毕业论文外文翻译--mimo空间多路复用与信道建模适用于毕业论文外文翻译中英文对照教材

1、南京邮电大学毕业设计 （ 论文 ） 外文资料翻译学院通信与信息工程学院专业通信工程学生姓名班级学号B070210 B07021021外文出处无线通信基础 (Fundamentals of wireless communications by David Tse)附件：1.外文资料翻译译文； 2.外文原文指导教师评价：1翻译内容与课题的结合度： 优 2翻译内容的准确、流畅： 优3专业词汇翻译的准确性： 优4翻译字符数是否符合规定要求：良中差良中差良中差符合不符合指导教师签名：年月日附件 1：外文资料翻译译文7mimo：空间多路复用与信道建模本书我们已经看到多天线在无线通信中的几种不同应用。在第

2、3 章中，多天线用于提 供分集增益，增益无线链路的可靠性，并同时研究了接受分解和发射分解，而且，接受天 线还能提供功率增益。在第 5 章中，我们看到了如果发射机已知信道，那么多采用多幅发 射天线通过发射波束成形还可以提供功率增益。在第 6 章中，多副发射天线用于生产信道 波动，满足机会通信技术的需要，改方案可以解释为机会波束成形，同时也能够提供功率 增益。章以及接下来的几章将研究一种利用多天线的新方法。我们将会看到在合适的信道衰 落条件下，同时采用多幅发射天线和多幅接收天线可以提供用于通信的额外的空间维数并 产生自由度增益，利用这些额外的自由度可以将若干数据流在空间上多路复用至MIMO信道中，

3、从而带来容量的增加：采用 n 副发射天线和接受天线的这类 MIMO信道的容量正比 于 n。过去一度认为在基站采用多幅天线的多址接入系统允许若干个用户同时与基站通信， 多幅天线可以实现不同用户信号的空间隔离。 20 世纪 90 年代中期，研究人员发现采用多 幅发射天线和接收天线的点对点信道也会出现类似的效应，即使当发射天线相距不远时也 是如此。只要散射环境足够丰富，使得接受天线能够将来自不同发射天线的信号分离开， 该结论就成立。我们已经了解到了机会通信技术如何利用信道衰落，本章还会看到信道衰 落对通信有益的另一例子。将机会通信与 MIMO技术提供的性能增益的本质进行比较和对比是非常的有远见的。

4、机会通信技术主要提供功率增益，改功率增益在功率受限系统的低信噪比情况下相当明 显，但在宽带受限系统的高信噪比情况下则很不明显。正如我们将看到的，MIMO技术不仅能够提供功率增益，还可以提供自由度增益，因此， MIMO技术成为在高信噪比情况下大幅 度增加容量的主要工具。MIMO通信是一个内容非常丰富的主题， 对它的研究将覆盖本书其余章节。 本章集中研 究能够实现空间多路复用的物理环境的属性，并阐明如何在MIMO统计信道模型中简明扼要地俘获这些属性。具体分析过程如下：首先通过容量分析，明确确定确定性MIMO信道多路复用容量的关键参数，之后介绍一系列 MIMO物理信道，评估其空间多路复用性能； 根据

5、这些实例的结果，我们认为在角域对 MIMO信道进行建模是非常自然地，同时讨论了 基于该方法的统计模型。本章采用的方法与第 2 章的方法是平行的，第 2 章就是从多径无 线信道的几个理想实例着手进行分析，从中了解了基本物理现象，进而研究更适用于通信 方案设计与性能分析的统计衰落模型。实际上，在特定的信道建模技术中，我们将会看到 大量的类似方法。我们贯穿始终的研究焦点是平坦衰落 MIMO信道，但也可以直接扩展到频率选择性 MIMO 信道，这方面的内容会在习题中加以介绍。7.1 确定性 mimo信道的多路复用容量包括 nt 副发射天线和 nt接受天线的窄带时不变无线信道可以用一个 nt*nt 阶确定

