Compressed SNR-and-Channel Estimation for Beam Tracking in 60-GHz WLAN

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Channel Estimation for LTE

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Contents
1 Introduction 2 LTE Downlink: Physical Layer
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Structure of Pilot Symbols . . . . . . . . . . . . . . . . . . . . 2.3 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Least Squares Channel Estimation . . . . . . . . . . . . 3.2 Linear Minimum Mean Square Error Channel Estimation 3.2.1 LMMSE Channel Estimation for Spatially Uncorrelated Channels . . . . . . . . . . 3.2.2 LMMSE Channel Estimation for Spatially Correlated Channels . . . . . . . . . . . 3.3 Approximate LMMSE Channel Estimation . . . . . . . . 3.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . 3.4.1 Comparison of Interpolation Techniques . . . . . 3.4.2 LMMSE Channel Estimation . . . . . . . . . . . 3.4.3 ALMMSE Channel Estimation . . . . . . . . . . 4.1 4.2 4.3 4.4 Least Square Channel Estimation . . . . . . . . . . . . . Linear Minimum Mean Square Error Channel Estimation Approximate LMMSE Channel Estimation . . . . . . . . Simulation Results . . . . . . . . . . . . . . . . . . . . . 4.4.1 Comparison of Fast Fading Channel Estimation . 4.4.2 Block Fading Channel Estimation . . . . . . . . . 4.4.3 ALMMSE Channel Estimation . . . . . . . . . .

角度域和时延域联合稀疏信道估计

角度域和时延域联合稀疏信道估计张跃明;张兵山;归琳;秦启波;熊箭【摘要】针对多输入多输出(MIMO)系统在双选信道下信道估计问题,以及挖掘信道在时延域和角度域的联合稀疏特性,提出了一种新的基于压缩感知的联合稀疏信道估计方案.首先,基于基扩展模型,将信道估计建模为结构化压缩感知问题,随后基于压缩感知模型,提出了两种新的贪婪算法,有效地恢复了时变信道参数.其中两步同时正交匹配追踪(TS-SOMP)算法先在时延域中找到所有非零抽头位置,然后估计非零角度域系数.两环同时正交匹配追踪(TL-SOMP)算法包括内外两个循环,在外部循环中找到一个非零抽头位置后,即可直接在内部循环求解非零角度域系数.最后,给出了归一化均方误差(NMSE)的仿真曲线,验证了本算法的有效性.【期刊名称】《上海师范大学学报（自然科学版）》【年(卷),期】2018(047)002【总页数】6页(P192-197)【关键词】信道估计;压缩感知;双选;系统;角度域【作者】张跃明;张兵山;归琳;秦启波;熊箭【作者单位】上海交通大学电子信息与电气工程学院,上海200240;北京跟踪与通信技术研究所,北京100094;上海交通大学电子信息与电气工程学院,上海200240;上海交通大学电子信息与电气工程学院,上海200240;上海交通大学电子信息与电气工程学院,上海200240【正文语种】中文【中图分类】TN929.50 引言在高速移动性环境中,宽带无线系统不但存在频率选择性衰落,也存在时间选择性衰落,这种场景被称为双选(DS)信道[1].对于DS信道场景中的多输入多输出(MIMO)系统,由于存在大量未知信道参数,很难获得准确的信道状态信息(CSI).为了高效地获得CSI,已经有研究人员提出了几种DS信道下MIMO系统的信道估计方案[2-3].然而,这些方案都基于丰富多径信道的假设,导频开销很大.越来越多的研究已经证实,许多实际的无线信道表现出稀疏性,因此可以将压缩感知(CS)理论用于信道估计[4].文献[5]基于信道在时延域的稀疏性,利用CS方法提高信道估计精度.实际环境中,由于基站(BS)周围的散射物有限,MIMO信道通常在角度域也表现出稀疏性[6].文献[7]和[8]同时利用了时延域和角度域的稀疏性,提出基于CS 的MIMO信道估计方案.然而,上述信道估计方案都是基于平坦衰落或时不变的信道模型,对于DS信道场景中的MIMO系统,还没有研究人员同时利用时延域和角度域的稀疏特性实现信道估计.针对DS信道场景中的MIMO系统,本文作者提出一种新的基于CS的联合稀疏信道估计方案.首先利用复指数基扩展模型(CE-BEM)对DS信道的时变性进行建模,从而将信道估计目标转化为角度域系数恢复问题,然后详细分析了待估计系数矩阵的稀疏结构,接着,提出两种新的贪婪算法对信道参数进行恢复,并通过MATLAB平台仿真实验,验证了本算法具有良好的性能.1 系统模型1.1 双选信道下的复指数扩展模型本文作者研究MIMO正交频分复用(OFDM)下行传输,设基站配备有Nt个发射天线,用户是单天线.用户端的接收信号(1)其中,F是傅里叶变换矩阵,Xnt(nt∈[1,Nt])是第nt个发射天线的发射数据,W表示高斯白噪声,是时域信道矩阵.利用CE-BEM对DS信道进行建模,(2)其中表示第nt个发射天线与用户在第1个时刻,第l条离散径的信道增益,bq(q∈[0,Q-1])是CE-BEM的基函数,是CE-BEM系数,ξl代建模误差.将公式(2)带入公式(1),得到:(3)其中,由的前L列构成,Z为高斯白噪声和CE-BEM建模误差.为了减少MIMO系统的导频开销,采用非正交导频模式,即不同发射天线的导频位置相同.此外,利用频域克罗内克函数(FDKD)导频配置方式,即G个有效导频左右分别放置Q-1个保护导频[9],其中有效导频值设为随机的1或-1,保护导频设为0.设有效导频序列为κval={k0,…,kG-1},则所有导频(包括有效导频和保护导频)序列表示为κ=∪{k-Q+1,…,k,…,k+Q-1},k∈κval.此处,重新定义Q个新子集(4)基于CE-BEM模型和上述稀疏导频模式,对应于κq的接收导频子载波[10](5)其中,为有效导频的值.1.2 建模与稀疏性分析将信道模型转换为角度域分析,第l个信道抽头对应的角度域信道矩阵表示为:(6)其中,Ut是一个酉矩阵,即这里为Ut的共轭转置,In为n阶单位向量,其(m,n)项为定义第l个信道抽头的第q个CE-BEM系数向量为角度域中与之对应的系数向量为满足:(7)结合(2)、(6)和(7)式,角度域信道矩阵可以表示为:(8)其中式中的接收导频载波(9)其中,从而,得到最终的结构化压缩信道估计模型(10)其中,R=([Y]κ1…[Y]κQ);M=IN⊗⊗表示Kronecker积;S是被估计的系数矩阵.因此将信道估计目标转换为求解接下来,分析矩阵S的稀疏结构.首先,考虑信道在时延域的稀疏性.在宽带系统中,时延间隔通常远大于采样周期[5],因此许多矩阵是零矩阵或者所有系数近似等于零.设时延域中的稀疏度是Kd,即中只有Kd个矩阵(对应序列ι={lt1,…,ltKd})有相对较大的系数,其它系数小的矩阵可以被忽略.因此,对所有nt∈[1,Nt],由于∉ι,(11)那么对每个中只有Kd个非零向量.其次,考虑信道在角度域的稀疏性.在实际的MIMO信道中,基站往往高于周围建筑物[6],因此,有用信号只集中在部分角度,角度域呈现出稀疏特性.设角度域中的稀疏度是Ka,即中只有Ka列(相应序列有相对较大的系数,而其它系数较小的列可以被忽略.与式(11)相似,对nt∉有:(12)很明显,对的每个向量应该是一个稀疏度为Ka的向量,且的每个向量中非零元素位置相同.综上所述,当且仅当l∈ι(|ι|=Kd),向量非零,并且对每个l的非零向量共享相同的非零位置.2 贪婪算法基于结构化压缩感知模型,提出两种新的贪婪算法来计算信道参数.两步同时正交匹配追踪(TS-SOMP)算法(图1)包括两个阶段:首先找到所有非零抽头位置.搜寻最佳序号mi∈[0,L-1]使残差最小.根据所获得的mi更新支持向量Ω和矩阵Θ.然后,并计算新的残差.估计非零角度域系数,用同时正交匹配追踪(SOMP)算法[11]计算非零角度域系数.SOMP算法用所选择的矩阵Θ,将接收信号R与稀疏度Kd×Ka作为输入,SΩ作为输出.两环同时正交匹配追踪(TL-SOMP)算法包括内外两层循环.在外部循环的每次迭代中,搜寻最佳序号mi∈[0,L-1]使残差最小.在内部循环的每次迭代中,计算最优序列kj∈[1,Nt]使最大.基于mi和kj,更新支持向量Ω和选择矩阵Θ,然后计算新的残差.最后,得到非零系数SΩ=Θ†R.采用正交匹配追踪(OMP)算法和SOMP算法也可以估计稀疏向量,然而,OMP算法忽略了不同系数向量的联合稀疏性,SOMP算法从NtL行中搜索Kd×Ka个非零行,搜索维度大,精度低.而本文作者提出的TS-SOMP算法中,在阶段1获得非零抽头位置之后,阶段2的未知行数减少至Kd×Nt≪Nt×L,估计的准确性会得到改善.此外,一旦TL-SOMP算法在时延域中找到一个非零抽头位置,就可以从Nt个未知行中估计出Ka个非零行,因此该算法会获得更高的估计精度.根据本算法估计系数向量由(7)式可以得到CE-BEM的系数利用文献[11]中提出的离散长椭球形序列(DPSSs)对估计的CE-BEM系数进行平滑处理再根据(2)式计算信道矩阵Hl.3 仿真结果与分析用MATLAB仿真验证所提算法的性能.表1列出了MIMO-OFDM的系统参数. 表1 仿真参数参数数值子载波数1024发射天线数8CP长64导频组40CE-BEM 阶3子载波间隔15kHz子载波频率3GHz调制QPSK仿真中移动台移动速度为350 km/h,Kd=3,Ka=3,使用斯坦福大学的Interim-1信道模型生成信道参数,信道抽头时延为[0,0.4,0.9] μs,增益是[0,-15,-20] dB.导频子载波数P=(2Q-1)G=200,导频模式由文献[11]中的随机算法获得.为了评估信道估计性能,使用归一化均方误差其中是真实信道参数,是估计值.图1给出了归一化均方误差(NMSE)随信噪比(SNR)变化的曲线.可以看出,所提出的两种算法比传统的SOMP/OMP算法优越.当归一化均方误差NMSE=-20 dB时,与传统SOMP算法相比,TL-SOMP算法实现了约2 dB的SNR增益.这是因为在搜索到时延域中的非零抽头位置之后,可以用较少的列来重建测量矩阵,从而有效地减少估计误差.图1 不同算法的NMSE性能比较4 结论针对DS信道的MIMO-OFDM系统,本文作者同时利用了时延域和角度域的稀疏性,提出了一种新的联合稀疏信道估计模型,并基于该模型提出了两种新的贪婪算法.TS-SOMP算法首先在时延域中找到所有非零抽头位置,然后估计非零角度域系数;TL-SOMP算法在外部循环中找到一个非零抽头位置后,即可直接在内部循环求解非零角度域系数.仿真结果表明,与传统的SOMP/OMP算法相比,本研究所提算法具有更高的估计精度.参考文献:[1] Ren X,Chen W,Tao M X.Position-based compressed channel estimation and pilot design for high-mobility OFDM systems [J].IEEE Transactions on Vehicular Technology,2015,64(5):1918-1929.[2] Aboutorab N,Hardjawana W,Vucetic B.A new iterative Doppler-assisted channel estimation joint with parallel ICI cancellation for high-mobility MIMO-OFDM systems [J].IEEE Transactions on VehicularTechnology,2012,61(4):1577-1589.[3] Muralidhar K,Sreedhar D.Pilot design for vector state-scalar observation Kalman channel estimators in doubly-selective MIMO-OFDM systems [J].IEEE Wireless Communications Letters,2013,2(2):147-150.[4] Zhang Y,Venkatesan R,Dobre O A,et al.Novel compressed sensing-based channel estimation algorithm and near-optimal pilot placement scheme [J].IEEE Transactions on Wireless Communications,2016,15(4):2590-2603.[5] Qi C H,Yue G S,Wu L A,et al.Pilot design schemes for sparse channel estimation in OFDM systems [J].IEEE Transactions on Vehicular Technology,2015,64(4):1493-1505.[6] Rao X B,Lau V K N.Distributed compressive CSIT estimation and feedback for FDD multi-user massive MIMO systems [J].IEEE Transactions on Signal Processing,2014,62(12):3261-3271.[7] Kim S.Angle-domain frequency-selective sparse channel estimation for underwater MIMO-OFDM systems [J].IEEE CommunicationsLetters,2012,16(5):685-687.[8] Pan Y Q,Meng X,Gao X M.A new sparse channel estimation for 2D MIMO-OFDM systems based on compressive sensing [C].Proceedings of the 6th International Conference on Wireless Communications and Signal Processing,Hefei:IEEE,2014.[9] Hrycak T,Das S,Matz G,et al.Practical estimation of rapidly varying channels for OFDM systems [J].IEEE Transactions on Communications,2011,59(11):3040-3048.[10] Gong B,Gui L,Qin Q B,et al.Block distributed compressive sensing-based doubly selective channel estimation and pilot design for large-scale MIMO systems [J].IEEE Transactions on VehicularTechnology,2017,66(10):9149-9161.[11] Cheng P,Chen Z,Rui Y,et al.Channel estimation for OFDM systems over doubly selective channels:a distributed compressive sensing based approach [J].IEEE Transactions on Communications,2013,61(10):4173-4185.。

基于图像结构模型的压缩感知图像重构方法

基于图像结构模型的压缩感知图像重构方法随着数字图像在各个领域的广泛应用，如视频监控、医学影像以及移动通信等，对图像传输和存储的要求也越来越高。

然而，由于图像数据量庞大，传输和存储的成本也随之增加。

为了解决这一问题，压缩感知（Compressed Sensing，CS）技术被提出并逐渐得到应用。

压缩感知技术的基本思想是在图像采集中对图像进行压缩，即不直接采集完整的图像数据，而是对其进行稀疏采样，然后通过稀疏的采样数据来重构完整的图像。

而图像结构模型就是其中一种常用的重构方法之一。

图像结构模型是一种基于图像自身的特性进行建模和重构的方法。

它利用图像的边缘、纹理和结构等特征来提取图像信息，从而实现更加准确和高质量的图像重构。

下面将介绍基于图像结构模型的压缩感知图像重构方法的具体步骤和原理。

一、图像结构模型的建立在压缩感知图像重构过程中，首先需要建立图像结构模型。

这个步骤涉及到对图像的稀疏表示，常用的方法有小波变换、稀疏表示字典以及图像分割等。

小波变换是一种常用的图像分析和压缩方法，通过将图像进行小波变换来提取图像的频域信息，进而实现图像的稀疏表示。

稀疏表示字典则是通过提前建立一个字典，将图像的局部结构进行编码，从而实现图像的稀疏表示。

图像分割是将图像划分为若干个小块，每个小块可以看做是具有相似结构的局部区域，从而实现图像的稀疏表示。

二、图像重构算法建立好图像结构模型后，下一步就是利用稀疏采样数据对图像进行重构。

常用的图像重构算法有基于最小二乘法的估计（Least Squares，LS）、基于迭代阈值法的估计（Iterative Shrinkage-Thresholding Algorithm，ISTA）以及基于广义估计最小二乘法的估计（Generalized Estimation of Signal and Noise，GESPAR）等。

LS方法是一种常见的图像重构算法，它通过将图像重构问题转换成一个最小二乘问题，通过最小化重构图像与原始图像之间的欧式距离来进行重构。

(综述)CHANNEL ESTIMATION FOR OFDM SYSTEMS

ቤተ መጻሕፍቲ ባይዱ
As in many other coherent digital wireless receivers, channel estimation is also an integral part of the receiver designs in coherent MIMO-OFDM systems [13]. In wireless systems, transmitted information reaches to receivers after passing through a radio channel. For conventional coherent receivers, the effect of the channel on the transmitted signal must be estimated to recover the transmitted information [14]. As long as the receiver accurately estimates how the channel modifies the transmitted signal, it can recover the transmitted information. Channel estimation can be avoided by using differential modulation techniques, however, such systems result in low data rate and there is a penalty for 3–4 dB SNR [15 19]. In some cases, channel estimation at user side can be avoided if the base station performs the channel estimation and sends a pre-distorted signal [20]. However, for fast varying channels, the pre-distorted signal might not bear the current channel distortion, causing system degradation. Hence, systems with a channel estimation block are needed for the future high data rate systems. Channel estimation is a challenging problem in wireless systems. Unlike other guided media, the radio channel is highly dynamic. The transmitted signal travels to the receiver by undergoing many detrimental effects that corrupt the signal

