从而实现高速率的传输。
现在是第三代移动通信系统中提高频谱利用率的一项技术。
空时编码的有效工作需要在发射和接收端使用多个天线,因为空时编码同时利用时间和空间两维来构造码字,这样才能有效抵消衰落,提高功率效率；并且能够在传输信道中实现并行的多路传送,提高频谱。
需要说明的是,空时编码技术因为属于分集的范畴,所以要求在多散射体的多径情况下应用,天线间距应适当拉开以保证发射、接收信号的相互独立性,以充分利用多散射体所造成的多径。
1 空时编码技术及其分类空时编码在不同天线所发送的信号中引入时间和空间的相关性,从而不用牺牲带宽就可以为接收端提供不编码系统所没有的分集增益和编码增益。
空时编码的基本工作原理如下:从信源给出的信息数据流,到达空时编码器后,形成同时从许多个发射天线上发射出去的矢量输出,称这些调制符号为空时符号(STS) 或者空时矢量符(STVS) 。
与通常用一个复数表示调制符号类似(复的基带表示) ,一个空时矢量符STVS可以表示成为一个复数的矢量,矢量中数的个数等于发射天线的个数。
目前提出的空时编码方式主要有：⑴正交空时分组码OSTBC (Orthogonal Space2 Time Block Coding) ；⑵贝尔分层空时结构BLAST(Bell Layered Space2Time Architecture) ；⑶空时格型编码STTC(Space2Time Trellis Coding) ；这3类接收机需要已知信道传输系数的空时编码,另外还有适于少数不知道信道传输系数情况的有效期分空时编码。
浅析发射分集与接收分集技术1 概述1.1 多天线信息论简介近年来,多天线系统(也称为MIMO系统)引起了人们很大的研究兴趣,多天线系统原理如图1所示，它可以增加系统的容量,改进误比特率(BER).然而,获得这些增益的代价是硬件的复杂度提高,无线系统前端复杂度、体积和价格随着天线数目的增加而增加。
使用天线选择技术，就可以在获得MIMO系统优势的同时降低成本。
图1 MIMO系统原理有两种改进无线通信的方法：分集方法、复用方法。
分集方法可以提高通信系统的鲁棒性，利用发送和接收天线之间的多条路径，改善系统的BER。
在接收端，这种分集与RAKE接收提供的类似。
分集也可以通过使用多根发射天线来得到，但是必须面对发送时带来的相互干扰。
这一类主要是空时编码技术。
另外一类MIMO技术是空间复用，来自于这样一个事实：在一个具有丰富散射的环境中，接收机可以解析同时从多根天线发送的信号，因此，可以发送并行独立的数据流，使得总的系统容量随着min(Mτ,M t)线性增长，其中Mτ和M t是接收和发送天线的数目。
1.2 空时处理技术空时处理始终是通信理论界的一个活跃领域。
在早期研究中，学者们主要注重空间信号传播特性和信号处理，对空间处理的信息论本质探讨不多。
上世纪九十年代中期，由于移动通信爆炸式发展，对于无线链路传输速率提出了越来越高的要求，传统的时频域信号设计很难满足这些需求。
工业界的实际需求推动了理论界的深入探索。
在MIMO技术的发展，可以将空时编码的研究分为三大方向：空间复用、空间分集与空时预编码技术，如图2所示。
1.3多天线分集接收是抗衰落的传统技术手段，但对于多天线发送分集，长久以来学术界并没有统一认识。
1995年Telatarp[3]首先得到了高斯信道下多天线发送系统的信道容量和差错指数函数。
他假定各个通道之间的衰落是相互独立的。
几乎同时， Foschini 和Gans 在[4]得到了在准静态衰落信道条件下的截止信道容量(OutageCapacity)。
MIMO原理理解空时编码MIMO（Multiple-Input Multiple-Output）是一种通信技术，利用多个发射天线和多个接收天线来提高传输速率和信号质量。
MIMO技术的一个重要应用是空时编码（Space-Time Coding），它通过在时间和空间上对数据进行编码和传输来提高通信系统的可靠性和效率。
空时编码的关键概念是空时块编码（Space-Time Block Coding，简称STBC），它将数据块分为多个时间步长，并使用多个天线同时发送这些时间步长的数据。
通过利用多个天线可同时传输多个数据流，空时编码可以提高信道容量和系统可靠性。
一个STBC系统通常有多个发射天线和多个接收天线。
在发送端，数据被分成多个时间步长，并以特定顺序通过发射天线发送。
每个时间步长的数据通过编码矩阵进行处理，编码矩阵是一个由特定规则生成的矩阵。
编码矩阵的每一行代表发送天线的输出，每一列代表时间步长的信号。
编码矩阵的作用是将时间步长数据分配到各个发送天线，并进行合适的编码处理。
在接收端，通过接收到的信号进行处理还原出信号的原始数据。
这里的处理涉及到两个关键概念：空间分集（Spatial Diversity）和空时编码解码（Space-Time Decoding）。
空间分集是指通过多个接收天线接收并处理信号，从而减少信号在传输过程中的失真和干扰。
多个接收天线可以接收到不同的信号路径，并通过对接收信号进行处理，可以提高信号的可靠性和防止丢失。
空时编码解码是指通过对接收到的信号进行解码处理，从中还原出原始数据。
解码的过程涉及到信号处理算法，包括线性等式求解和最小均方误差等方法。
总的来说，空时编码通过将数据块分成多个时间步长，并在多个发射天线上同时发送这些时间步长的数据，从而提高传输速率和系统可靠性。
通过空间分集和空时编码解码的技术，接收端可以测量和估计信号的失真和干扰，并通过信号处理算法还原出原始数据。
空时编码在无线通信系统中得到了广泛应用，可以显著提高系统的性能和可靠性。
无线通信系统的发展历程与趋势现代无线通信系统中最重要的两项基础是多址接入（Multiple Access)和双工(Multiplexing）。
从1G到4G的无线通信系统演进史基本上就是在这两项技术上进行不断改进.多址接入技术为不同的用户同时接入无线通信网提供了可能性。
给出了三种最典型的多址接入技术：FDMA、TDMA和CDMA的比较.双工技术为用户同时接收和发送数据提供了可能性.两种最典型的双工技术:FDD模式和TDD模式。
中国无线通信科技发展史和未来走向范文当今，全球无线通信产业的两个突出特点体现在:一是公众移动通信保持增长态势,一些国家和地区增势强劲,但存在发展不均衡的现象；二是宽带无线通信技术热点不断，研究和应用十分活跃。
1 无线通信技术的发展历程随着国民经济和社会发展的信息化,人们要通信息化开创新的工作方式、管理方式、商贸方式、金融方式、思想交流方式、文化教育方式、医疗保健方式以及消费与生活方式。
无线通信也从固定方式发展为移动方式，移动通信发展至今大约经历了五个阶段: 第一阶段为20年代初至50年代初，主要用于舰船及军有,采用短波频及电子管技术,至该阶段末期才出现150MHZ VHF单工汽车公用移动电话系统MTS。