6、性矩阵 H 描述， H 具有哪些决定信道空间多路复用容量的重要属性呢？我们通过对信道容量的分 析来回答这个问题。7.1.1 通过奇异值分解分析容量时不变信道可以表示为： y = Hx+w_其中 x、y与 w分别表示一个码元时刻的发射信号、 接受信号与高斯白噪声 （为简单起 见省略了时标），信道矩阵 H 为确定性的，并假定在所有时刻都保持不变，而且对于发射 机和接收机是已知的。 这里的 hij 为发射天线 j 到接受天线 i 的信道增益， 对发射天线的信 号的总功率约束为 P。 这就是矢量高斯信道，将矢量信道分解为一组并行的、相互独立的标量高斯子信道就可以 计算出该信道的容量。油线性代数的基本原

7、理可知，每个线性变换都能够表示为三种运算 的组合：旋转运算、比例运算和另一次旋转运算。用矩阵符号表示，矩阵H 具有如下奇异值分解（ SVD）：其中， 与 为（旋转）酉矩阵 1，是对角元素为非负实数、非对角线元素为零的矩形矩阵 2。对角线元素为矩阵 H的有序奇异值，其中 nmin：=min（nt，nr ）。因为所以平方奇异值为矩阵 HH*的特征值，同时也是矩阵 H*H 的特征值。注意，奇异值共有 nm 个，可以将 SVD重新写成为：SVD 分解可以解释为 2 个坐标变换：即如果输入用 V 的各种定义的坐标系统表示，并 且输出用 U的各列定义的坐标系统表示，那么输入 / 输出关系是非常简单的。我们

8、已经在第 5 章讨论时不变频率选择性信道以及具有完整 CSI 的时变衰落信道时看 到了高斯并并行信道的例子。时不变 MIMO信道也是另外一个例子，这里空间维所起的作 用与其他问题中时间维和频率维的作用是相同的。大家熟知的容量表达式为：其中， P1*, ,P nmin*为注水功率分配：通过选择 满足总功率约束 ，各 对应于信道的一个特征模式（也称特征信 道）。各非零特征信道能够支持一路数据流，因此， MIMO信道能够支持多路数据流的空间 多路复用。基于 SVD的可靠通信结构与第三章介绍的 OFDM系统之间存在明显的相似之处， 在这 2 种情况下，都是利用变换将矩阵信道转换为一组并行的独立子信道。

9、在OFDM系统中，矩阵信道由上式中的轮换矩阵 C 给出，该矩阵由 ISI 信道和加在输入码元上的循环前 缀定义， ISI 信道与 MIMO信道的重要区别在于，前者的 U、V 矩阵不依赖与 ISI 信道的特 定实现，而后者的 U、V 矩阵则依赖与 MIMO信道的特定实现。7.2 MIMO 信道的物理建模通过本节的内容我们将了解到 MIMO信道的空间多路复用性能对于物理环境的依赖程 度，为此，我们将研究一系列理想化实例并分析骑信道矩阵的秩和条件数，这些确定性实 例同时表明了下一节中讨论的 MIMO信道统计建模的常规方法。具体地讲，本节的讨论局 限于均匀线性天线阵列，即天线一均匀的间隔分布于一条直线

10、上，分析的细节取决于特定 的天线结构，但是我们要表达的概念于此无关。7.2.1 视距 SIMO信道最简单的 SIMO信道只有一条视距信道（如下所示），图中为不存在任何反射体和散 射体的自由空间， 并且各天线对之间仅存在直接信号路径， 天线间隔为 ，其中 为 载波波长， 为归一化接受天线间隔，即归一化为载波波长的单位，天线阵列的尺寸比 发射机与接收机之间的距离小得多。发射天线与第 i 副接受天线之间信道的连续时间冲激响应为：其中，di为发射天线与第 i 副接受天线之间的距离， c 为光速， a为路径衰减，假定路径衰 减对所有天线对都相同。设 di /c 1/W,其中 W为传输带宽，则可得基带信道