OFDM Channel Estimation by

OFDM Channel Estimation bySingular Value DecompositionOve Edfors,Associate Member,IEEE,Magnus Sandell,Associate Member,IEEE, Jan-Jaap van de Beek,Student Member,IEEE,Sarah Kate Wilson,Member,IEEE,and Per Ola B¨o rjesson,Member,IEEEAbstract—In this paper we present and analyze low-rank channel estimators for orthogonal frequency-division multiplex-ing(OFDM)systems using the frequency correlation of the channel.Low-rank approximations based on the discrete Fourier transform(DFT)have been proposed,but these suffer from poor performance when the channel is not sample spaced.We apply the theory of optimal rank-reduction to linear minimum mean-squared error(LMMSE)estimators and show that these estimators,when using aﬁxed design,are robust to changes in channel correlation and signal-to-noise ratio(SNR).The perfor-mance is presented in terms of uncoded symbol-error rate(SER) for a system using16-quadrature amplitude modulation(QAM). Index Terms—Channel estimation,OFDM.I.I NTRODUCTIONW IRELESS digital communication systems using multi-amplitude modulation schemes,such as quadrature am-plitude modulation(QAM),generally require estimation and tracking of the fading channel.In general,this means a more complex receiver than for differential modulation schemes, such as differential phase-shift keying(DPSK),where the receivers operate without a channel estimate[1].In orthogonal frequency-division multiplexing(OFDM)sys-tems,DPSK is appropriate for relatively low data rates,such as in the European digital–audio broadcast(DAB)system [2].However,for more spectrally efﬁcient OFDM systems, coherent modulation is more appropriate.The structure of OFDM signaling allows a channel estimator to use both time and frequency correlation.Such a two-dimensional estimator structure is generally too complex for a practical implementation.To reduce the complexity,separating the use of time and frequency correlation has been proposed [3].This combined scheme uses two separateﬁnite-impulse response(FIR)Wienerﬁlters,one in the frequency direction and the other in the time direction.Paper approved by O.Andrisano,the Editor for Fading Channels of the IEEE Communications Society.Manuscript received August15,1996;revised July15,1997and February15,1998.This work was presented in part at the1996Vehicular Technology Conference(VTC’96),Atlanta,GA,April 28–May1,1996.O.Edfors is with the Department of Applied Electronics,Lund University, SE–22100Lund,Sweden.M.Sandell is with Bell Laboratories,Lucent Technologies,Swindon SN5 6PP,U.K.J.-J.van de Beek,S.K.Wilson,and P.O.B¨o rjesson are with the Division of Signal Processing,Lule˚a University of Technology,SE–97187Lule˚a, Sweden.Publisher Item Identiﬁer S0090-6778(98)05166-6.In this paper we present and analyze a class of block-oriented channel estimators for OFDM,where only the fre-quency correlation of the channel is used in the estimation. Whatever their level of performance,they may be improved with the addition of a secondﬁlter using the time correlation [3],[4].Though the linear minimum mean-squared error(LMMSE) estimator using only frequency correlation has lower complex-ity than one using both time and frequency correlation,it still requires a large number of operations.We introduce a low-complexity approximation to the frequency-based LMMSE estimator that uses the theory of optimal rank reduction[5]. Other types of low-rank approximations,based on the discrete-time Fourier transform(DFT),have been proposed for OFDM systems before[6]–[8].The work presented in this paper was inspired by the observations in[8],where it is shown that DFT-based low-rank channel estimators have limited performance for nonsample-spaced channels and high signal-to-noise ratios (SNR’s).After presenting the OFDM system model and our scenario in Section II,we introduce the estimators and derive their complexities in Section III.We analyze the symbol-error rate (SER)performance in Section IV,where we also discuss design considerations.The proposed low-rank estimator is compared to other estimators in Section V and a summary and concluding remarks appear in Section VI.II.S YSTEM D ESCRIPTIONA.System ModelFig.1displays the OFDM baseband model used in this paper.We assume that the use of a cyclic preﬁx(CP)[9] both preserves the orthogonality of the tones and eliminates intersymbol interference(ISI)between consecutive OFDM symbols.Further,the channel is assumed to be slowly fading, so it is considered to be constant during one OFDM symbol. The number of tones in the systemisFig.1.Baseband model of an OFDM system.CP denotes the cyclicpreﬁx.Fig.2.The OFDM system,described as a set of parallel Gaussian channelswith correlated attenuations.the system.In matrix notation we describe the OFDM systemasis the receivedvector,is a diagonal matrixcontaining the transmitted signalingpoints,is a channel attenuation vector,andis assumed to be uncorrelated withthechannelimpulses(2)whereare zero-mean complex Gaussian random variables with a power-delayproﬁleimpulses,an exponentially decaying power-delayproﬁleanddelays that are uniformly andindependently distributed over the length of the CP.For correlation properties of this channel model,see Appendix A.C.ScenarioOur scenario consists of a wireless 16-QAM OFDM system,designed for an outdoor environment,that is capable of carrying digital video.The system operates with a 500-kHz bandwidth and is divided into 64tones with a total symbolperiod of136s constitute the CP.One OFDM symbol thus consists of 68samples,four of which constitute theCPs)for the power-delayproﬁle.III.L INEAR E STIMATION A CROSS T ONESIn the following section we present a reduced-complexityLMMSE estimate of the channelattenuationsfrom the receivedvectorand the transmitteddata The complexity reduction of the LMMSE estimator consists of two separate steps.In the ﬁrst step we modify the LMMSE by averaging over the transmitted data,obtaining a simpliﬁed estimator.In the second step we reduce the number of mul-tiplications required by applying the theory of optimal rank reduction [5].A.LMMSE EstimationThe LMMSE estimate of the channelattenuations in (1),given the receiveddata and the transmittedsymbols,is[8]is the varianceof the additive channel noise,andis the channel autocorrelation matrix.Thesuperscriptin (3)with itsexpectation,we obtainthe simpliﬁedestimatorEDFORS et al.:OFDM CHANNEL ESTIMATION933whereneeds to be calculatedonly once.Under these conditions the estimationrequiresestimatorisis a diagonal matrix withentriesas a transform,2the singularvalueth transform coefﬁcient after transforming the LSestimateSince is unitary,this transformation can be viewedas rotating thevectoris the one-sided bandwidthandis the length of theCPestimator in(7)isshown in Fig.4,where the LS estimate is calculatedfromThe low-rank estimator can beinterpreted asﬁrst projecting the LS estimates onto a subspace1Since we are dealing with Hermitian matrices,the k’s are also eigenval-ues.However,we use the terminology of the SVD since it is more generaland can be used in optimal rank reduction of nonsquare matrices.2The transform in this special case of low-rank approximation is theKarhunen–Loeve(a.k.a.Hotelling)transform of h:Fig.3.Relative channel power k=E fj h k j2g of the transform coefﬁcients.The system uses64tones and the channel parameters are L=4andrms=1;see Sections II-B andII-C.Fig.4.Block diagram of the rank-p channel estimator.and then performing the estimation.If the subspace has a smalldimension and can describe the channel well,the complexity ofthe estimator will be low while showing a good performance.C.Estimator ComplexityThe low-rank estimators will have an irreducible errorﬂoordue to the part of the channel that does not belong to thesubspace.To eliminate this errorﬂoor up to a given SNR,weneed to make sure that our estimator rank is sufﬁciently large.This prompts an analysis of the computational complexity oftherank-tois,the lower the computational complexity,but the largerthe approximation error becomes.Following the analysis inSection III-B,we can expect a good approximationwhenestimator is used directly on all tones in thesystem.One solution to this problem is to partition the tonesinto reasonably sized blocks and,at a certain performanceloss,perform the estimation independently in these blocks.By dividing the channel attenuationsinto934IEEE TRANSACTIONS ON COMMUNICATIONS,VOL.46,NO.7,JULY 1998Referring again to the dimension of the space of essentially time-and band-limited signals [11],the expected number ofessential base vectors is reducedfromto Hence,the complexity of the estimator decreases accordingly.To illustrate the idea,let us assume a systemwithand the ratio between the length of the CP and the number oftones......By estimating the channelattenuationsanddenotes a channel with differentstatisticsthanestimate (7)becomes (see AppendixD)th diagonal elementof,cf.(6).Sinceelements can be expectedto contain most of the power.This property will ensure only a small performance loss when the estimator is designed for wrong channel statistics.Fixed FIR estimators have been investigated in [3]and [13],where it is shown that a design for the worst correlation is robust to mismatch.This design rule turns out to hold for low-rank estimators as well.Hence,we will design the estimator for a uniform power-delay proﬁle [3].As for mismatch in SNR,a design for a high SNR is preferable.This can intuitively be explained by the fact that a channel estimation error is concealed in noise for low SNR,whereas it tends to dominate for high SNR where the noise is low.Hence,it is important to keep the channel estimation error low at high SNR,which justiﬁes a design for high SNR.This interpretation is conﬁrmed in Fig.5,where the SER curves for a design SNR of 0,10,and 20dB are shown.B.Rank Reduction The MSE of therank-(10)which is the sum of the channel power in the transform coefﬁcients not used in the estimate.This MSEﬂoor will cause an irreducible error ﬂoor in the SER’s.EDFORS et al.:OFDM CHANNEL ESTIMATION935Fig.6.SERﬂoor as function of estimator rank.The irreducible errorﬂoor is the main limitation on thecomplexity reduction achieved by optimal rank reduction.TheSERﬂoors are shown as a function of the rank in Fig.6.Ifthe rank is too low,the irreducible errorﬂoor will becomevisible for the SNR of interest.By choosing the appropriaterank on the estimator,we can essentially avoid the impactfrom the SERﬂoor up to a given SNR.For a full rankestimator,no SERﬂoor exists.From Fig.6,it canbe seen that the irreducible errorﬂoor decreases rapidly forrank936IEEE TRANSACTIONS ON COMMUNICATIONS,VOL.46,NO.7,JULY1998Fig.9.Low-rank estimator for the PSAM case.For each OFDM symbol,Ppilots are used to estimate N tones.Fig.10.The MSE of the low-rank estimator and the FIR Wienerﬁlterestimator for the PSAM case.The two estimators have the same computationalcomplexity(eight multiplications per tone).carrier.Every OFDM symbol is partitioned into subsymbolsconsisting of384subcarriers,each containingbecomesThe correlation matrix for the attenuation vector’s independent)(11)whereEDFORS et al.:OFDM CHANNEL ESTIMATION 937and the power-delay proﬁleisSubstituting in (11)andnormalizingto unity givesusandestimator [5]isthenistheupper left cornerof,i.e.,we excludeall butthe,so it is difﬁcult to further reduce (13).However,in the case of all pilots wehaveWe note that they share thesame singular vectors,i.e.,the onesofestimator (13)nowbecomesisthe upper left cornerofare the Euclid-ian inner products,requiringmultiplications.The linear combinationofalsorequires mul-tiplications.The estimation thusrequiresmultiplications and the total number of multiplications per tonebecomes Similarly,therank-whereand re-quirevectors oflengthmultiplications.Sinceestimatorin (7)for the case of all pilots (the data is known to the receiver).We also present the MSE ﬂoor,which bounds the achievable MSE from below in low-rank approximations of the LMMSE estimator.To get a general expression for the MSE for therank-has thecorrelationand the real SNRis From (1)and (4),wehave,where the noiseterm has the autocovariancematrixThe estimationerrorestimator (7)is (15)and the average MSEis938IEEE TRANSACTIONS ON COMMUNICATIONS,VOL.46,NO.7,JULY1998To simplify the expression,we use the facts that:•if is a unitary matrix;•when is a diagonalmatrix with the elementsth transform coefﬁcient,i.e.,the,by what wecall the MSEﬂoorEDFORS et al.:OFDM CHANNEL ESTIMATION939Sarah Kate Wilson(M’87)received the A.B.degree in mathematics from Bryn Mawr College,Bryn Mawr,PA,in1979,and the M.S.and Ph.D.degrees in electrical engineering from StanfordUniversity,Stanford,CA,in1987and1994.From1979to1985she was a Program-mer/Analyst with the IIT Research Institute atthe Electromagnetic Compatibility Analysis Center.From1985to1986she was a Research Engineerwith SRI International,working with signalprocessing algorithms for lasar radar systems.From 1987to1989she was a Signal Processing Engineer with Nellcor,Inc.,a medical electronics company.She was an Assistant Professor of electrical and computer engineering with Purdue University,West Lafayette,IN,from 1994to1997.She is currently an Assistant Professor with the Division of Signal Processing,Lule˚a University of Technology,Lule˚a,Sweden.Per Ola B¨o rjesson(S’85–M’80)was born in Karl-shamn,Sweden,in1945.He received the M.Sc.degree in electrical engineering,the Ph.D.degreein telecommunication theory,and the Docent inTelecommunication Theory degree from Lund Insti-tute of Technology,Lund,Sweden,in1970,1980,and1983,respectively.Since1988he has been a Professor of signalprocessing with Lule˚a University of Technology,Lule˚a,Sweden.His primary research interest isin high performance communication systems,in particular,high-data-rate wireless and twisted pair systems.He is presently researching signal processing techniques in communication systems that use OFDM or discrete multitone(DMT)modulation.He emphasizes the interaction between models and real systems from the creation of application-oriented models based on system knowledge to the implementation and evaluation of algorithms.。