第二阶段为50年代到60年代,此时频段扩展至UHF450MHZ，器件技术已向半导体过渡,大都为移动环境中的专用系统，并解决了移动电话与公用电话网的接续问题。
第三阶段为70年代初至80年代初频段扩展至800MHZ,美国Bell研究所提出了蜂窝系统概念并于70年代末进行了AMPS试验。
第四阶段为80年代初至90年代中，为第二代数字移动通信兴起与大发展阶段，并逐步向个人通信业务方向迈进;此时出现了D-AMPS、TACS、ETACS、GSM/DCS、cdmaOne、PDC、PHS、DECT、PACS、PCS等各类系统与业务运行。
第五阶段为90年代中至今，随着数据通信与多媒体业务需求的发展，适应移动数据、移动计算及移动多媒体运作需要的第三代移动通信开始兴起，其全球标准化及相应融合工作与样机研制和现场试验工作在快速推进，包括从第二代至第三代移动通信的平滑过渡问题在内.2 第一代无线通信系统采用频分多址（Frequency Division Multiple Access）技术组建的模拟蜂窝网也被称为第一代（First Generation，下称1G）无线通信系统。
差分空时分组编码的研究作者：刘小群来源：《现代电子技术》2010年第21期摘要:一般在空时编码解码时接收端需要信道状态信息(CSI),因而必须获得精确的信道估计,而差分空时编码(DSTC)接收端在解码时不需要CSI,因而不需要信道估计。
在信道衰落快或信息传输速率高的情况下,实时而精确的信道估计非常困难或代价太高,此时接收端不能获得CSI,因而需要差分空时编码。
对非相干系统中空时编码的编译码原理、特点和性能进行了分析和比较,并对其中的部分空时编码给出了具体的实例和仿真结果。
关键词:非相干系统; 信道状态信息; 差分空时编码; 信道估计中图分类号:TN929.5-34文献标识码:A文章编号:1004-373X(2010)21-0013-02Study on Differential Space-Time CodingLIU Xiao-qun(Department of Physics and Information Technology, Baoji University of Science and Arts, Baoji 721016, China)Abstract: An accurate channel estimation at receiving end is needed for decoding of common space-time coding, while the channel state information (CSI) and channel estimation are not needed for DSTC. Under the circumstances where wireless channels fade very rapidly or the data rate is very high, the channel estimation is too hard or too costly to detect, the DSTC is required. In this paper, the encoding and decoding theories, features, and performances of space-time coding for incoherent system are introduced, and the comparison between them is presented. The examples and simulation results are proposed.Keywords: incoherent system; channel state information; differential space-time coding; channel estimation0 引言从相干空时编码的解码方式可以看出,接收端需要确切知道信道状态信息(Channel State Information,CSI)的情况[1-3],当然当信道相对于数据传输速率缓慢变化时,发射机可以通过发送训练序列进行信道检测使接收机能够进行正确的信道估计,接收机要获得理想的信道状态信息(CSI),可以用相干检测的方法解码[4]。
SPACE-TIME CODING AND SIGNAL SPACE DIVERSITY IN THE PRESENCE OF CHANNEL ESTIMATION ERRORSTolga KurtSchool of Information Technologyand EngineeringUniversity of OttawaK1N6N5,Ontario,CanadaE-mail:tkurt@site.uottawa.caHakan Delic¸Department of Electrical andElectronics EngineeringBoˇg azic¸i University Bebek34342Istanbul,Turkey E-mail:delic@.trAbstractJoint space-time(ST)coding and constellation rotation is considered in the presence of imperfect channel state infor-mation.The combined system with two transmit antennas is shown to be more resistant to channel estimation errors than ST coding.Experiments involving several cases of channel estimation errors verify related theory reported in the liter-ature.Keywords:Space-time coding,signal space diversity, channel estimation error,transmit diversity1.INTRODUCTIONA well-known approach for increasing link quality against multipath fading is to apply receiver diversity.For wireless communication systems where it is not feasible to deploy multiple antennas at the receiver,transmitter diversity of-fers a powerful alternative.Many techniques incorporating space-time(ST)coding have been proposed in recent years (see e.g.