11、增益为：其中， f c为载波频率。 SIMO信道可以写成： y=hx+w。其中， x 为发射码元， w 为噪声， y 为接受矢量。有时将信道增益矢量 h=h 1, hnt t 称为信号方向或由发射信号在接收天线阵 列上感应出的空间特征图。由于发射机与接收机之间的距离远大于接收天线阵列的尺寸，所以从发射天线到各接 收天线的路径为 1 阶并行的，并且其中，d 为从发射天线到第一副接收天线之间的距离，为视距路径到接收天线阵列的入射角， 为在视距方向上接收天线 i 相对于接受天线 1 的位移。并且通常被称为相对于接收天线阵列的方向余弦。因此，空间特征图h=h 1, hnt t 为即有相对时延引起的相位

12、差为 的连续天线处的接收信号。为了符号表示方便， 定义为方向余弦上的单位空间特征图。 最佳接收机只是将有噪声接收信号投影到该信号方向上，也就是最大比合并或接收波 束成形，对不同的时延进行调整，从而使天线的接收信号能够进行相长合并，得到nt 倍的功率增益，所获取的容量为：于是， SIMO信道提供了功率增益，但没有提供自由度增益。 在介绍视距信道时，有时将接收天线阵列称为相位阵列天线。8. MIMO: 容量与多路复用结构本章研究 MIMO衰落信道的容量，讨论能够从信道中提取所期望的多路复用增益的收 发信机结构，特别是集中研究发射机未知信道的情况。在快衰落MIMO信道中，可以证明：1 在高信噪比时，

13、独立同分布瑞利快衰落信道的容量有nminlogSNRb/s/Hz 确定，其中nmin为发射天线数 nt与接收天线数 nr 的最小值，这是自由度增益。2 在低信噪比时，容量近似为 nrSNRlog2eb/s/Hz ，这是接收波束成形功率增益。3 在所有信噪比时，容量与 nmin 呈线性比例关系，这是由于功率增益与自由度增益合 并造成的。此外，如果发射机也能够跟踪信道， 那么还存在发射波束成形增益以及机会通信增益。 利用确定性时不变 MIMO信道的容量获取收发信机，其结构比较简单：在适当的坐标 系统中对独立数据流进行多路复用，接收机将接收矢量变换到另一个适当的坐标系统中， 分别对不同的数据流进行译

14、码。如果发射机未知信道，那么必须事先固定独立数据流被多 路复用所选取的坐标系统。连同联合译码，这种发射机结构实现了快衰落信道的容量，在 文献中也将改结构称为 V-BLAST结构 1。83 节讨论比独立数据流的联合最大似然译码更简单的接收机结构， 虽然可以支持信 道全部自由度的接收机结构有若干种，其中的一种特殊结构是合并使用最小均方误差估计 与串行干扰消除，即 MMSE-SIC接收机可以获取容量。慢衰落 MIMO信道的性能可以通过中断概率和相应的中断容量来表征。在低信噪比时， 一个时刻利用一副发射天线就可以获取中断容量，实现满分集增益ntnr 和功率增益 nr。另一方面，高信噪比时的中断容量还受

15、益于自由度增益，要简洁地刻画其特征更加困难， 此问题留到第 9 章再分析。虽然采用 V-BLAST结构可以实现快衰落信道的容量，但该结构对于慢衰落信道则是严 格次最优的，实际上，它甚至还没有实现 MIMO信道期望的满分集增益。为了说明这一问 题，考虑通过发射天线直接发送独立数据流，在这种情况下，各数据流的分集仅限于接收 分集，为了从信道中获取满分集，须对发射天线进行编码。将发射天线编码与 MMSE-SIC 结合起来的一种修正结构 D-BLAST2 不仅能够从信道中获取满分集， 而且其性能还接近于中 断容量。8.1 V-BLAST 结构首先考虑时不变信道 ym=Hxm+wm m=1,2, 当发射

16、机已知信道矩阵 H时，有 7.1.1 节可知，最优策略是在 H*H 的特征矢量的方向 上发射独立数据流，即在由矩阵 V 定义的坐标系统中发射，该坐标系统与信道有关。考虑 到要处理发射机未知信道矩阵时的衰落信道，归纳出入如下图所示的结构，图中nt 个独立的数据流在由酉矩阵 Q 确定的任意坐标系统中进行多路复用，该酉矩阵未必与信道矩阵 H 有关，这就是 V-BLAST结构。对数据流进行联合译码， 为第 k 个数据流分配的功率为 Pk（使 得功率之和 P1+Pnt 等于 P，即发射总功率约束），并利用速率为 Rk的容量获取高斯码进 行编码，总的速率为几种特殊情况如下：1 如果 Q=V并且通过注水分配