channel Estimation techniques based on pilot arrangement in ofdm systems

Channel Estimation Techniques Based on Pilot Arrangement in OFDM SystemsSinem Coleri,Mustafa Ergen,Anuj Puri,and Ahmad BahaiAbstract—The channel estimation techniques for OFDM systems based on pilot arrangement are investigated.The channel estimation based on comb type pilot arrangement is studied through different algorithms for both estimating channel at pilot frequencies and interpolating the channel.The estimation of channel at pilot frequencies is based on LS and LMS while the channel interpolation is done using linear interpolation,second order interpolation,low-pass interpolation,spline cubic interpo-lation,and time domain interpolation.Time-domain interpolation is obtained by passing to time domain through IDFT(Inverse Discrete Fourier Transform),zero padding and going back to frequency domain through DFT(Discrete Fourier Transform). In addition,the channel estimation based on block type pilot arrangement is performed by sending pilots at every sub-channel and using this estimation for a specific number of following symbols.We have also implemented decision feedback equalizer for all sub-channels followed by periodic block-type pilots.We have compared the performances of all schemes by measuring bit error rate with16QAM,QPSK,DQPSK and BPSK as modulation schemes,and multi-path Rayleigh fading and AR based fading channels as channel models.Index Terms—Cochannel interference,communication chan-nels,data communication,digital communication,frequency division multiplexing,frequency domain analysis,time domain analysis,time-varying channels.I.I NTRODUCTIONO RTHOGONAL Frequency Division Multiplexing (OFDM)has recently been applied widely in wireless communication systems due to its high data rate transmission capability with high bandwidth efficiency and its robustness to multi-path delay.It has been used in wireless LAN standards such as American IEEE802.11a and the European equivalent HIPERLAN/2and in multimedia wireless services such as Japanese Multimedia Mobile Access Communications.A dynamic estimation of channel is necessary before the de-modulation of OFDM signals since the radio channel is fre-quency selective and time-varying for wideband mobile com-munication systems[1].The channel estimation can be performed by either inserting pilot tones into all of the subcarriers of OFDM symbols with a specific period or inserting pilot tones into each OFDM symbol. The first one,block type pilot channel estimation,has beenManuscript received February19,2002;revised June12,2002.This work was supported by the Office of Naval Research and National Semiconductor. S.Coleri,M.Ergen,and A.Puri are with Electrical Engineering, UC Berkeley,Berkeley,CA,USA(e-mail:{csinem;ergen;anuj}@ ).A.Bahai is with Electrical Engineering,Stanford University,Stanford,CA, USA(e-mail:ahmad.bahai@).Publisher Item Identifier10.1109/TBC.2002.804034.developed under the assumption of slow fading channel.Even with decision feedback equalizer,this assumes that the channel transfer function is not changing very rapidly.The estimation of the channel for this block-type pilot arrangement can be based on Least Square(LS)or Minimum Mean-Square(MMSE). The MMSE estimate has been shown to give10–15dB gain in signal-to-noise ratio(SNR)for the same mean square error of channel estimation over LS estimate[2].In[3],a low-rank ap-proximation is applied to linear MMSE by using the frequency correlation of the channel to eliminate the major drawback of MMSE,which is complexity.The later,the comb-type pilot channel estimation,has been introduced to satisfy the need for equalizing when the channel changes even in one OFDM block. The comb-type pilot channel estimation consists of algorithms to estimate the channel at pilot frequencies and to interpolate the channel.The estimation of the channel at the pilot frequencies for comb-type based channel estimation can be based on LS, MMSE or Least Mean-Square(LMS).MMSE has been shown to perform much better than LS.In[4],the complexity of MMSE is reduced by deriving an optimal low-rank estimator with singular-value decomposition.The interpolation of the channel for comb-type based channel estimation can depend on linear interpolation,second order in-terpolation,low-pass interpolation,spline cubic interpolation, and time domain interpolation.In[4],second-order interpola-tion has been shown to perform better than the linear interpola-tion.In[5],time-domain interpolation has been proven to give lower bit-error rate(BER)compared to linear interpolation.In this paper,our aim is to compare the performance of all of the above schemes by applying16QAM(16Quadrature Amplitude Modulation),QPSK(Quadrature Phase Shift Keying),DQPSK(Differential Quadrature Phase Shift Keying) and BPSK(Binary Phase Shift Keying)as modulation schemes with Rayleigh fading and AR(Auto-Regressive)based fading channels as channel models.In Section II,the description of the OFDM system based on pilot channel estimation is given.In Section III,the estimation of the channel based on block-type pilot arrangement is discussed.In Section IV,the estimation of the channel at pilot frequencies is presented.In Section V,the different interpolation techniques are introduced. In Section VI,the simulation environment and results are described.Section VII concludes the paper.II.S YSTEM D ESCRIPTIONThe OFDM system based on pilot channel estimation is given in Fig.1.The binary information is first grouped and mapped ac-0018-9316/02$17.00©2002IEEEFig.1.Baseband OFDM system.cording to the modulation in “signal mapper.”After inserting pi-lots either to all sub-carriers with a specific period or uniformly between the information data sequence,IDFT block is used totransform the data sequence oflength into time do-mainsignalis the DFT length.Following IDFT block,guard time,which is chosen to be larger than the expected delay spread,is inserted to prevent inter-symbol interference.This guard time includes the cyclically extended part of OFDM symbol in order to eliminate inter-carrier interference (ICI).The resultant OFDM symbol is given asfollows:(2)wherewill pass through the frequency selective timevarying fading channel with additive noise.The received signal is givenby:(3)whereis Additive White Gaussian Noise (AWGN)andcan be represented by[5]:is the total number of propagationpaths,thpath,is theis delay spreadindex,th path delay normalized by the sampling time.Atthe receiver,after passing to discrete domain through A/D and low pass filter,guard time isremoved:for(5)Thenis sent to DFT block for the followingoperation:(6)Assuming there is no ISI,[8]shows the relation of theresulting,(7)where(8)Then the binary information data is obtained back in “signal demapper”block.III.C HANNEL E STIMATION B ASED ON B LOCK -T YPEP ILOT A RRANGEMENT In block-type pilot based channel estimation,OFDM channel estimation symbols are transmitted periodically,in which all sub-carriers are used as pilots.If the channel is constant during the block,there will be no channel estimation error since the pi-lots are sent at all carriers.The estimation can be performed by using either LS or MMSE [2],[3].If inter symbol interference is eliminated by the guard in-terval,we write (7)in matrixnotation.........is Gaussian and uncorre-lated with the channelnoise (11)COLERI et al.:CHANNEL ESTIMATION TECHNIQUES BASED ON PILOT ARRANGEMENT IN OFDM SYSTEMS225whereand.and represents the noisevariance.When the channel is slow fading,the channel estimation in-side the block can be updated using the decision feedback equal-izer at each sub-carrier.Decision feedback equalizer fortheThe channel response attheis used to find the estimated trans-mittedsignal(14)is mapped to the binary data through“signaldemapper”and then obtained back through“signal mapper”as.(15)Since the decision feedback equalizer has to assume that thedecisions are correct,the fast fading channel will cause thecomplete loss of estimated channel parameters.Therefore,asthe channel fading becomes faster,there happens to be a com-promise between the estimation error due to the interpolationand the error due to loss of channel tracking.For fast fadingchannels,as will be shown in simulations,the comb-type basedchannel estimation performs much better.IV.C HANNEL E STIMATION AT P ILOT F REQUENCIES INC OMB-T YPE P ILOT A RRANGEMENTIn comb-type pilot based channel estimation,the(16)where th pilotcarrier value.Wedefine as the fre-quency response of the channel at pilot sub-carriers.The esti-mate of the channel at pilot sub-carriers based on LS estimationis givenby:(17)where th pilotsub-carrier respectively.Since LS estimate is susceptible to noise and ICI,MMSEis proposed while compromising complexity.Since MMSEincludes the matrix inversion at each iteration,the simplifiedlinear MMSE estimator is suggested in[6].In this simplifiedversion,the inverse is only need to be calculated once.In[4],the complexity is further reduced with a low-rank approxima-tion by using singular valuedecomposition.Fig.2.Pilot arrangement.V.I NTERPOLATION T ECHNIQUES IN C OMB-T YPEP ILOT A RRANGEMENTIn comb-type pilot based channel estimation,an efficient in-terpolation technique is necessary in order to estimate channelat data sub-carriers by using the channel information at pilotsub-carriers.The linear interpolation method is shown to perform betterthan the piecewise-constant interpolation in[7].The channelestimation at thedata-carrier(18)The second-order interpolation is shown to fit better than linearinterpolation[4].The channel estimated by second-order inter-polation is givenby:226IEEE TRANSACTIONS ON BROADCASTING,VOL.48,NO.3,SEPTEMBER 2002TABLE IS IMULATION PARAMETERSinterpolation (spline function in MATLAB )produces a smooth and continuous polynomial fitted to given data points.The time domain interpolation is a high-resolution interpolation based on zero-padding and DFT/IDFT [8].After obtaining the estimatedchannelpoints with the followingmethod:(22)VI.S IMULATIONA.Description of Simulation1)System Parameters:OFDM system parameters used in the simulation are indicated in Table I:We assume to have perfect synchronization since the aim is to observe channel estimation performance.Moreover,we have chosen the guard interval to be greater than the maximum delay spread in order to avoid inter-symbol interference.Simulations are carried out for different signal-to-noise (SNR)ratios and for different Doppler spreads.2)Channel Model:Two multi-path fading channel models are used in the simulations.The 1st channel model is the ATTC (Advanced Television Technology Center)and the Grande Al-liance DTV laboratory’s ensemble E model,whose static case impulse response is givenby:(24)whereis chosen to be close to 1in order to satisfy the assumption that channel impulse response does not change within one OFDM symbol duration.In thesimulations,COLERI et al.:CHANNEL ESTIMATION TECHNIQUES BASED ON PILOT ARRANGEMENT IN OFDM SYSTEMS227Fig. 5.BPSK modulation with Rayleigh fading (channel 1,Doppler freq.70Hz).Fig.6.QPSK modulation with Rayleigh fading (channel 1,Doppler freq.70Hz).The channel estimation at pilot frequencies is performed by using either LS or LMS.Then all of the possible interpola-tion techniques (linear interpolation,second order interpolation,low-pass interpolation,spline cubic interpolation,and time do-main interpolation)are applied to LS estimation result to inves-tigate the interpolation effects and linear interpolation is applied to LMS estimation results to compare with the LS overall esti-mation results.B.Simulation ResultsThe legends “linear,second-order,low-pass,spline,time do-main”denote interpolation schemes of comb-type channel es-timation with the LS estimate at the pilot frequencies,“block type”shows the block type pilot arrangement with LS estimate at the pilot frequencies and without adjustment,“decision feed-back”means the block type pilot arrangement with LS estimate at the pilot frequencies and with decision feedback,and“LMS”Fig.7.16QAM modulation with Rayleigh fading (channel 1,Doppler freq.70Hz).Fig.8.DQPSK modulation with Rayleigh fading (channel 1,Doppler freq.70Hz).is for the linear interpolation scheme for comb-type channel es-timation with LMS estimate at the pilot frequencies.Figs.5–8give the BER performance of channel estimation algorithms for different modulations and for Rayleigh fading channel,with static channel response given in (23),Doppler fre-quency 70Hz and OFDM parameters given in Table I.These re-sults show that the block-type estimation and decision feedback BER is 10–15dB higher than that of the comb-type estimation type.This is because the channel transfer function changes so fast that there are even changes for adjacent OFDM symbols.The comb-type channel estimation with low pass interpola-tion achieves the best performance among all the estimation techniques for BPSK,QPSK,and 16QAM modulation.The per-formance among comb-type channel estimation techniques usu-ally ranges from the best to the worst as follows:low-pass,spline,time-domain,second-order and linear.The result was ex-pected since the low-pass interpolation used in simulation does the interpolation such that the mean-square error between the228IEEE TRANSACTIONS ON BROADCASTING,VOL.48,NO.3,SEPTEMBER2002Fig.9.16QAM modulation with AR fading(channel1).Fig.10.16QAM modulation with Rayleigh fading(channel2,Doppler freq.70Hz).interpolated points and their ideal values is minimized.Theseresults are also consistent with those obtained in[4]and[5].DQPSK modulation based channel estimation shows almostthe same performance for all channel estimation techniques ex-cept the decision-feedback method.This is expected because di-viding two consecutive data sub-carriers in signal de-mappereliminates the time varying fading channel effect.The errorin estimation techniques result from the additive white noise.The BER performance of DQPSK for all estimation types ismuch better than those with modulations QPSK and16QAMand worse than those with the BPSK modulation for high SNR.The effect of fading on the block type and LMS estimationcan be observed from Fig.9for autoregressive channel modelwith different fading parameters.As the fading factor“COLERI et al.:CHANNEL ESTIMATION TECHNIQUES BASED ON PILOT ARRANGEMENT IN OFDM SYSTEMS229worse than that of the best estimation.Therefore,some perfor-mance degradation can be tolerated for higher data bit rate for low Doppler spread channels although low-pass interpolation comb-type channel estimation is more robust for Doppler fre-quency increase.A CKNOWLEDGMENTThe authors are grateful to Prof.P.Varaiya for his help.R EFERENCES[1] A.R.S.Bahai and B.R.Saltzberg,Multi-Carrier Digital Communica-tions:Theory and Applications of OFDM:Kluwer Academic/Plenum, 1999.[2]J.-J.van de Beek,O.Edfors,M.Sandell,S.K.Wilson,and P.O.Bor-jesson,“On channel estimation in OFDM systems,”in Proc.IEEE45th Vehicular Technology Conf.,Chicago,IL,Jul.1995,pp.815–819.[3]O.Edfors,M.Sandell,J.-J.van de Beek,S.K.Wilson,and P.O.Br-jesson,“OFDM channel estimation by singular value decomposition,”IEEE mun.,vol.46,no.7,pp.931–939,Jul.1998.[4]M.Hsieh and C.Wei,“Channel estimation for OFDM systems based oncomb-type pilot arrangement in frequency selective fading channels,”IEEE Trans.Consumer Electron.,vol.44,no.1,Feb.1998.[5]R.Steele,Mobile Radio Communications.London,England:PentechPress Limited,1992.[6]U.Reimers,“Digital video broadcasting,”IEEE Commun.Mag.,vol.36,no.6,pp.104–110,June1998.[7]L.J.Cimini,“Analysis and simulation of a digital mobile channel usingorthogonal frequency division multiplexing,”IEEE mun., vol.33,no.7,pp.665–675,Jul.1985.[8]Y.Zhao and A.Huang,“A novel channel estimation method for OFDMMobile Communications Systems based on pilot signals and transform domain processing,”in Proc.IEEE47th Vehicular Technology Conf., Phoenix,USA,May1997,pp.2089–2093.[9] A.V.Oppenheim and R.W.Schafer,Discrete-Time Signal Processing,New Jersey:Prentice-Hall Inc.,1999.[10]“Digital video broadcasting(DVB):Framing,channel coding and mod-ulation for digital terrestrial television,”,Draft ETSI EN300744V1.3.1 (2000-08).[11]Y.Li,“Pilot-symbol-aided channel estimation for OFDM in wirelesssystems,”IEEE Trans.Vehicular Technol.,vol.49,no.4,Jul.2000.Sinem Coleri is a Ph.D.student in the Department of Electrical Engineering and Computer Science at University of California,Berkeley.She received her B.S.from Bilkent University in June2000.Her research interests include com-munication theory,adhoc networks,and mobile IP.Mustafa Ergen is a Ph.D.student in the Department of Electrical Engineering and Computer Science at University of California,Berkeley.He received his M.S.degree from University of California Berkeley in May2002and his B.S. degree from Middle East Technical University as a METU Valedictorian in June 2000.His research interests are in wireless networks and communication theory.Anuj Puri received his Ph.D.from the University of California,Berkeley in December1995.He was with Bell Labs of Lucent Technologies until December 1998.Since then he has been with the Department of Electrical Engineering and Computer Sciences at UC Berkeley.His interests are in wireless networks and embedded systems.Ahmad Bahai received his M.S.degree in electrical engineering from Impe-rial College,University of London in1988and his Ph.D.degree in electrical engineering from University of California at Berkeley in1993.From1992to 1994he worked as a member of technical staff in the wireless communications division of TCSI.He joined AT&T Bell Laboratories in1994where he was Technical Manager of Wireless Communication Group in Advanced Commu-nications Technology Labs until1997.He has been involved in design of PDC, IS-95,GSM,and IS-136terminals and base stations,as well as ADSL and Cable modems.He is one of the inventors of Multi-carrier CDMA(OFDM)concept and proposed the technology for the third generation wireless systems.He was the co-founder and Chief Technical Officer of ALGOREX Inc.and currently is the Chief Technology Officer of National Semiconductor,wireless division.He is an adjunct/consulting professor at Stanford University and UC Berkeley.His research interests include adaptive signal processing and communication theory. He is the author of more than30papers and reports and his book on Multi-Car-rier Digital Communications is published by Kluwer/Plenum.Dr.Bahai holds five patents in the Communications and Signal Processing field and currently serves as an editor of IEEE Communication Letters.。

非均匀块稀疏信号的压缩采样与盲重构算法

理论证明。在此基础上，提出了一种块稀疏阶数和块分布未知情况下的非均匀块稀疏信号盲重构算法，按照逐次递减的块长度，对非均匀块稀疏信号进行多次均匀切割，利用正交匹配追踪算法逐次剔除均匀块中的零值位置，从而精确估计信号中非零块位置，实现信号的准确重构。理论分析了算法的性能，仿真实验进一步验证了算法的有效性和实用性。关键词：信号处理；压缩采样；块稀疏；约束等距常数；盲重构算法中图分类号：TN911.72 DOI: 10.3724/SP.J.1146.2012.00598 文献标识码： A 文章编号：1009-5896(2013)02-0445-06
2
块稀疏信号的定义
文献[5]将 RIP 推广至 k 阶块稀疏向量，得到了 Block-RIP，并定义其约束等距常数为 δB 。其实无论对于 k 阶稀疏向量，还是 k 阶块稀疏向量，都属于 k 阶子空间联合稀疏向量[4]的特例，其测量矩阵都需要满足 RIP 特性，所不同的是其约束等距常数各有差异。从子空间联合的角度，任意 k 阶稀疏信号 x ∈ N 都可以被看作是来自于一个子空间联合 M ：
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OPTimization, L-OPT)，并将 OMP 和 MP 算法推广至块稀疏信号提出了 BMP 和 BOMP 算法，文献 [10]中提出的 CoSaMP 算法也可以用来完成块稀疏信号的重构。但是，上述算法均需要预先知道信号的稀疏度及块的分布，而在实际应用中，该条件通常是很难满足的，因此，本文提出了一种信号稀疏度及块分布未知的盲重构算法，并对算法进行了理论分析和仿真验证。
⎛N ⎞ ⎛L ⎞ ⎟ ⎜ ⎟ ⎜ ⎟ ⎟ ⎜ m'k = ⎜ ，而对于 k 阶均匀块稀疏信号。 m = ⎟ ⎟ ⎜ k ⎜ ⎟ ⎟ ⎜ ′ k ⎜ k ⎟ ⎟ ⎜ ⎝ ⎠ ⎝ ⎠

无线信道测量与建模方法研究

摘要下一代移动通信系统网络融合加快，移动互联网应用高速发展，使得有关的新技术和新应用成为移动通信系统研究的重大内容。

在新的应用场景下，由于存在多径传播和时变性，作为传播媒介的无线信道，对无线通信系统的性能有着巨大的影响。

因此，无线信道的测量与建模对于其传输技术的研究有着重要的指导意义。

本文基于无线信道的传播特性，对无线信道的测量与建模方法进行研究。

主要研究内容如下：首先，简单回顾了无线信道的传播特性，包括大尺度传播特性和小尺度传播特性。

介绍了无线信道测量与建模的基本原理，对现有的测量方法和建模方法进行了归纳和总结。

最后以信道模型在无线电导航频率规划中的应用，说明信道建模的工程实践意义，通过仿真计算，指配结果与美国联邦航空局标准吻合，提供了一种简单有效的频率指配方法。

然后，本文研究了大尺度衰落信道建模方法，对采用最小二乘法的经典大尺度衰落建模作了说明。

基于确定性的环境地形，重点对基于射线跟踪的信道建模方法做了介绍，并采用WinProp的传播估计模型，对典型场景进行了传播预测。

预测结果显示，基于射线跟踪的建模方法能够适应性地跟踪具体传播环境，对场景信道实现更精准地建模。

类似地，研究了小尺度衰落信道建模方法。

首先介绍了小尺度衰落信道的特性描述和抽头延迟线模型，为了建立小尺度衰落信道模型，重点对基于解相关算法、扩频滑动相关法、压缩感知的信道估计方法进行了研究，对其原理分别做了介绍，并在一定条件下作了仿真分析。

结果表明：解相关算法不依赖于探测波形，都能够实现原始信道的估计，但其估计性能的优劣与探测脉冲的形状有关，更符合理想冲激脉冲的波形有着更高的估计性能；扩频滑动相关法抗噪声性能良好，能够很好地估计出多径信道。

在多种伪噪声序列中，m序列实现简单，有着优良的自相关性能，是最为常用的伪噪声序列；压缩感知算法充分利用无线信道的稀疏性，可以在一定条件下实现信道的精确估计，其中正交匹配追踪算法实现简单，重构效果良好，应用较为广泛。