[8,9]and the references therein).In[1]and[11] orthogonal designs achieving full diversity are presented. However,these orthogonal designs exist only for the cases where number of antennas is equal to2,4and8,and rate-1 codes exist uniquely only for two antennas.Alternatively,signal space diversity combats fading by rotating the constellation and applying componentwise in-terleaving[2].The interleaver is required for the indepen-dent fading of the real and imaginary parts of the constel-lation points.Although this is a bandwidth and power effi-cient solution,it introduces additional complexity and time delay as a result of the interleaving procedure.Recently,another model that uses both signal space di-versity and ST coding is introduced in order to achieve full CCECE2004-CCGEI2004,NIAGARA FALLS, MAY/MAI20040-7803-8253-6/04/$17c 2004IEEE diversity for more than two antennas,while simultaneously eliminating the interleaver from the system design[5,12]. In[5],no extra gain is achieved from the introduction of rotated constellations with two antennas,which is expected because the Alamouti scheme[1]exploits all the diversity in the system.The impact of channel estimation errors on the system performance has been investigated for transmit diversity with ST coding.Specifically,the criteria that are customarily used in code design for coherent receivers do not induce any penalty in the diversity order when the channel state in-formation(CSI)is imperfect,even though the bit error rate may suffer[6,10].This is intuitively plausible because di-versity gains become observable at high signal-to-noise ra-tios(SNR),where estimates are very reliable[6].Bit error probability computations and formulas for a complex Gaus-sian error distribution are presented in[3,4].In all relevant work[2,5,12],the channel is assumed to be perfectly known and constant throughout the code block. In this paper,we present joint ST coding and signal space diversity for two transmit antennas,and show that the com-bined system is more resistant to channel estimation errors, compared to ST coding alone.The organization of the paper is as follows:In Section II,we present the system model which employs a simple scheme that combines the diversity techniques of[1]and [2].We test the performance of the joint diversity system for different estimation error types in Section III,and follow that with the conclusions in Section IV.2.SYSTEM MODELWe consider a hybrid system that combines the diversity ideas in[1]and[2](hereafter referred to as joint diversity). The system architecture is given in Fig. 1.Let a0and a1 be two rotated complex constellation points that are consec-utively transmitted.For simplicity,we assumeπ/8-rotated quadrature phase-shift keying(QPSK)symbols[2].With−1are