一种基于压缩感知的信道估计方法

一种基于压缩感知的信道估计方法作者：苏子业来源：《价值工程》2020年第24期摘要：利用水声信道稀疏特性，提出了一种基于压缩感知的信道估计方法。

首先对基于零前缀正交频分复用（zeros-Padded orthogonal frequency division multiplexing，ZP-OFDM）的水声通信系统接收端信号进行两次多普勒频移补偿并建立了离散信号模型，接着在传统正交匹配追踪（orthogonal matching pursuit，OMP）算法的框架下提出了一种改进的算法，该算法依据上次迭代中残差值和观测值的比例，加入相对应的加权矩阵以减小异常样本对本次迭代结果的影响，然后在所提算法的基础上，结合频域过采样的方法估计出水声信道参数。

仿真结果表明，改进的算法性能优于传统OMP算法，且更加有效的提高系统可靠性和有效性。

Abstract： Exploiting the sparse channel in underwater acoustic （UWA） communication， an improved channel estimation method based on compressed sensing was proposed. Frist of all， a received discrete signal model was established in zeros Padded-orthogonal frequency division multiplexing （ZP-OFDM） UWA communication system after compensating for the Doppler shift two times. Secondly an improved algorithm was proposed based on the structure of orthogonal matching pursuit （OMP）， where an corresponding weighted matrix was added to decrease the impact of the outliers in this iteration by the ratio of the residuals and measurements in the last iteration. Then the improved algorithm and frequency domain oversampling method was jointly to have channel parameters estimated. The simulation results verify that the improved algorithm outperforms the traditional OMP algorithm， and the improved algorithm can enhance the system's reliability better.關键词：零前缀正交频分复用;频域过采样;改进正交匹配追踪算法Key words： zeros Padded-orthogonal frequency division multiplexing （ZP-OFDM）;frequency domain oversampling;improved orthogonal matching pursuit （OMP）algorithm中图分类号：G353.1 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; 文献标识码：A ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;文章编号：1006-4311（2020）24-0210-030 ;引言水声信道是双选择性信道，但信道的大多数能量仅仅存在于少数的时延点和多普勒频移因子上，即水声信道是典型的稀疏信道[1]。

无线英语词汇汇总及简写

Access Link Control Application Part接入链路控制应用部分ALCAP Access Point Name接入点名称APN Access Preamble接入前缀AP Access Service Class接入服务级别ASC Access service class接入业务类ASC Access Stratum接入层AS Accounting计费分配（归属环境，服务网络Acknowledged Mode确认模式AM Acknowledged mode data确认方式数据AMD Acknowledgement证实、确认ACK Acquisition Indication捕获指示AI Acquisition Indication Channel捕获指示信道AICH Acquisition Indicator捕获指示AI Acquisition Indicator Channel接入指示信道AICH ACTIVE State激活状态Adaptive MultiRate自适应多速率AMR Adaptive MultiRate (speech codec)适配多速率AMR Adaptive Multirate Codec自适应多速率编解码器AMR Address Translation and Mapping Function地址翻译和匹配功能Addressing of Managed Entities管理实体寻址Adjacent Channel Interference Ratio相邻信道干扰率ACIR Adjacent Channel Leakage Power Ratio邻道泄漏功率比ACLR Adjacent Channel Power Ratio邻道功率比ACPR Adjacent Channel Selectivity邻近信道选择性ACS Adjacent Channel Selectivity邻道选择ACS Administration of the SGSN - MSC/VLR AssociaSGSN - MSC/VLR关系管理Admission and load control准入和负载控制Admission Control Function允许控制功能Advanced Addressing高级寻址Air Interface User Data空中接口用户数据Algebraic code excitation linear prediction代数码激励线性预测ACELP Allowable PLMN允许接入PLMNAlternate procedures可变通规程American National Standard Institute美国国家标准组织ANSI Amplitude limitation for normalization归一化限幅AMR-Adaptive Multi-Rate codec自适应多速率编解码器Area Coverage Probability区域覆盖概率Associated Control Channel相关控制信道ACCH Association of Radio Industries and Business无线产品工商联合会（日）ARIB Attenuator衰减器Audit trail mechanism审计跟踪机制Authentication and Authorization Function鉴权和授权功能Authentication triplet/quintuple鉴权三元组/五元组Authentication vector鉴权矢量Automatic Establishment of Roaming Relations漫游关系的自动建立Autonomous Swap自动交换Average transmit power平均发射功率Average Transmitter Power Per Traffic Channe每业务信道平均发射功率Bandwidth on demand按需求分配带宽BoD baseline capabilities基线能力Baseline Implementation Capabilities基线实施能力Bearer IP service承载IP业务Best effort QoS最低限度服务质量，尽力而为的Best effort service最低限度业务Block error rate块误码率BLER Broadband signaling system #7宽带7号信令系统BB SS7 Broadcast channel (logical channel)广播信道（逻辑信道）BCCH Broadcast channel (transport channel)广播信道（传输信道）BCH Broadcast control functional entity广播控制功能实体BCFE Broadcast/Multicast Control protocol广播/多播控制协议BMC Burn-in room老化房Call Deflection呼叫偏转CD Camp on a cell驻扎于一个小区Capability Class能力类型Capacitance coupling电容耦合Card session板卡对话CDR redirection（including multi-redirectionCDR 重定向Cell Radio Network Temporary Identifier/Iden小区无线网络临时标识C-RNTI Cell Selection and Reselection小区选择和再选择Channel assignment indication channel信道分配指示信道CA-ICH Channel estimation信道估计Channel Identifier（AAL2）通道标识CID channel rotation correction信道纠偏/去信道衰落channelization mode信道化模式Chargeable Event可计费事件Charging Data Collection Function计费数据收集功能Charging Gateway Functionality计费网关功能CGF China wireless telecommunications standard g中国无线电信标准组CWTS Ciphering Algorithm加密算法Ciphering Function加密功能Ciphering key密钥CK Circuit Service电路业务CS Class-A mode of operation （A GSM GPRS MS caA类工作方式 (for GPRS)或A类手Class-B mode of operation B类工作方式 (for GPRS)或B类手Class-C mode of operation C类工作方式 (for GPRS)或C类手Code acquisition码询问Code Division Multiple Access码分多址接入CDMA Code Division Multiple Address Testbed码分多址测试床Code division test bed, EU research project码分测试床CODIT Code tracking码跟踪Coherence bandwidth相干带宽Coherence detection相干检测Coherence time相干时间Collision detection indication channel冲突检测指示信道CD-ICHCombined GPRS / IMSI attach联合GPRS / IMSI附着Combined GPRS / IMSI Attach Procedure联合GPRS/IMSI 附着规程Combined Hard Handover and SRNS Relocation P联合硬切换和SRNS重定位规程Combined Inter SGSN RA/LA Update联合SGSN 间路由区/位置区更新Combined RA/LA update联合路由区/位置区更新Combined RA/LA Updating联合路由区/位置区更新Common Channel公用信道Common Object Request Broker Architecture公共对象请求代理结构CORBA Common Part Convergence Sublayer公共部分汇聚子层CPCS Common transport channel公共传输信道CCH Communication bypath通信旁路CCBS Completion of Calls to Busy Subscriber用户忙呼叫结束,指忙用户呼叫完Compressed mode measurement procedure压缩模式测量规程Compression Function压缩功能Conducting cable导线Conformance Test遵从性测试Connected Mode已连接模式Connection Frame Number连接帧号CFN Connection mode连接模式Constant bandwidth恒定带宽CW Continuous Wave (unmodulated signal)持续波（未调制信号）/连续波（Control Radio Network Controller控制无线控制器CRNC Controlling RNC控制RNC CRNC Conversational service对话业务Cordless Telephony System - Fixed Part无绳电话系统-固定部分CTS-FP Core Network核心网络CN Corner effect角落效应Corporate code企业码Corporate personalization企业个体化CPCH status indication channel CPCH 状态指示信道CSICH Cross-talking串话Cryptographic Checksum密码校验和CS mode of operation (for UMTS MS)电路域工作方式 (for UMTS)CS Paging电路域寻呼CTS licence exempt frequencies CTS许可证免除载频CTS operator procedure for enrolment of CTS-无绳电话系统-固定部分登记运营CTS-MS originated calls无绳电话系统移动台发起呼叫CTS-MS terminated calls无绳电话系统移动台结束呼叫Cumulative distribution function累积分配功能CDF Current eaqualization output device均流输出装置Current LSA当前 LSACurrent-limiting impedance限流电阻Data Integrity Procedure数据一致性规程De-personalization去个人化De-pilot pattern去导频图案Decapsulation解封装Decision feedback决策反馈DFDedicated control functional entity专用控制功能实体DCFE Dedicated File专用文件DF Dedicated NBAP专用NBAP D-NBAP Dedicated Physical Channel专用物理信道DPCH Delay locked loop时延锁定环Delay spread时延扩展Delete Subscriber Data Procedure删除用户数据规程Delivered QoS交付服务质量Despreading解扩Destination user目的地用户Diagnostic Test诊断测试Digital enhanced cordless telephone数字增强型无绳电话DECT Digital Signature数字签名Direct sequence spreading spectrum-code divi直接序列扩频-码分多址DS-CDMA Direct-Sequence Code Division Multiple Acces直接序列码分多址接入DS-CDMA Discontinuous Reception非连续性接收DRX Discontinuous Transmission非连续性发射DTX Distribution service信息分发业务Diversity Handover分集切换DHO Domain Name Server Function域名服务器功能Doppler spread多普勒扩频Downlink下行DL Downlink Tunnel下行隧道Drift RNS漂浮RNS,漂移网络控制器DRNC DRX cycle DRX周期Dust granule灰尘颗粒Dust-proof plastic tape防尘橡胶条Dynamic Allocation of Radio Resources无线资源动态分配Dynamic channel allocation动态信道分配DCA Dynamic PDP Addresses动态 PDP地址EDGE Compact EDGE 压缩Electromagenetic wave radiation电磁波辐射Electromagnetic shielding电磁屏蔽Elementary File基础文件EF Elementary procedure基本规程EP embedded IP内嵌IP核EMC conformance specification EMC遵从规格Encapsulation function封装功能Encrypted connection加密连接Encryption and algorithm management加密和算法管理Enhanced Data rates for GSM Evolution GSM演进增强数据速率EDGE Enhanced full rate speech codec增强型全速率语音编解码器EFR Enhanced Multi-Level Precedence and Pre-empt增强型多层优先和抢占业务eMLPP Enrolment of CTS-FP无绳电话系统-固定部分登记Enrolment of CTS-MS无绳电话系统-移动台登记Equivalent Isotropic Radiated Power全向有效辐射功率EIRP Equivalent Isotropic Radiated Power等价同性辐射功率EIRPError concealment of lost frames失帧错误隐藏Error Vector aMplitude误差矢量幅度EVM Essential UE Requirement (Conditional)用户设备基本要求（有条件的）Essential UE Requirement (Unconditional)用户设备基本要求（无条件的）Exception procedures例外规程Exclusive access排他性（唯一）接入Explicit Call Transfer直接呼叫转移，显式呼叫转移ECT Explicit Diversity Gain (dB)显分集增益(dB)External PDN Address Allocation外部PDN地址分配Extra SDU delivery probability额外业务数据单元发送概率fading factor衰落因子Fast Uplink Signaling Channel快速上行信令信道FAUSCH File identifier文件标识First despreading预解扩Fixed Network User Rate固定网用户速率Floating point C-Code浮点C码Forward Access Channel前向接入信道FACH Forward error control前向差错控制Frame Error Rate误帧率FER Frame protocol帧协议FP Fraud Information Gathering System (FIG)虚假消息收集FIG Freedom Of Mobile multimedia Access FOMA移动电话FOMA Future radio wideband multiple access system未来无线宽带多址系统FRAMES Gateway GPRS Support Node网关GPRS支持节点GGSN Gateway Location Register网关位置寄存器GLR Gateway MSC关口MSC GMSC General Packet Radio Service（System）通用分组无线业务（系统）GPRS Generic Frequency List (GFL)通用载频列表Geographical routing地理选路GLObal NAvigation Satellite System全球导航卫星系统GLONASS Global Positioning System全球定位系统GPS GPRS attach when the MS is already IMSI-atta已IMSI附着的移动台GPRS附着GPRS Mobile IP Interworking GPRS 移动 IP 互通GPRS Tunnelling Protocol for User Plane GPRS 隧道协议用户面部分GTP-U Granularity period粒度周期Group call area组呼叫区域Group call initiator组呼（叫）发起方Group Call Register群组呼叫寄存器GCR Group identification (group ID)组标识Groupwise serial interference cancellation组系列干扰取消GSIC Guaranteed service可保证业务Handoff Gain/Loss (dB)切换增益/损耗Hard decision硬判决Hard handover硬切换Heartbeat detection circuit心跳检测电路Heartbeat path心跳路径Home Environment归属环境Home Environment Value Added Service Provide归属环境增值业务提供商HE-VASP Hot Billing热计费（实时计费）ID-1 SIM带ID的SIM 卡Identity Check Procedures身份检查规程IMEI check violation IMEI校验违规Immediate Service Termination (IST)即时业务终止IST Implementation capability实施能力INACTIVE State非激活状态Incompatible Encryption不兼容加密Independent Transmit Clock独立传输时钟ITC Information Data Rate信息数据速率Initial Convergence Time初始汇聚时间Initial paging information初始寻呼信息Initial paging occasion初始寻呼时机Insert Subscriber Data Procedure插入用户数据规程Insulation washer绝缘垫片Integrity key一致性密钥IKInter PLMN handover PLMN间切换Inter SGSN Intersystem Change SGSN间系统间变化Inter system handover系统间切换Inter-cell handover小区间切换Inter-path interference路径间干扰IPI inter-PLMN backbone network PLMN间骨干网Inter-SGSN Routing Area Update SGSN 间路由区更新Inter-symbol interference符号间干扰、码间干扰ISI Interactive service交互业务Intercept invocation截收/拦截激活Intercept of calls placed on HOLD (call wait呼叫保持（呼叫等待和多方业务Intercept of forwarding calls前转呼叫截收/拦截Intercept product截收/拦截产品Intercept related information截收/拦截相关信息intercept target截收/拦截目标Interception Area截收/拦截域IA Interference cancellation干扰抵消IC Interference rejection combining干扰拒绝合并IRC Interference Signal Code Power干扰信号码功率ISCP International mobile telephony国际移动电话业务Internet engineering task force因特网工程任务组IETF Intra SGSN Intersystem Change SGSN内系统间变化intra-PLMN backbone network PLMN内骨干网Intra-SGSN Routing Area Update SGSN 内路由区更新IP over ATM基于ATM的IP传输IPoA IRP Information Service IRP 信息业务IRP Solution Set IRP 解决方案集Joint Detection联合检测JDJoint Predistortion联合预矫正JPKey identification密钥标识Key pair密钥对Law enforcement agency合法拦截/截收实施机构LEA Lawful Interception合法截收Layer Functions分层功能Link budget链路预算Link level performance链路级性能Load factor负载因子local code本地码Local service本地业务Localized Service Area本地化业务区域LSA Localized service area support in active mod活动模式下本地化业务区域支持Localized service area support in idle mode空闲模式下本地化业务区域支持Location Dependent Interception与位置相关截收拦截Location Measurement Unit位置统计单元LMU Location Registration位置注册LR Location services位置业务LCS Logical Link Establishment Function逻辑链路建立功能Logical Link Maintenance Functions逻辑链路维护功能Logical Link Management Function逻辑链路管理功能Logical Link Release Function逻辑链路释放功能Logical Model逻辑模型Logical O&M逻辑操作维护Loose coupling松散耦合Low Bitrate Multimedia Telephony Service低比特率多媒体电话业务low-speed access and TransCoder Module低速接入及码变换模块TCM LSA exclusive access cell本地化业务区域唯一接入小区LSA only access LSA （本地化业务区域）唯一接LSA preferential access cell本地化业务区域优先接入小区LSA Priority LSA 优先级Macro cell宏蜂窝Macro diversity handover宏分集切换Malicious Reconfiguration of the GPRS DeviceGPRS设备恶意重配置Managed entities被管理的实体Management Information Model管理信息模型MIM Mandatory storage必要存储Mandatory UE Requirement必要用户设备要求Manufacturer-Dependent State与生产商相关状态Master File主文件MF Matched filter匹配滤波器、匹配过滤器MF Maximum likelihood sequence detection最大可能序列检测、最大或然序MLSD Maximum output power最大输出功率Maximum peak power最大峰值功率Maximum Total Transmitter Power (dBm)最大总发射功率Maximum Transmitter Power Per Traffic Channe每业务信道最大发射功率Mean bit rate平均比特速率Mean transit delay平均传输时延Measurement package（统计）测量包Measurement schedule（统计）测量进程安排Measurement task（统计）测量任务Measurement types（统计）测量类型Medium Access Control媒质接入控制MAC Medium Access Control-Common公共介质接入控制MAC-C Medium Access Control-Dedicated专用介质接入控制MAC-D Message Authentication Code信息鉴权码Message Screening Function消息过滤功能Message transfer part (broadband)消息传输部分－（宽带）MTP3b messaging service消息业务Minimum mean square error最小均方差MMSEMM Information Procedure移动性管理信息规程Mobile IP移动IP MIP Mobile Number Portability移动号码可携带性MNP Mobile-Originated Short Message移动起始短消息SM MO Mobile-originated SMS Transfer移动始发短消息业务转发Mobile-Terminated Short Message移动终结短消息SM MT Mobile-terminated SMS （MT SMS) Transfer移动终结短消息业务转发Mobility Management States移动性管理状态Mobility Management Timer Functions移动性管理定时器功能Modelling of measurement jobs（统计）测量任务建模Motion picture experts group动画专家组MPEG Movable floor活动地板MS Information Procedure移动台信息规程MS Network Capability移动台网络能力MS Radio Access Capability移动台无线接入能力MSC Basic Configuration MSC 基本配置MSBMulti mode terminal多模式终端Multicast service多播业务，多点传送业务Multimode and multimedia TDMA多模和多媒体 TDMAMultimode terminal多模终端Multipath多径Multipath selection多径提携、多径选择Multiple access interference多接入干扰MAI Multirate ACELP多速率ACELP MR-ACELP Multiuser detection多用户检测MUD Name Binding名称匹配，名字限定Narrowband Telephony Service窄带电话业务Near-far interference远近干扰Negotiated QoS协商业务质量Negotiation phase协商阶段Network Access Control Functions网络接入控制功能Network configuration evaluation网络配置评估Network Determined User Busy (condition)网络决定用户忙（条件）NDUB Network dimensioning网络规模Network Interworking网络互通Network operation modes I网络运营模式INetwork operator specific services网络运营商特有业务Network subset code网络子集码No Artefacts in Residual Noise残留噪音中无膺象No Degradation in Clean Speech无纯语音降级No Speech Clipping and no Reduction in Intel话音无剪切及话音可辩识性无降Node availability notification节点可用通知Node B3G 基站NodeB Application Part NodeB应用部分NBAP Noise Suppression噪音抑制Noise Suppression for the AMR Codec AMR编解码器噪音抑制Nomadic Operating Mode流动运营模式Non-Access Stratum非接入层NAS Non-pilot symbol非导频位、非导频符号Non-realtime Multimedia Messaging Service非实时多媒体消息业务Non-volatile memory非易失存储器Normal call or operation普通呼叫或运营Normal procedure正常规程Numbering Plan Identification编号方案标识NPID Octet Stream Protocol八位位组流协议One Stop Billing一次性（一站式）帐单Open Identification of MS (authentication re移动台开放标识（鉴权重试）Open loop power control开环功率控制Open Service Architecture开放的业务体系结构OSA Oppurtunity Driven Multiple Access机会驱动的多址接入ODMA Optimal Routing最佳路由Optional storage可选存储Optional UE Requirement用户设备可选要求Orthogonal factor正交因子Orthogonal Frequency Division Multiplex正交频分复用OFDM Orthogonal Variable Spreading Factor正交可变扩频因子OVSF Out-band带外Outage损耗（停工期）Outstanding Alarm突出告警P-TMSI Reallocation Procedure P-TMSI 再分配规程P-TMSI Signature P-TMSI 签名Packed encoding rules分组编码规则PER Packet Data Protocol（信息）包数据协议PDP Packet data protocol分组数据协议PDP Packet Data Protocol States分组数据协议状态Packet Domain Access Interfaces分组域接入界面Packet Domain Core Network Nodes分组域核心网节点Packet Domain PLMN Backbone Networks分组域PLMN骨干网Packet Routing and Transfer Functions分组路由和转发功能Packet switched paging procedures分组交换寻呼规程Packet Switched Service分组交换业务PS Packet Terminal Adaptation Function分组终端适配功能Packet transfer mode（信息）包传送模式Packet-TMSI分组TMSI P-TMSI Padding填充Page indicator寻呼指示（器）PI Paging and notification control function ent寻呼和通知控制功能实体PNFE Paging Block Periodicity寻呼块周期Paging Co-ordination寻呼协商（或寻呼协调）Paging Co-ordination for GPRS GPRS 寻呼协商Paging DRX cycle寻呼DRX周期Paging indicator channel寻呼指示信道PICH Paging Message Receiving Occasion寻呼消息接收时机Paket Data Convergence Protocol分组数据汇聚层协议PDCP Parallel Concatenated Convolutional Code并行卷积码PCCC Parallel interference cancellation并行干扰抵消PIC Path loss路径损耗PU Payload unit有效负载单元、净负载单元,有效PDP Context Activation PDP 上下文激活PDP context activation procedure PDP上下文激活规程PDP Context Deactivation PDP 上下文去激活PDP context deactivation procedure PDP上下文去激活规程PDP Context Modification PDP 上下文修改PDP context modification procedure PDP上下文修改规程PDP Context Preservation PDP 上下文保留PDP context preservation procedure PDP上下文预留规程Peak bit rate峰值比特速率Periodic RA Update Timer Function定时路由区更新定时器功能Personal communication systems个人通信系统PCS Personal digital cellular个人数字蜂窝PDC Personal Service Environment个人业务环境Physical channel data stream物理信道数据流Physical Common Packet Channel公共分组物理信道PCPCH Physical Downlink Shared Channel物理下行共享信道PDSCH Physical Downlink Shared Channel下行共享物理信道PDSCH Physical random access channel物理随机接入信道PRACH Physical shared channel物理共享信道PSCH Pico cell微微蜂窝Pilot pollution导频污染Pilot signal导频信号Plug-in SIM插入式SIM 卡PN-offset planning PN-偏差规划point-to-multipoint service点对多点业务Pole capacity极点容量Ported number转网号码Porting process转网过程Power Control Preamble功率控制前缀PCP Pre-defined virtual connection预定义虚拟连接PVC Pre-paging预寻呼Predictive service可预计业务Preferential access优先接入Primary Common Control Physical Channel主公共控制信道P-CCPCH Primary Common Pilot Channel主公共导频信道P-CPICH Processing Gain处理增益Propagation models传播模型PS mode of operation (for UMTS MS)分组域工作方式 (for UMTS)PS/CS mode of operation (for UMTS MS)分组域/电路域工作方式 (for U Pseudo-range伪范围Public impedance coupling公共阻抗耦合Pulse shaping脉冲形状Pulverized paint易粉化的涂料Purge Function清除功能QoS profile业务质量概况QoS Profile Negotiated协商的服务质量QoS session业务质量对话期Radio Access Bearer无线接入承载RAB Radio Access Network Application Part无线接入网络应用部分RANAP Radio Bearer无线承载RB Radio link addition无线链路增加Radio link controller无线链路控制器Radio link removal无线链路清除Radio Link Set无线链路集Radio Network Controller无线网络控制器Radio Network System无线网络系统RNS Radio Network System Application Part无线网络系统应用部分RNSAP Radio Network Temporary Identifier无线网络临时标识RNTI Radio Priority Levels无线优先级别Radio Resource Functionality无线资源功能Radio Resource Management无线资源管理RRM RAKE combination RAKE合并RAKE receiver RAKE 接收机RAN application part RAN应用部分RANAP Real time实时RT received signal code power接收信号码功率RSCP Received Signal Code Power接收信码功率RSSI Received Signal Strength Indicator接收信号强度指示/接收信号场强Receiver Antenna Gain (dBi)接收天线增益Receiver Noise Figure (dB)接收机噪音系数Receiver Sensitivity (dBm)接收机灵敏度Receiving Entity接收实体Recipient network接收网络Record pointer记录指针Reference configuration参考配置Regional Subscription区域签约Regionally Provided Service地区性业务Registration Area注册区域Registration Function登记功能Relay Function中继功能Relay/Seed Gateway中继/种子网关Relaylink中继链路Reliabilty and availability可靠性和可用性Renewable card续值卡Repeater转发器、中继器、直放站Reriodic RA updates定期路由区更新Residual error rate残余误码率、剩余差错率Resource access资源接入Resource availability资源可获得性Resource unit资源单元RU Reverse Link反向链路Rising edge active上跳沿有效RNS application part RNS应用部分RNSAP Roll-off factor滚动因子Root Relay根中继Routing Area Update路由区更新RAU Routing Function选路功能RRC Connection无线资源控制连接RRC State Machine无线资源状态机Saturation interval饱和区间SDU error probability业务数据单元误码概率SDU loss probability业务数据单元丢失概率SDU misdelivery probability业务数据单元误传送概率SDU transfer delay业务数据单元传输时延SDU transfer rate业务数据单传输速率Secondary Common Control Physical Channel辅助公共控制物理信道、“从”SCCPCH Secondary Common Control Physical Channel从公共控制信道S-CCPCH Secondary Common Pilot Channel从公共导频信道S-CPICH Secondary Synchronization Code从同步码Sector扇区Secured Packet安全包Security audit trail reports安全审计跟踪报告Security Header安全包头Security management object model安全管理对象模型Security measurement Object Model安全统计对象模型Security object classes安全对象类型Seed种子Segmentation And Reassembly分段和重组、分割重组SAR Selection mechanism选择机制Selective RA Update选择性路由区更新Sequence Number, Sequence-number序列号、顺序号码、序号SN Service accessibility performance业务可接入特性Service Announcements业务通知Service Area Identity服务区识别Service bit rate业务比特速率Service Capabilities业务能力Service category业务类别Service Continuity and Provision of VHE via业务连续性以及通过GSM/UMTS提Service delay业务时延Service Execution Environment业务执行环境Service Implementation Capabilities业务执行能力service integrity performance业务一致特性service operability performance业务可操作特性Service Request Procedure业务请求规程Service retainability performance业务可保持特性Service specific co-ordination function特定业务协调功能SSCF Service specific connection oriented protoco面向连接的特定业务协议SSCOP Service Specific Segmentation And Reassembly特定业务拆装子层SSSAR Service-less UE无业务用户设备Serving Mobile Location Center服务移动位置中心SMLC Serving RNC服务RNC SRNC Serving RNS Relocation Procedures服务RNS重定位规程Settlement结算Shannon capacity limit仙农容量限制Shared Resources Module共享资源模块SRM Short Message Mobile Originated短消息发送功能SMMO Short Message Mobile Terminated短消息接收功能SMMT Short Message Service Centre短消息（业务）中心SMSC Signal-Interference Ratio信干比SIR Signal-to-Interference Ratio信干比SIR Signal-to-noise ratio信噪比SNR Signaling ATM adaptation layer for network t网络-网络信令ATM 适配层SAAL-NNI Signaling ATM adaptation layer for user to n用户-网络接口信令ATM 适配层SAAL-UNI Signaling radio bearer信令无线承载SRB Signaling Virtual Connection信令虚拟连接SVC Signals Transfer Board信号转接板WSTB Silence indicator静默指示SID Simple control transmission protocol简单控制传输协议SCTP Simple Mail Transfer Protocol简单邮件传输（送）协议SMTP Simultaneous use of services业务的同时使用Site Selection Diversity TPC基站选择发射分集SSDT Site Selection Diversity Transmission位置选择分集发射SSDT SMS Advanced Cell Broadcast短消息业务高级小区广播Soft Blocking软阻塞Soft Handover软切换SHO Space division duplex空分双工SDD Space Time Transmit Diversity空间-时间发射分集STTD Space Time Transmit Diversity空时发分集STTD Spectral efficiency频谱效率Spectrum allocation频谱分配Spectrum efficiency频谱有效性Speech Path Delay话音路径延迟Spreading扩频Spreading and modulation扩频和调制Spreading code扩频码Spreading Frequency Multi-path composite Acc扩频多路复合接入SSMA SS7 ISUP Tunnelling7号信令系统ISUP隧道ITUN State Changed Event Report状态变更事件报告State Transitions状态迁移Stateless Address Autoconfiguration Procedur无状态地址自动配置规程Static PDP address静态 PDP地址Step步进Storage card存储卡Store-and-forward存储并转发Subscribed QoS预订的服务质量Subscriber Management Function用户管理功能Subscription checking for Basic Services基本业务预定检查Subscription checking for Supplementary Serv补充（附加）业务预定检查Successive interference cancellation连续干扰取消SIC Suitable Cell适合小区Supervision PlugBoard监控接插板XSPB Support of Localized Service Area本地化业务区域支持SoLSA Support of Private Numbering Plan专用编号支持方案SPNP Surface Acoustic Wave (SAW) filter声表面波滤波器Switched transmit diversity分集分组发送STTD Synchronous Transport Mode-1同步传输模式-1STM-1 System frame number系统帧号SFN System Frame Number系统帧号计数器SFN System information block系统消息块SIB Tandem Free Operation免（无）二次编解码操作TFO Target channel type field目标信道类域TCTF Technical specification(s)技术规范TS Telecommunication technology commission (Jap电信技术委员会（日本）TTC Telecommunications Technology Association (K电信技术协会（韩国）TTA Text telephony service文本电话业务TFO call免（无）二次编解码操作的呼叫The Shared InterWorking Function共享互通功能SIWF Time division CDMA, combined TDMA and CDMA时分码分多址TD/CDMA Time Division Duplex时分双工TDDTSTD Time Switched Transmit Diversity时间交换发射分集/时间切换发分Toolkit工具包Transit delay传输时延Transmission Convergence传输汇聚Transmission power control传输功率控制TPC Transmission Time Interval发射时间间隔、发送时间间隔、TTI Transmit adaptive antennas发送适配天线TxAA Transmit Format Combined Indicator发送格式组合指示TFCI Transmit Power Control发送功率控制TPC Transmitter Antenna Gain (dBi)发射天线增益Transparent mode透明模式TRTransport Block传输块Transport Block Set传输块集Transport format传输格式TF Transport Format Combination传输格式组合TFC Transport Format Combination Indicator传输格式组合指示TFCI Transport Format Combination Set传输格式组合集TFCS Transport Format Indicator传输格式指示TFI Transport Format Set传输格式集TFS Tunnel End Point Identifier隧道端点标识TEID Tunnelling Function隧道功能Tunnelling of non-GSM signaling Messages Fun非-GSM信令消息隧道功能Turning point probability转向点概率UE用户设备，用户终端UE Capability用户设备能力UE Service Capabilities用户设备业务能力UMTS Open Service UMTS 开放业务UMTS Subscriber identity module UMTS用户识别卡USIM UMTS Terrestrial radio access (ETSI)UMTS 陆地无线接入UTRA UMTS Terrestrial radio access network UMTS 陆地无线接入网UTRAN UMTS to GSM Inter SGSN Change UMTS to GSM SGSN间变化Unacknowledged Mode非确认模式UM Unconstrained Delay Data非强制时延数据Unencrypted connection未加密连接UMTS Universal Mobile Telecommunications System/U通用移动通讯系统/通用移动电信Universal resource locator通用资源定位器URL Universal Terrestrial radio access (3GPP)全球陆地无线接入UTRA Universal Terrestrial Radio Access Network全球陆地无线接入网UTRAN Unsecured Acknowledgement不安全确认Unstructured Supplementary Service Data未结构化补充（附加）业务数据USSD Unstructured Supplementary Service Data (USS非结构化附加业务数据增强Uplink shared channel上行共享信道USCH Uplink Tunnel上行隧道User Data and GMM/SM signaling Confidentiali用户数据和GMM/SM信令机密性User Determined User Busy (condition)用户决定用户忙（条件）UDUB User Identity Confidentiality用户身份机密性User Plane用户平面UP User procedure for enrolment of CTS-FP无绳电话系统-固定部分登记用户User Registration Area用户注册域URA UTRAN Radio Network Temporary Identifier UTRAN无线网络临时标识U-RNTI UTRAN Registration Area UTRAN 登记区URA UTRAN Registration Area Identity UTRAN 登记区识别Valid LSA合法LSAValid path有效径Variable bit rate service可变比特速率业务Videotelephony视频电话voice broadcast call语音广播呼叫Voice Broadcast Service语音广播业务VBSVoice group call语音组呼叫Voice Group Call Service语音群组呼叫业务VGCS Voice over IP基于IP的语音VoIP Voltage wave shape distortion电压波形失真Warrant reference number许可参照数（截收）Wideband Telephony Services宽带电话业务Wireless video无线视频Work Station工作站WS Zero Forcing迫零准则ZF无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）The process of apportioning charges无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）Adjacent channel interference ratio无线（WCDMA）Adjacent channel leakage ratio, cau无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）The purpose of admission control is无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）A PLMN which is not in the list of 无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）The average transmitter output powe无线（WCDMA）The mean of the total transmitted p无线（WCDMA）无线（WCDMA）Capabilities that are required for 无线（WCDMA）Set of Implementation capabilities,无线（WCDMA）无线（WCDMA）The lowest of all QoS traffic class无线（WCDMA）A service model which provides mini无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）burn-in无线（WCDMA）无线（WCDMA）The UE is in idle mode and has comp无线（WCDMA）A piece of information which indica无线（WCDMA）无线（WCDMA）A link between the card and the ext无线（WCDMA）无线（WCDMA）The C-RNTI is a UE identifier allo无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）An activity utilising telecommunica无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）A GSM GPRS MS can operate in one of无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）A Channel not dedicated to a specif无线（WCDMA）无线（WCDMA）Common Part无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）Connected mode is the state of User无线（WCDMA）无线（WCDMA）The type of association between two无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）A role an RNC can take with respect无线（WCDMA）An interactive service which provid无线（WCDMA）无线（WCDMA）An architectural term relating to t无线（WCDMA）无线（WCDMA）Code which when combined with the n无线（WCDMA）Allows a corporate customer to pers无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）Frequency band that may be allocate无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）The process of deactivating the per无线（WCDMA）无线（WCDMA）无线（WCDMA）无线（WCDMA）。