obtained.Next,the symbols b0,b1are space-time coded according to the Alamouti scheme,and eventu-ally transmitted through the two transmit antennas..The received baseband signals arer0=h0b0+h1b1+n0,r1=−h0b∗1+h1b∗0+n1,(1) where h0,h1and n0,n1are the complex channel coeffi-cients and the complex additive white Gaussian noise for antennas1and2,respectively.Space-time processing via Alamouti-type decoding of r0,r1and component-deinterleaving achieve maximum diversity gain as in[1]with the availabil-ity of CSI.To account for channel estimation errors,con-sider the channel matrix H asH=h0+ξ0h1+ξ1h0+ξ2h1+ξ3(2)where the columns of H correspond to channels seen by dif-ferent antennas,and rows correspond to channel consitions at different time instants.The estimation errors{ξi}3i=0are modeled as random variables with zero-mean additive,com-plex white Gaussian distributions and variances{σ2i}3i=0, respectively.Hence,(1)becomesr0=(h0+ξ0)b0+(h1+ξ1)b1+n0r1=−(h0+ξ2)b∗1+(h1+ξ3)b∗0+n1.(3) The zero-mean assumption ensures that the estimates are unbiased,which is necessary to preserve the diversity order regardless of the CSI imperfections[6].The optimal com-bining of[1]givesˆb=(|h0|2+|h1|2)b0+I0+h∗0n0+h1n∗1ˆb1=(|h0|2+|h1|2)b1+I1+h∗1n0−h0n∗1(4) where the interference terms I0,I1areI0=h∗1(ξ0b0+ξ1b1)+h0(ξ∗2b1+ξ∗3b0)I1=h1(ξ∗3b0+ξ∗2b1)+h∗0(ξ1b1−ξ0b0)(5) For high SNR,the interference terms in(5)are the per-formance limiting factors,rather than the noise components in(4).On the other hand,if h0,h1,ξ0,ξ1,ξ2andξ3are all mutually uncorrelated as per the independent fading as-sumption[10],then so are I0and I1.This fact can be ex-ploited through signal space diversity.If component inter-change is again applied for the symbols at the receiver as ˆa0= {ˆb0}+i {ˆb1},ˆa1= {ˆb1}+i {ˆb0},then both the real and the imaginary parts of the symbols are contaminated by random but uncorrelated interference, which results in a system that is more tolerant to channel estimation errors.In the next section we support this idea via simulation results.3.SIMULATIONSThe simulations are performed for the system model given in the previous section for1000independent channel real-izations.Each run is terminated when1000errors are ob-served.The transmitter sendsπ/8-rotated QPSK symbols as in Fig. 2.The complex Gaussian distributed channel gain has unity variance.Several channel estimation error scenarios are considered.When there is no estimationerror,Fig.2.Theπ/8-rotated QPSK constellation[2].the results in[5]and our simulations both indicate that the performance is the same for the Alamouti scheme with or without signal space diversity.Hence,in the bit error ratemore likely to happen in the second time slot due to the vari-ations in the channel coefficients over time.The gain of the joint diversity scheme is given in Fig.4,which exhibits the same slopes as those in Fig.