稀疏恢复和傅里叶采样

Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Leslie A. Kolodziejski Chair, Department Committee on Graduate Students
2
Sparse Recovery and Fourier Sampling by Eric Price
Submitted to the Department of Electrical Engineering and Computer Science on August 26, 2013, in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy in Computer Science
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Department of Electrical Engineering and Computer Science August 26, 2013
Certiﬁed by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Piotr Indyk Professor Thesis Supervisor

译文英

Adaptive MIMO-OFDM Systems with Estimated Channel StateInformation at TX SideM.Codreanu,D.Tujkovic and tva-ahoCentre for Wireless Communications,University of Oulu,P.O.Box 4500,FIN-90014,Oulu,Finland,Abstract—Adaptive MIMO-OFDM systems employing eigenmode based signalling have a great potential to increase thespectral efficiency when the channel state information(CSI)isccurately known at transmitter(TX)side.However,the perfec CSI is a too strong assumption for a wireless system operating in frequency selective channels.In the presence of CSI errors,the eigenmodes orthogonality is lost and a spatial equalizer is used at each subcarrier to remove the inter-eigenmodes interference In this paper we propose using a first order matrix inversion approximation(based on truncated Neumann expansion)to find an upper bound for the covariance matrix of the decision variable at equalizer’s output. Based on this upper-bound we are able to find a new bit and power loading algorithm which maximizes the throughput subject to maximum transmit power and maximum frame error rate constraints. The effect of CSI errors on the achievable spectral efficiency is studied by computer simulations for different antenna correlation setups. The results clearly show that the proposed method is robust against CSI errors and channel spatial correlation. The achieved spectral efficiency a low and medium SNR is larger that the outage capacity with no CSI at TX side.Index Terms—adaptive radio link, bit and power loading MIMO,OFDM, correlated fading.I.INTRODUCTIONBy applying orthogonal frequency division multiplexing (OFDM)to a multiple-input multiple-output(MIMO)system the frequency selective MIMO channel is turned into a se of frequency flat fading MIMO channels which can be in dividedly processed.If the channel state information(CSI)is known at the transmitter(TX)side, the channel matrix can be decomposed for each subcarrier using singular value decomposition(SVD).As a result aset of orthogonal sub channels is obtained in the space domain[3][4][5].We will refer to these elementary sub-channels as eigenmodes in the sequel.We are considering a time division duplex(TDD)systems where the CSI is obtained at TX based on radio channe reciprocity.However,the perfect CSI knowledge at TX side is a too strong assumption for a wireless system and in the presence of CSI errors,the eigenmodes orthogonality is lost.A two-dimensional eigen-beamformer combined with the Alamouti’s encoder has been proposed to exploit the partial CSI knowledge at TX side. As discussed ,with practical QAMs constellation levels such architecture suffer from a strong rate limitation at high SNRSince it cannotexploit the multiplexing gain offered by the MIMO channel.In this paper we consider the same layered system architecture proposed in our recentwork[9]where a spatial equalizer is used at each subcarrier to remove the inter-eigenmodes interference. By using the first order inverse matrix approximation we find an upper-bound for the covariance matrix of the decision variable at equalizer’s output and propose a new bit and power loading algorithm which maximizes the throughput subject to maximum transmit power and maximum frame error rate constraints. The numerical results clearly show that the proposed method efficiently exploits the spatial multiplexing gain of the MIMO channel and is robust against CSI errors. II.SYSTEM MODELThe block diagram of the considered adaptive MIMO-OFDM system with Csubcarriers,T transmit and R receive antennas is depicted in Fig.1.The input-output relationfor the OFDM modulator/demodulator chain is given by where l is the()()()()c c l c c y l H x l n l =+ (1)temporal index,c represents the subcarrier index, ()c x l and ()c y l denotes for the c’th columns in the pre-processor output matrix ()T C X l ⨯∈ and OFDM de- modulator output matrix ()R C Y l ⨯∈ respectively,nc(l) represents the noise vector 0~(0,)R CN N I and()c H l rep-esents the channel’s matrix at time instant l.The entry[Hc(l)]r,t ～CN(0,1)represents the complex channel gain between TX a ,[()]~(0,1)c r t H l CN ntenna t and RX antenna r at subcarrier c.The frame length L is chosen to be smaller than the coherence time of the channel.To simplify the notation,the time index l will be skipped in the following.We adopt the CSI error model presented in [7]:the estimated channel matrix at TX sideis given by c c cH H N =+ where Nc represents the channel estimation error having independent and identically distributed(i.i.d.)entries 2,[]~(0,)c r c N N CN σwith known 2Nσ. The linear pre-combining is performed with the unitary matrix ˆc V ，obtained by SVD of the estimated channel matrix,ˆˆˆˆH c c c c H U V =Λ. The transmitted vector at the subcarrier c isgiven by 1/2ˆc c c c x V P d =，where min(,)c r R T ≤ denotes the number of active eigenmodesdecided by the bit and power loading algorithm,is the vector ofcomplex data symbols transmitted at subcarrier c,the matrix 1,,(,...,)c c rc c P diag P P =controls the power allocated to each eigenmode(the constellation power is nor-malized to2,{||}1i c E d =)and '1,2,,ˆ[,,...,]c c rc c c V v v v = contains the firsts rc columns of Vc.The received signal at c’th subcarrier can be expressed as followsc y =c c c H x n +='1/2ˆˆ()c c c c c cH N V P d n -+ =''1/2ˆˆˆˆˆˆ()H H c c c c c c c c c cU V V U N V P d n Λ-+ =''1/2ˆˆ()c c c c c c U N P d n Λ-+ （2）where ''ˆˆc R r H c c c c N U N V ⨯=∈ contains the i.i.d.entries '2,[]~(0,)c r c N N CN σ，'ˆcΛ is an cR r ⨯dimensional matrix with the elements 1/21/21/21,2,,,,...c c rc c λλλon the main diagonal and all other entries are zeros and ,i c λdenotes for the eigenvalues of Hermitian matrix.The matrix ''1/2ˆˆ()c c c c cT U N P =Λ-expresses the cumulative effect of signal processing at the TX side and channel propagation on the transmitted data signal and can be obtained at the receiver side by inserting pilot symbols for channel estimation in lieu of dc.The estimation of Tc is beyond the scope of this paper and we will assume in the following that it is perfectly known at the receiver side.The powerful turbo codes(TC) are used for channel coding due to their large coding gain. The encoding is performed jointly in time and frequency domains,so that a code word covers the selected eigenmodes from a given layer during consecutive OFDM symbols belonging to one transmission frame.III.THE SNR AT THE EQUALIZER’S OUTPUTWe analyze the case when the linear post-combiner(or spatial equalizer1)is implemented by zero forcing(ZF)equal-izer structure.However,as will be shown by simulations,We will use the terms”equalizer”and”post -combiner”interchangeable in . The sequel essentially the same results are obtained with an linear mini- mum meansquared error(LMMSE)equalizer.The covariance matrix of the decision variables†c c cd T y = generated by the post-combiner is given by ZF de C ={()()}H nc c c c cE d d d d -- =10()H c c N T T - =1/2''''11/20ˆˆ{()()}H c c c c c c N P N N P ---Λ-Λ-（3） By partitioning the matrix c R r ⨯ψ∈ as follows122c cN ψ⎡⎤Λ-⎡⎤ψ==⎢⎥⎢⎥ψψ⎣⎦⎣⎦（4）where c R r ⨯ψ∈ ，c Λ = 1/21/21/21,2,,(,,...,)c c rc c diag λλλand c N contains the firsts c r lines of 'cN ，is straightforward toobserve that 110H Hψψ-ψψ≥ (positive semidefinite), thus1/211011Z F H d e c cC N P P ----≤ψψ （5） The matrix 11-ψ can be expressed as follows11-ψ=111()c c r c cI N ---Λ-Λ =111[()]c n cr c c n I N ∞--=Λ+Λ∑ (6)where the last equality has been obtained from Neumann expansion and is valid if and onlyif 1221cc N-Λ< The left side of the convergence condition can be bounded as follows: 1222112,222Max rc c c c cc N WN N σλλ---Λ<Λ= (7) Where MaxW λdenotes the largest eigenvalue of the c r ⨯c r Wishart matrix 2/Hc cW N N σ=.Therefore,a sufficientcondition for(6)to hold is2,c M a x r c N Wλσλ> (8) The probability that(8)is satisfied can be made close to one by removing theeigenmodes with a gain lower that a predefined threshold.Let %()x c p r 为Max W λbe the %x percentile of Max W λ.If at the first step of the bit loading algorithm all the eigenmodeswith gain 2,%()rc c N x c p r λσ<px%(rc)are removed,the convergence condition is satisfied with a probability higher than x%.Since the distribution of random variable Max W λdepends onlyon rc,the x%percentile is pre-deaminated and saved into a look-up-table(LUT).An example of such LUT is shown in Table I.By retaining only the first order term in(6)(linear approx-imation)theexpression(5)can be approximated as{}1/2111211/20ZF H H dc c c rc c c c c c c c c cC N P I N N N N P -------≈Λ+Λ+Λ+ΛΛ (9) andthe i’thelement of the diagonal can be bounded asfollows 22,,01/2,1,,,,1c r c c i j i i ZFdc i i j i cj c i c i c j i N N N C P λλλ=≠⎧⎫⎡⎤⎡⎤⎪⎪⎣⎦⎣⎦⎡⎤≈++⎨⎬⎣⎦⎪⎪⎩⎭∑22,0%%1/21,,,,(1)1c r c i i N x x j i c j c i c i c j i N N p P σλλλ=≠⎧⎫⎡⎤⎣⎦⎪⎪<++⎨⎬⎪⎪⎩⎭∑ (10) where the notation %x a b < means that the random variable a is lower than b with a probability larger than %x .IV .BIT AND POWER LOADING ALGORITHMAs we can see in(10), ,ZF dc i i C ⎡⎤⎣⎦ depends on all estimated Eigenvalues ,j c λnot onlyon ,j c λ.Therefore joint eigenmodes optimization is required to find the optimum bit and power loading allocation.This paper focuses on a downlink with T≥R=2 which is a realistic assumption given the complexity and size limitations of mobile terminals.However, the extension to R>2 is straightforward.To maximize the throughput subject to the maximum transmitted power and the maximum frame error rate(FER) constraints,we modify the bit and power loading introduced in [9]to take into account the eigenmode’s coupling and SNR variation among the eigenmodes.2C eigenmodes in total are divided into two clusters,consisting of the strongest and the weakest eigenmodes from each subcarrier,respectively. Since only a small difference between the eigenmodes gains belonging to the same cluster is experienced,the same MCS can be used for all selected eigenmodes belonging to the same cluster(except the most severely faded eigenmodes).We have shown that this method reduces the required signaling overhead by a factor of C with a negligible throughput degradation compared to the universally accepted Hughes-Hartogs algorithm [12].We assume that the set of K distinct modula-tion/coding schemes(MCS)is available,and the same MCS is used for all selected eigenmodes belonging to the same cluster.We denote by k b （1,...,k K =）, the SNR required by the k’th MCS to achieve the target FER in an parallel AWGN channel where the SNR varies amongst the eigenmodes according to random part of(10).These SNR values are obtained by off-line simulationsand saved into a LUT.Without the loss of generality,we assume that available MCSs k b and their corresponding SNRs k γk are given in an ascending order, 12...K b b b <<<与12...K γγγ<<<.Let k1 and k2,be the indeces of the MCSs selected in the strongest and the weakest clusters,respectively.The power required at the strongest eigenmode of the c’th subcarrier to guarantee the target FER constraint can be expressed as while the(1)(2)1,2,220101%1,1,1,1,2,::(1)(1)cck N k N x c c c c c P P N N p P γσγσλλλλ===++(11) Power required at the weakest eigenmode is given by2202%2,2,1,2,(1)(1)k N x N c c c cN p P γσσλλλ=++ (12) If the weakestcluster is skipped,i.e.rc=1,the second term in(11)iszero,therefore (2)1,c Pshould be interpreted as the supplementary power allocated to the strongest eigenmode to compensate the interference created by the weakest eigen-mode.Based on this observation,we define the bit-wise power efficiencies for each eigenmode as follows1)1(,11)(,1)(k ceff cb P k P =，2)2(,1,221)(,2),(k cc eff c b P P k k P +=(13)where (),eff i cP expresses how much power costs every loaded bit in(i,c)eigenmode.Similar to HH algorithm,for a given pair (k1,k2),the throughput can be maximized by allocating the total available power PT to the eigenmodes starting from the most efficient one and stopping the process when the power limit has been reached.The power allocation process should be applied for each possible combination of modulation schemes.However,the number of combinations can be significantly reduced by taking into account the fact that the strongest cluster will use a MCS which has at least the same spectral efficient as the one selected for a weakest cluster.The proposed loading algorithm can be summarized as follows:1)Setupahighenoughprobability,x%tosatisfythecon-vergencecondition(8)2.Then,for each subcarrier,find the maximum number of used eigenmodes asfollows:set c r =min(,)T R and while 2,%()rc c N x c p r λσ<, decrement c r , c r =c r -1.2)For all possible MCS pairs(k1,k2),1≤k2≤k1≤K,perform the following next steps:a)Compute the bit-wise power efficiencies (),eff i cP given by(13)and order the eigenmodes according to their efficiencies.b)Allocate the total available power PT to the eigen-modes starting from the most efficient one and stop the process when the power limit has been reached.c)Compute the total number of bits allocated, 221121),(k k k k s b s b k k B += where 1k s and 2k s represent the number of eigenmodes selected in the strongest andFig.2.Spectral Efficiency and FER with Estimated CSI at TX,Independent Rayleigh Fading,T=4,R=2 Antennasweakest cluster,respectively.3)The selected MCS pair to maximize the throughput is and the power allocated1222m i n 001212,1,2,...,|(,)(,)arg maxk k k k K b s l k k B k k =>=(14)to the selected eigenmodes isgiven by(11)and(12)where ),(),(020121k k k k =. The supplementary constraint, min 22l s b k k >in(14)is used to avoid very short code words in case of strong correlation between antennas and/or very low SNR values.In such cases the performance of e.g.turbo codes would decrease and the target FER cannot bemaintained.Theγk values for look -up-table are determined by setting a frame length equal to min l .V .NUMERICAL RESULTSFor the simulations we have assumed a block fading channel model,where fading coefficients were kept constant over one coded frame and are independent from frame to frame.One coded transmitted frame consists of 16 OFDM symbols.The OFDM system bandwidth is 20 MHz using C=64 subcarriers.The length of the OFDM symbols is 80 samples(4 microseconds),where the first N CP =16 are reserved for CP.The channel’s delay taps are independently fading with power delay profile specified by ETSI BRAN Channel A[14].For each delay tap,the spatial fading correlation was gen-eratedaccordingtoastochasticMIMOchannelmodel.Twocases,”medium”and”strong”correlated antennas areconsidered.They are defined by the correlation.The medium correlated channel models an indoor radio link while the strong correlated channel is used to reflect an outdoor-to-indoor link with thebase station antenna located above surrounding scatterers.We are assuming a time division duplex(TDD)system where the channel is perfectly known at receiver side and it is estimated at the transmitter side based on a pilot symbol appended at the end of the reverse frame.By using the low complexity least square(LS)based channel estimator described the normalized mean square error isequalto dB CN SNR cpN 102log 10-=σ,assuming that the average SNRs are the same attransmitter and receiver.The MCSs used for the adaptation process are 4QAM,16QAM and 64QAM,all turbo encoded and punctured to rate=1/2.By using an iterative receiver with 8 iterations per frame,the SNRs required by each MCS to achieve the target maximum FER=10-2 are {}321,,γγγand {3.6dB,9.2dB,13.6dB} for a minimum codeword lengthmin l =500bts.For numerical results we have considered a(T×R)=(4×2)antennas system operating in Rayleigh fading channel.The spectral efficiency and FER results are shown in Fig.2 andFig.3 for independent and correlated antennas respectively.As a reference,each figure shows the ergodic channel capacity with perfectly known channel at both sides and theoutage channel capacity for an outage rate=target FER) with channel known at receiver only.The first one represents the upper-bound of the spectral efficiency achievable with the optimal channel coding by adapting the transmission rate and the power according to each instantaneous channel realization. The second one represents the maximum spectral efficiency achievable by any fix rate transmission system which does not use the channel knowledge at the TX side.The spectral efficiency at a given error rate represents a good measure for evaluate the performance of a system with tight delay constraint.For systems where the delay constraint is not so tight the most important measure is the effective spectral efficiency obtained by employing some higher level error correction methods like automatic repeat request(ARQ). Therefore,for each simulated case the effective spectral effi-ciency obtained by employing a simple ARQ protocol is also shown.As we can see in Fig.2,the maximum FER constraint can be satisfied even in presence of CSI estimation errors. The resulted FER is lower than the maximum limit and well balanced between the two clusters for all SNR values of practical interest.The achievedspectral efficiency is larger than for SNR<8dB and it follows it closely up to the saturation point.This means that the proposed system will outperform any system which do not use the CSI at TX side.In case of medium correlated antennas,Fig.3(a),the proposed CSI errors compensation method works reasonably well.The resulted average FER is lower than maximum limit but it is slightly unbalanced between the two clusters.The system achieves a spectral efficiencylarger than.(a)T=4,R=2 Medium Correlated Antennas(b)T=4,R=2 Strong Correlated AntennasFig.3.Spectral Efficiency and FER with Estimated CSI at TX,Correlated Rayleigh Fadingfor NR<9dB.In the extreme case of strong correlated antennas,Fig.3(b),the resulted FER is quite unbalanced between the clusters,therefore for SNR>8dB the average FER is dominated by the FER at the weakest cluster.Note that in this case the absolutevalue of the correlation coefficient between transmit antennas is 0.96(see[15]for more detailed description of environment).This unusual and extremely high spatial correlation wouldproduce worst performance for any layered scheme which uses spatial multiplexing concept.Since the maximum FER constraint is satisfied at the strongest cluster and the amount of information allocated to the weakest cluster is very small,the degradation in effective spectral efficiency is negligible.VI.SUMMARY AND CONCLUSIONSA new link adaptation method employing MIMO-OFDM eigenmode based signalling with imperfect CSI at the TX side is proposed in this letter.The effect of CSI errors has been evaluated by using the first order inverse matrix approximation(based on truncated Neumann expansion)to find an upper bound for the covariance matrix of the decision variable.We have proposed a new bit and power loading algorithm applicable to a channel coded system,which maximizes the throughput subject to maximum transmit power and maximum frame error rate constraints.The effect of CSI errors on the achievable spectral efficiency was studied by computer sim-ulations for different antennas correlation setups.The results show that the achieved spectral efficiency at low and medium SNR is larger that the outage capacity with no CSI at TX side.。

基于压缩感知的毫米波大规模MIMO信道估计

基于压缩感知的毫米波大规模MIMO信道估计作者：刘海波杜江黄天赐马腾来源：《中国新通信》2022年第08期摘要：在毫米波大规模MIMO系统中，由于毫米波的路径损耗极其严重，在空间中只有少量的可用信道存在，加上大规模天线形成的高增益窄细波束，使得波束域信道更加稀疏。

针对信道稀疏性的特点，可以与压缩感知理论很好地结合，本文分析了正交匹配追踪算法和稀疏度自适应匹配追踪算法在信道估计的优缺点，并将一种改进的稀疏度自适应匹配追踪算法应用到毫米波大规模MIMO信道估计中，可以取得较好的估计效果。

关键词：毫米波;MIMO;压缩感知;稀疏度自适应一、引言毫米波（Millimeter Wave，mmWave）的频段在30GHz～300GHz之间，频谱资源丰富，且与大规模天线结合，能够弥补毫米波自身所带来的高路损，是5G通信的关键技术之一[1]。

在毫米波大规模MIMO系统中，能否掌握信道状态信息对预编码十分重要。

只有精确估计出信道的信息状态，才能够利用大规模MIMO多天线优势提供更多自由度，从而提升信道容量[2]。

因此，信道估计至关重要。

压缩感知（Compressive Sensing，CS）理论被提出后，被广泛运用在各个领域中[3]，如图像处理、语音编码和雷达监测等。

在毫米波大规模MIMO信道，毫米波路径损耗极高，只有少数的可用信道在空间中可以进行通信，大规模MIMO在空间中生成的高增益窄细波束使得信道更加稀疏。

运用毫米波信道稀疏的特点，可以将压缩感知理论很好地应用在信道估计中，将信道估计问题转化为稀疏信号重构问题，以实现低复杂度、高精度的信道估计。

在压缩感知理论中，贪婪迭代算法由于计算复杂度低的优点被广泛使用。

文献[4]利用正交匹配追踪（Orthogonal Matching Pursuit，OMP）算法估计稀疏多径信道，比传统的LS算法复杂度低，精度高。

然而，OMP算法的实现条件是以信道的稀疏度作为前提，这在实际应用中，信道的稀疏性往往是未知的，所以使用价值比较低。

基于压缩采样值的跳频信号检测和参数估计

基于压缩采样值的跳频信号检测和参数估计跳频通信具有抗干扰、低截获和易组网等优点,在民用和军事通信中有广泛的应用。

近年来为了提高抗干扰能力,跳频通信有向宽频带、高跳速发展的趋势。

这给基于奈奎斯特采样架构的跳频捕获系统带来了诸多问题,最突出的就是前端采样数据量大、后续传输和处理困难。

在不损失信息的前提下,压缩感知技术能以极低的速率采集宽带稀疏信号,为解决跳频信号的非协作接收和处理提供了新的思路。

本文主要研究基于压缩信号处理(Compressive Signal Processing, CSP)的跳频信号检测和参数估计算法。

相对于基于奈奎斯特采样值的传统处理方式,基于少量压缩采样值的压缩跳频信号处理方式能有效的降低运算量,简化信号处理流程,从而提高系统工作的时效性。

现将本文主要研究内容和创新点总结如下：1.在噪声水平已知时,针对高斯白噪声中的未知信号检测问题,提出一种压缩能量检测算法(Compressive Energy Detection, CS-ED)。

根据单个压缩采样值在不同假设条件下其数字特征不同的特点,该算法将压缩采样值的方差作为判决依据,完成检测任务。

实验结果表明,该算法相对于传统的能量检测算法,CS-ED算法用少量检测性能的损失换取了算法时效性较大的提高。

2.在噪声水平未知时,提出一种基于压缩信号处理的压缩自相关检测算法(Compressive Auto-Correlative Detection,CS-ACD)。

该算法充分利用了信号的稀疏性和传感矩阵的严格等距特性,由稀疏系数自相关向量的不同统计分布进行检测判决。

仿真结果表明,在相同的压缩采样次数下,相对于重构原信号后再做检测的算法,CS-ACD算法拥有更低的错误概率；通过和现有压缩检测算法的对比,在信噪比大于-2dB时,CS-ACD算法可在保证检测性能的前提下降低运算量。

3.针对仅存在单个跳频信号的情况,提出一种基于压缩信号处理的跳频信号跳变时刻估计算法(Compressive Hopping Transition time Estimation, CS-HTE)。

基于压缩感知的DRM信道估计

基于压缩感知的DRM信道估计聂阳【摘要】For characteristics of spectrum limitation of Digital Radio Mondiale(DRM) , in order to obtain accurate channel status information with lower pilot overhead, the paper sets up a relationship between compressed sensing theory and channel estimation problem, build DRM channel estimation model based on compressed sensing and analyzes and verifies the impacts of the inserting method and quantity of pilots on the estimation performance. Compared with least-squares algorithm, channel estimation algorithm based on compressed sensing may not only obtain accurate and reliable estimation results with lower cost but also improve the estimation performance of channels while raising the spectrum utilization.%针对数字调幅广播(Digital Radio Mondiale,DRM) 系统频谱有限的特点,为了以较少的导频开销获得精确的信道状态信息,本文将压缩感知理论与信道估计问题相联系,建立基于压缩感知的DRM 信道估计模型,并分析和验证导频插入方式和数量对信道估计性能的影响.与LS(Least Square) 方法相比,基于压缩感知的DRM 信道估计不但能够以更少的导频获得精确可靠的估计结果,而且在提升信道估计性能的同时提高频谱利用率.【期刊名称】《中国传媒大学学报（自然科学版）》【年(卷),期】2018(025)001【总页数】4页(P63-66)【关键词】压缩感知;数字调幅广播;信道估计【作者】聂阳【作者单位】中国传媒大学广播电视数字化教育部工程研究中心,北京 100024【正文语种】中文【中图分类】TN934.31 引言模拟调幅广播具备范围覆盖广泛，便于移动接收、成本接收低等优点，长期以来被认为是区域化广播覆盖的有效手段之一，但也存在业务类型单一和信号易受干扰等缺点。