(3).Thus,diversity orders are preserved even if the CSI is imperfect,which is consistent with the theory reported in[6]and[10].The gain of the joint diversity for the case whenσ20=σ21=σ22=σ23=0.01is displayed in Fig.5.Unlike the previous experiments,the bit error rate deteriorates slightly here due to the back-to-back erroneous estimates.Finally,we evaluate the impact of the variance of the error random variables.The BER performances under the parameter setsσ20=σ21=0,σ22=σ23=0.02andσ20=σ21=0,σ22=σ23=0.04are presented respectively in Fig.6and Fig.7.The performance of combined ST cod-ing and constellation rotation degrades with increased error variance,approaching that of space-time coding alone.Fig.5.The effect of channel estimation errors on the trans-mit diversity schemes forσ20=σ21=σ22=σ23=0.01.For all the cases presented above,the BER performance offered by space-time coding improves when it is employed in conjunction with signal space diversity described in the form of constellation rotation,even though there is no ap-preciable gain in diversity order.While there is no BER gain up to E b/N0=5dB,the improvement becomes noticeable around E b/N0=15dB,when the diversity gain kicks in and estimation errors are less pronounced.4.CONCLUSIONSIn this paper,we considered joint space-time coding of[1] and signal space diversity of[2].Even though constella-tion rotation on top of the Alamouti scheme does not offerFig.6.The effect of channel estimation errors on the trans-mit diversity schemes forσ20=σ21=0,σ22=σ23=0.02.Fig.7.The effect of channel estimation error on the transmit diversity schemes whenσ0=σ1=0,σ2=σ3=0.04 additional diversity gain for two antennas,the combination is very robust to CSI imperfections,which may be worth the incurred complexity.Under unbiased channel estimates with variances comparable to those of the channel gains,the diversity order is verified to be independent of estimation errors.In[7],a rule of thumb is prescribed where the CSI can be regarded as near-perfect so long as the error variance is negligible compared to the reciprocal of the SNR.This rule is satisfied in the experiments above for the E b/N0= 10−15dB range,and the results are in agreement with[7], particularly for the joint diversity system.5.REFERENCES[1]S.M.Alamouti,“A simple transmitter diversity scheme forwireless communications”,IEEE Journal on Selected Areas in Communications,V ol.16,No.8,pp.1451-1458,October 1998.[2]J.Boutros and E.Viterbo,“Signal space diversity:a powerand bandwidth efficient diversity technique for the Rayleigh fading channel”,IEEE Transactions on Information Theory, V ol.44,No.4,pp.1453-1467,July1998.[3]X.Feng and C.Leung,“Performance sensitivity comparisonof two diversity schemes”,IEE Electronics Letters,V ol.36, No.9,pp.838-839,April2000.[4] D.Gu and C.Leung,“Performance analysis of transmitdiversity scheme with imperfect channel 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