基于卡尔曼滤波的快时变稀疏信道估计新技术

基于卡尔曼滤波的快时变稀疏信道估计新技术袁伟娜;王嘉璇【摘要】针对高铁以及山区环境下正交频分复用(orthogonal frequency division multiplexing,OFDM)通信系统的信道估计问题,提出一种基于卡尔曼滤波的快时变稀疏信道估计方法.该方法基于快时变信道的基扩展模型(basic expansion model,BEM),应用压缩感知(compressed sensing,CS)理论进行稀疏时延估计,并应用卡尔曼滤波(Kalman filter,KF)技术对BEM系数进行估计,进而获得信道增益.仿真结果表明,在相同信噪比(signal to noise ratio,SNR)条件下,随着归一化多普勒频移(frequency-normalized Doppler shift,FND)增大,新方法的信道估计均方差(mean square error,MSE)性能优于传统方法,如当SNR为20 dB,FND为0. 1时,新方法较传统方法性能提升了4 dB,表明对信道时变性具有更优的鲁棒性;在相同的多普勒频移条件下,随着SNR增加,各方法的均方差均有所改善,新方法改善更明显,如当FND为0. 2时,在信道估计均方差为0. 06的条件下,新方法较传统方法获得了6 dB的信噪比增益,表明对抗信道噪声能力更强.%A fast time-varying sparse channel estimation method based on the Kalman filter is proposed for channel estimation of an orthogonal frequency division multiplexing communication system operating in high-speed railways and mountain areas. Based on the basic expansion model (BEM), compressed sensing (CS)was employed for the estimation of sparse delays,and a Kalman filter (KF) estimator was utilised for estimating the BEM coefficients. The channel gains were then computed easily. The simulation results show that under the same signal-to-ratio (SNR)condition,with the increase in frequency-normalised Doppler shift (FND),the MSE of the new method issuperior to that of traditional methods,such as SNR is 20 dB and FND is 0. 1,and a 4 dB performance improvement is achieved. Under the same Doppler shift condition,the same result is obtained as that with the increase in SNR,such as FND is 0. 2 and MSE is 0. 06,and a 6 dB SNR gain is achieved. These results show that the new method is more robust to variation in channel time and stronger against noise compared with traditional methods.【期刊名称】《西南交通大学学报》【年(卷),期】2018(053)004【总页数】7页(P835-841)【关键词】信道估计;基扩展模型;卡尔曼滤波;压缩感知【作者】袁伟娜;王嘉璇【作者单位】华东理工大学信息科学与工程学院,上海200237;华东理工大学信息科学与工程学院,上海200237【正文语种】中文【中图分类】TN929.5OFDM (orthogonal frequency division multiple-xing)技术具有高频谱利用率和抗多径干扰能力,目前在3GPP(3rd generation partnership project)、4G LTE (long term evolution)等多种无线通信标准中得到了广泛应用.随着无线通信技术的发展,人们对许多从前未被重视的应用场景下的通信质量需求提高,比如:信道具有稀疏特性的偏远空旷的郊外山区,或信道具有快速变化的高速铁路等场景.信道估计的性能是衡量通信系统性能的主要标准,因此对于复杂多样化信道估计技术的研究具有重要的意义[1-3].在郊区山区等呈现稀疏特性的信道环境下,信道多径时延分布是零散的,即由几个具有明显响应的主径,以及大部分低于一定阈值近似为0的径组成.如果仍假设主径连续集中在前几径,误差将大大增加,而如果对最大时延内所有径数进行估计,估计数量也将增加.压缩感知(compress sensing, CS)的提出对稀疏信道估计问题提供了很大的帮助,文献[4-6]基于CS算法分别研究了单天线和多天线OFDM系统时不变稀疏信道估计,文献[7-9]基于CS算法和传统估计算法研究了时变稀疏信道估计,文献[10]采用卡尔曼滤波算法(Kalman filter, KF)与CS相结合的算法研究慢时变稀疏信道估计,此处的慢时变指单个符号内信道响应不变而相邻符号间是变化的,该算法不适合用于快时变信道的估计.在高铁等信道环境中,由于多普勒效应的存在,信道在一个符号周期内快速变化,称其为快时变信道,此时,待估计的信道参数数量大大增加.文献[11-12]采用基扩展模型(basic expansion model, BEM)对每一个OFDM符号块对应的快时变信道建模,该模型可以对快时变信道特性进行较好的拟合,同时也可以降低估计参数数量,然后采用LS(least square)、 LMMSE(linear minimum mean square error)和ML(maximum likelihood)对BEM系数进行估计,没有考虑相邻符号块间信道参数的关系.文献[13]考虑了相邻符号块信道参数的关系,采用KF算法对相邻符号对应的BEM信道模型系数进行估计,从而获得信道估计,但研究的是非稀疏信道,将该算法应用于稀疏信道估计时,性能较差.目前,尚未查阅到考虑相邻符号块间信道参数关系的快时变且稀疏的信道估计算法.本文提出一种新的快时变稀疏信道估计方法.该方法基于快时变稀疏信道的BEM模型,采用CS算法进行主径估计,再结合KF算法估计BEM系数,进而获得信道估计值.同时,实验仿真表明,本文提出的方法有效地减小了信道估计的误差.1 基于BEM的快时变信道模型OFDM系统的时域接收信号模型为(1)式中:x、y分别为发送与接收的OFDM符号;h(n,l)为一个OFDM符号周期内第l径第n个采样点的信道响应;N为一个符号周期总采样点数;(·)N表示模为N的循环移位;L为最大时延内总径数;w(n)是第n个采样点的均值为0、方差为σ2的加性高斯白噪.BEM采用一组基函数的线性组合,可以较好地拟合快时变信道的信道响应,表示如式(2).(2)式中:n=0,1,…,N-1;l=0,1,…,L-1;bq(n)、gq(l)和Q分别为BEM的基函数、系数和阶数.通常假定在一个OFDM符号内,BEM系数保持不变,而基函数是一组固定的正交基,因此采用BEM可以将待估计的信道参数由NL个降到(Q+1)L个,大大减少了估计数量.得到BEM系数估计值后,再经过BEM模型即可获得信道响应.常用的BEM基函数有:复指数基扩展模型(complex exponential BEM, CE-BEM)、过采样复指数基扩展模型(generalized complex exponential BEM, GCE-BEM)、多项式基扩展模型(polynomial BEM, P-BEM)、离散卡-洛基扩展模型(discreteKarhuen-loève BEM, DKL-BEM)和离散椭圆基扩展模型(discrete prolate spheroidal BEM, DPS-BEM).式(2)写成矩阵形式为(3)式中:bq=(bq(0),bq(1),…,bq(N-1))T;Gq为N×N维的Toeplitz循环矩阵;h为N×N维的时域信道矩阵.Gq和h表示如式(4)～(5).(4)(5)式(1)写成矩阵形式为y=hx+w,(6)式中:y=(y(0),y(1),…,y(N-1))T;x=(x(0),x(1),…,x(N-1))T;w=(w(0),w(1),…,w(N-1))T.则相应的频域接收信号为Y=FhFHX+W=HX+W,(7)式中:Y=Fy;X为OFDM符号,X=(FH)-1x;F为N点傅里叶变换矩阵,F=(Fij), i,j=0,1,…,N-1,H为一个N×N大小的频域信道矩阵;W为频域的噪声.将式(3)代入后可表示为Y=FhFHX+W=(8)式中:FL为一个与多径位置对应的参数矩阵,由的相应列组成;gq=(gq(0),gq(1),…,gq(L-1))T.令A=Fdiag(bq)FH,式(8)可以表示为(9)令为L(Q+1)×1维的BEM系数向量,A=(A0,A1,…,AQ),Δ=IQ+1⊗(diag(X)FL),⊗表示Kronecker积,则式(9)可表示为Y=AΔg+W,(10)再令S=AΔ,则频域接收信号最终可表示为Y=Sg+W.(11)基于梳状导频辅助的估计方法,式(7)中导频处的接收信号可表示为YP=SPgP+Sdgd+WP,(12)式中:WP为导频处的噪声;SPgP为有效接收数据，p=1,2,…,P，P∈N；Sdgd为数据子载波对导频子载波的干扰,令d=Sdgd,则有YP=SPgP+d+WP.(13)2 基于压缩感知的稀疏信道时延估计在稀疏信道的环境下,不需要完整地估计最大时延内所有径数的增益,只需对有明显增益的主要时延处Ldelay径进行估计.因此,要在信道增益估计前先在L中找出主径的位置Ldelay.压缩感知理论的提出,给处理稀疏信号提供了一种思路.压缩感知是一种在稀疏条件下寻找欠定线性系统解的算法,可以用低于奈奎斯特采样频率去高度重建信号.对于一个未知的信号X∈CN,X中只有K个非零元素(K≪N),即信号X的稀疏度为K.选择一个观测矩阵Φ∈CM×N对X进行测量,观测过程表示为Y=ΦX+V,(14)式中:V为噪声.得到观测信号Y∈CM,其中M<N,可以利用压缩感知算法从Y中重建出X.正交匹配追踪(orthogonal matching pursuit, OMP)[14]算法是一种常见的基于贪婪迭代的压缩感知重构算法,其基本思想是初始化残差跟原始索引集,每次迭代通过计算内积,不断地找到与残差相关度最高的原子,并更新索引集,最后逐步逼近系数向量.利用OMP进行时延估计的过程如下:步骤1 初始化索引集T0=∅.步骤2 计算φt,Y|,式中:φt为Φ中的列;Γλ为Φ中所有列数.步骤3 更新索引集Tn={Tn-1,φt},LS估计步骤4 计算残差rn=Y-TnXn,并更新φt,rn|.步骤5 重复步骤3、4,直到残差小于阈值或Tn的列数达到设定值K.为了在稀疏信道估计中应用上述理论,需要构建稀疏信号和观测矩阵.假设发送端的所有导频信号为XP,则对应位置的接收端信号YP表示为YP=HPXP+WP,(15)式中:XP、YP均为NP×1维向量;WP为NP×1维导频处噪声;HP为NP×NP维频域信道响应,其对角元素为第p个导频位置处的频响,表示为(16)式中:又由于导频处的多径信道频响表示为(17)式中:为第l径快时变信道在1个符号周期内的平均时域响应;Pp为第p个导频在子载波中对应的位置.在快时变环境下,每径信道响应在1个符号周期内每个采样点处都不同,但其平均值也可以表示总体的稀疏性.则可将1个符号周期内所有导频符号处对应的频响表示为(18)式中:HP=(H0,H1,…,HNP-1)T;Φ=(Φpl),为NP×L维矩阵.由于信道的稀疏性,最大时延内的所有径中,只有少数几径具有高能量的明显增益.换句话说,假设信道的稀疏度为K,则的L个元素中,只有K个元素有值,且K≪L.因此,式(18)可看作CS的观测方程,为被观测的稀疏信号,Φ为观测矩阵.可通过上述的OMP算法,找到对应主径的索引集Ldelay,FL则为Ldelay对应的参数矩阵.例如,估计结果Ldelay为{1,2,4,7,11},则FL为的1、2、4、7、11列组成的矩阵.3 基于卡尔曼滤波的信道估计建立好上述快时变稀疏信道模型后,可应用信道估计算法对BEM系数g进行估计.传统的信道估计算法通常为LS和LMMSE.LS算法通常将包括模型误差、噪声等在内的干扰全部作为噪声处理,即式(13)中d 和WP均当作噪声.LS的目标可以描述为找到合适的使得Y与之间的方差最小,即(19)则可解得g的LS估计值为(20)LS算法不需要信道和噪声的统计信息,因而复杂度较低.但同时也限制了性能的进一步提升,在干扰比较大或是信噪比较差的时候,信道估计的性能可能不够理想. LMMSE算法将待估计参数g视为随机变量,其核心思想是使得Y与之间的均方误差最小,即(21)则可解得LMMSE估计值为(22)式中:Rg、Rd和RW分别为BEM系数、发送数据和噪声的自相关矩阵. LMMSE算法考虑了噪声和信道的统计信息,因此性能优于LS.但同时复杂度也较高,而且要获取信道的统计信息也非常困难,如果得到的统计信息和实际信道不匹配,将会带来较大的误差.通常采用特定的信道,如本文采用的是Jakes模型信道[15],以方便计算信道的统计信息.上述方法(LS或LMMSE)均是在对每一个OFDM符号块对应的信道参数分别进行BEM建模的基础上进行估计的,相邻符号块的参数之间并无相关.然而,在实际情况中,相邻OFDM符号之间对应的信道参数是随时间平滑渐进变化的[13].因此,考虑到这种情况,可以用自回归(autoregression, AR)模型[16]来描述和刻画相邻符号间对应的信道增益的这种动态变化,为了降低复杂度,这里选用一阶AR模型,如式(23).hml=Ahlh(m-1)l+uml,(23)式中:hml为第m个OFDM符号第l径的信道响应向量;Ahl为信道系数的状态转移矩阵;uml为模型误差,是协方差为Ul的复高斯向量.由于hml的BEM模型可写作hml=Bgml,(24)式中:hml=(hm(0,l),hm(1,l),…,hm(N-1,l))T;gml=(g0(l),g1(l),…,gQ(l))T;B=(b0,b1,…,bQ)为BEM基函数矩阵.所以,经过BEM模型转换后的基系数可建立相似的AR模型,如式(25). gml=Aglg(m-1)l+uml,(25)式中:Agl为BEM基系数的状态转移矩阵.AR模型参数可通过尤尔-沃克(Yule-Walker)方程解得(26)因为BEM系数是零均值的相关复高斯变量,其相关矩阵为(27)式中:s为相关移位的大小.又由于本文采用的是Jakes模型信道[15],则(28)式中:为第l径的信道功率;fmax为最大多普勒频移;Ts采样周期;Ns=N+NCP为添加了CP的OFDM符号采样点数,NCP为循环前缀的长度;J0(·)为第1类零阶Bessel函数.将各径的AR模型结合表示为gm=Aggm-1+um,(29)式中:为L(Q+1)×1的BEM系数向量;Ag=diag{Ag0,Ag1,…,Ag(L-1}为L(Q+1)×L(Q+1)的状态转移矩阵;为L(Q+1)×1的误差向量,其协方差为U=diag{U0,U1,…,UL-1}.在本文中,将式(29)看作KF算法的状态方程,将第m个符号对应频域接收信号看作KF测量方程,表示如式(30).(30)采用KF算法估计多个OFDM符号对应的BEM系数[13],具体步骤如下所示:步骤1 初始化g0=0L(Q+1)×1,P0=Rg(0),Rg(s)=diag{Rg0(s),Rg1(s),…,Rg(L-1)(s)}.步骤2 时间更新方程gm|m-1=Aggm-1,步骤3 测量更新方程gm=gm|m-1+Km(Ym-Smgm|m-1),Pm=Pm|m-1-KmSmPm|m-1.步骤4 重复步骤2、3,得到多个符号对应的估计值上述步骤中:gm|m-1、gm、Pm和Pm|m-1分别为第m个符号的参数预测值、参数估计值、估计误差协方差矩阵和预测估计误差协方差矩阵;为噪声方差;IN为N阶单位方阵.KF算法需要信道的统计信息,且计算复杂度较高,但由于考虑了相邻符号之间的平滑关系,因此估计性能优于LS或LMMSE.估计得到BEM系数后,应用式(3)得到信道增益4 实验仿真通过Matlab仿真结果对算法性能进行验证.仿真参数参考文献[17]设置,如表1所示,仿真中采用QPSK (quadrature phase shift keying)调制,梳状导频,瑞利多径信道模型,GCE-BEM(Q=2).参考指标归一化多普勒频移表示为(31)式中:v为移动速度;c为光速;fc为载波频率.表1 仿真参数表Tab.1 Simulation parameters子载波数CP长度导频长度采样间隔/μs载频/GHz总径数主径数12816322.52205图1为信噪比(SNR)为20 dB时,随着fnd逐渐增大(fnd=0.1,0.2,0.3分别对应于速度v=150,300,450 km/h),各方法的信道估计NMSE(normalized MSE).其中,KF 曲线对应于未采用CS时延估计(即认为主径连续集中在前5径且只估计前5径)[13]时的估计误差,其他3条曲线分别对应于采用OMP与LS、LMMSE和KF 3种方法的结合.图2为fnd=0.2时,随着信噪比SNR增加,各方法的信道估计NMSE.图1 SNR为20 dB,fnd增大时,各方法的NMSE对比Fig.1NMSE vs. fnd for SNR is 20 dB图2 fnd=0.2,SNR增大时,各方法的NMSE对比Fig.2NMSE vs. SNR for fnd=0.2图1和图2中：OMP-KF (orthogonal matching pursuit-KF)曲线为本文算法;OMP-LS和OMP-LMMSE曲线分别为将OMP与LS和LMMSE相结合的算法，这两种算法未考虑相邻符号块信道参数的变化关系；KF曲线为文献[13]中算法.从图1中可以看出,fnd增大时各方法的估计误差都有所增加.其中,OMP-KF算法与只使用KF相比,由于应用了OMP进行稀疏信道环境下的时延估计,故误差远低于直接使用KF[13]的算法;而同时进行了时延估计的情况下,OMP-LMMSE算法考虑了噪声和信道的统计信息,因此误差低于OMP-LS,而OMP-KF算法由于考虑了相邻符号之间的平滑关系,其误差更低于OMP-LMMSE.从图2中可以看出,与图1趋势相同,进行了时延估计的OMP-KF算法误差低于直接使用KF[13]的算法;而同样进行了时延估计时,在SNR较低时,OMP-KF算法的NMSE低于OMP-LS和OMP-LMMSE,SNR增加时,OMP-KF算法优势也增大,在SNR达到20 dB以后,误差变化趋于平缓.5 结束语针对快时变稀疏环境下OFDM系统的信道估计问题,本文基于快时变信道的BEM模型,采用压缩感知算法进行稀疏环境的时延估计,再采用卡尔曼滤波对BEM系数进行估计,从而得到信道增益.由于该算法综合考虑了快时变、稀疏信道以及连续符号间的信道参数的平滑特性,相对于只考虑慢时变或非稀疏信道的算法,一定程度上提升了信道估计性能,最后通过仿真实验进行了验证.参考文献:【相关文献】[1]WU J, FAN P. A survey on high mobility wireless communications: challenges, opportunitie s and solutions[J]. IEEE Access, 2016, 4(1): 450-476.[2]FAN Pingzhi, ERDAL P. Guest editorial: special issue on high mobility wireless communicat ions[J]. Journal of Modern Transportation, 2012, 20(4): 197-198.[3] 周杲,范平志,郝莉. 基于OFDM的DFT加扰矢量码分多址接入技术[J]. 西南交通大学学报,2017,52(1): 148-155.ZHOU Gao, FAN Pingzhi, HAO Li. 0FDM based DFT scrambling vector code division multip le access[J]. Joumal of Southwest Jiaotong University, 2017, 52(1): 148-155.[4] ROOZBEH M, ARASH A, Compressive sensing-based pilot design for sparce channel estimation in OFDM systems[J]. IEEE Communicatio ns Letters, 2017, 21(1): 4-7.[5]LEE D. MIMO OFDM channel estimation via bock stagewise orthogonal mnatching pursuit [J]. IEEE Communications Letters, 2016, 20(10): 2115-2118.[6]ROOZBEH M, ARASH A. Determinitic pilot design for sparce channel estimation in MISO/ multi-user OFDM systems[J]. IEEE Transactions on Wireless Communications, 2017, 16(1): 129-140.[7] 叶新荣,朱卫平,张爱清,等. OFDM系统双选择性慢衰落信道的压缩感知估计[J]. 电子与信息学报,2015,37(1): 169-174.YE Xinrong, ZHU Weiping, ZHANG Aiqing, et al. Compressed sensing based on doubly-selective slow-fading channel estimation in ofdm systems cbannel estimation[J]. Journal of electronics a nd information, 2015, 37(1): 169-174.[8] TAN Guoping, HERFET T. A framework of analyzing OMP-based channel estimations in mobile OFDM systems[J]. IEEE Wireless Communications Let ters, 2016, 5(4): 408-411.[9] MA Xu, YANG Fang, LIU Sicong, et al. Structured compressive sensing-based channel estimation for time frequency training OFDM systems over doubly selective channel[J]. IEEE Wireless Communications Letters, 2017, 6(2): 266-269.[10]CHEN B, CUI Q, YANG F, et al. A novel channel estimation method based on Kalman filter compressed sensing for time-varying OFDM system[C]∥Inter national Conference on Wireless Communications & Signal Processing. [S.l.]: IEEE, 2014: 1-5.[11]RABBI M F, HOU S W, KO C C. High mobility orthogonal frequency division multiple acces s channel estimation using basis expansion model[J]. IET Communications, 2010, 4(3): 353 -367.[12] SHENG Zhichao, TUAN H D. Pilot optimization for estimation of high-mobility OFDM channels[J]. IEEE Transactions on Vehicular Technology, 2017, 66(10): 8795 -8806.[13] HIJAZI H, ROS L. Joint data QR-detection and Kalman estimation for OFDM time-varying Rayleigh channel complex gains[J]. IEEE Transactions on Communications, 2010, 5 8(1): 170-178.[14]BERGER C R, ZHOU S, PREISIG J C, et al. Sparse channel estimation for multicarrier underw ater acoustic communication: from subspace method to compressed sensing[J]. IEEE Tran sactions on Signal Process, 2010, 58(3): 1708-1721.[15]JAKES W C, COX D C. Microwave mobile communications[M]. [S.l.]: IEEE Press, 1974: 28-46.[16]BADDOUR K E, BEAULIEU N C. Autoregressive modeling for fading channel simulation[J]. I EEE Transactions on Wireless Communications, 2005, 4(4): 1650-1662.[17] QI F, JU Y, SUN S, et al. BEM-based reconstruction of time-varying sparse channel in OFDM systems[C]∥Vehicular Technology Conference. [S.l.]: IEEE, 2013: 1-5.。

频率选择性瑞利衰落信道中自适应均衡和信道估计的性能分析概要

收稿日期:2009-05-12作者简介:刘冬生(1969-,男,江西安福人,讲师,硕士,主要从事无线局域网协议和信号处理研究.0引言近年来,移动通信和无线网络取得很大的发展。

然而,相对于有线信道的稳定性和预测性而言,无线信道具有很大的随机性和时变性。

众所周知,无线通信信道最明显的特征是多径衰落效应和时间变化特性[1-2],就是存在一条以上的信号传播路径,且信道特性随时间变化较快,具有明显的随参信道特性。

多径衰落效应是由于障碍物的折射,散射或反射等原因造成。

不同路径到达的信号由于行程不同,信号的幅度和时间延迟将会不同。

对高速无线通信,多径效应可导致信道的频率选择性衰落。

另外,发射机,接收机或者它们之间物体的运动,使得信道的物理性质发生变化,造成信道参数随时间变化(时域和接收信号频谱的多普勒(Doppler 扩展(频域,也即无线通信信道具有时变(时间选择性和频率选择衰落特性,无线信道的这些特性对接收信号将产生严重失真[3]。

为了得到较好的系统性能,与有线通信相比,无线通信系统一般采用较复杂的信道编码、交织、分集和均衡等技术。

因此,研究信道特性及其仿真实现方法对通信系统的设计与性能分析具有重要意义。

许多学者对信道特性及信道建模等问题进行了大量的研究,取得了较丰富的成果,其中文献[4]对信道特性描述、信道建模和信道分析等问题进行了较详细的说明,而文献[5]对信道仿真的理论和实现方法进行了全面的介绍。

本文主要对其中的一种信道模型即频率选择性瑞利衰落信道模型进行分析与仿真。

1频率选择性瑞利衰落信道的性能分析1.1瑞利衰落信道简介在衰落信道的处理数字通信系统中,可以使用冲激响应幅度的统计特性描述信道,建立信道模型。

常用的信道模型有瑞利(Rayleigh 信道和莱斯(Ricean 信道。

当存在大量路径,且无直达路径时,则接收信号的幅度是瑞利分布的,信道是瑞利信道,其冲激响应的包络分布满足如下概率密度分布函数(pdf [6]:f (r =r exp -r 2220≤r ≤∞0r <≤≤≤≤≤0(1式中,r 是接收信号振幅,r 2是瞬时接收功率,2σ2是多径信号平均功率。

音频信号能量分析和识别阈值

音频信号能量分析和识别阈值
取直方图的波谷作为阈值的方法称为模态法，如果直方图凹凸激烈，难于确定波谷的位置，为了便于发现波谷，采取在直方图上对领域点平均化的方法，邻域五点法。

除了模态法还有p参数法（p-tile method）,判别分析法（discriminant analysis method），可变阈值法（varible thresholding）等。

p参数法是指当物体占整个图像的比例已知时如p%,在直方图上，从暗灰度一侧起（或者亮灰度一侧）的累积像素数占总像素数p%的地方的灰度值作为阈值。

判别分析法是当直方图分成物体和背景两部分时，利用两部分统计量的不同来确定阈值的方法。

可变阈值法是在背景灰度多变的情况下使用的，对图像的不同位置设置不同的阈值。

利用残留冗余量的联合信源信道解码在EVRC语音解码器中的应用

利用残留冗余量的联合信源信道解码在EVRC语音解码器中的应用阿哈麦德;尤肖虎;高西奇【期刊名称】《东南大学学报（英文版）》【年(卷),期】2002(018)002【摘要】The enhanced variable rate codec (EVRC) is a standard for the "Speech Service Option 3 for Wideband Spread Spectrum Digital System," which has been employed in both IS-95 cellular systems and ANSI J-STC-008 PCS (personal communications systems). This paper concentrates on channel decoders that exploit the residual redundancy inherent in the enhanced variable rate codec bitstream. This residual redundancy is quantified by modeling the parameters as first order Markov chains and computing the entropy rate based on the relative frequencies of transitions. Moreover, this residual redundancy can be exploited by an appropriately "tuned" channel decoder to provide substantial coding gain when compared with the decoders that do not exploit it. Channel coding schemes include convolutional codes, and iteratively decoded parallel concatenated convolutional "turbo" codes.%宽带扩频系统的语音服务采用增强型的可变比率编码器,该标准已在IS95和JSTC008个人移动通信系统得到应用.本文致力于利用增强可变比率编码器中内在残留冗余信息的信道解码器.由于残留冗余信息可以用一阶马尔夫模型表示,同时相关频率的变化可以用熵率来表示,从而,信道解码器可利用这种残留冗余量.仿真结果表明,和没有利用这种信息量的解码器相比,由于编码增益,系统性能有明显改善,其中,信道编码采用了卷积码、Turbo码两种方式.【总页数】5页(P103-107)【作者】阿哈麦德;尤肖虎;高西奇【作者单位】东南大学移动通信国家重点实验室,南京,210096;东南大学移动通信国家重点实验室,南京,210096;东南大学移动通信国家重点实验室,南京,210096【正文语种】中文【中图分类】TN929.533因版权原因，仅展示原文概要，查看原文内容请购买。