17、的方式确定功率， 则得到如图 7-2 所示的容量获取结构。2 如果 Q=Int ，则独立数据流被发送到不同的发射天线。下面利用与第 5 章关于球体填充的类似论述，讨论最高可靠通信速率的上界：其中， Kx为发射信号 x 的协方差矩阵，是多路复用坐标系和功率分配的函数：考虑在长度为 N 的码元时间块内的通信，长度为 nrN的接收矢量一高概率位于体积与下式 成比例的椭圆体内：该公式是与并行信道相对应的体积公式的直接推广，并在习题 8-2 中加以证明。由于必须 考虑到各码字周围为非混叠噪声球空间才能却保可靠通信，所以能够填充的码字的最大数 量为比值：现在就可以得出结论，可靠通信速率的上界为上式。采用

18、V-BLAST 结构能够达到该上界吗？注意到独立数据流在 V-BLAST结构中多路复 用，是否可能需要对数据流进行编码才能达到上界式？为了解决这个问题，考虑 MISO 信 道的特殊情况（ nt=1），并在该结构中设 Q=Int，即独立数据流由各发射天线发送。这恰好 就是 6.1 节介绍的上行链路信道，发射天线类似于用户，由这一节的内容可知，该上行链 路信道的总容量为：这恰恰是特殊情况下的上界式。因此，数据流独立的 V-BLAST结构完全能够达到上界式。 在一般情况下，可以将 V-BLAST结构与包括 nt 副接收天线、信道矩阵为 HQ的上行链路信 道进行类比，与一副发射天线的情况相同，上界式就

19、是该上行链路信道的总容量，因此采 用 V-BLAST结构可以达到。这种上行链路信道的详细研究见第 10 章。8 2 快衰落 MIMO信道快衰落 MIMO信道为 ym=Hmxm+wm m=1,2, 其中， Hm 为随机衰落过程。为了恰当地定义容量（由随时间变化的信道衰落取平均获 得的）的概念，现做出如下（与前几章相同的）假定，即假定 Hm 为平稳遍历过程，作 为归一化处理，设 E|h ij | 2=1，与前面的研究方法一样，考虑相干通信：接收机准确地跟 踪信道衰落过程。首先研究发射机仅具有衰落信道统计特征的情况，最后研究发射机也能 够准确跟踪衰落信道的情况（完整 CSI），这种情况非常类似于时不

20、变 MIMO信道的情况。附件 2：外文原文7. MIMO I: spatial multiplexingand channel modelingIn this book, we have seen several different uses of multiple antennas in wireless communication. In Chapter 3, multiple antennas were used to provide diversity gain and increase the reliabilityof wireless links. Both receive an

21、d transmit diversitywere considered. Moreover, receive antennas can also provide a power gain. In Chapter 5, we saw that with channel knowledge at the transmitter, multiple transmit antennas can also provide a power gain via transmit beamforming. In Chapter 6, multiple transmit antennas were used to

22、 induce channel variations, which can then be exploited by opportunistic communication techniques. The scheme can be interpreted as opportunistic beamforming and provides a power gain as well.In this and the next few chapters, we will study a new way to use multiple antennas. We will see that under

23、suitable channel fading conditions, having both multiple transmit and multiple receive antennas (i.e., a MIMO channel) provides an additional spatial dimension for communication and yields a degree-of- freedom gain. These additional degrees of freedom can be exploited by spatially multiplexing sever

24、al data streams onto the MIMO channel, and lead to an increase in the capacity: the capacity of such a MIMO channel with n transmit and receive antennas is proportional to n.Historically, it has been known for a while that a multiple access system with multiple antennas at the base-station allows se

25、veral users to simultaneously communicate with the base-station. The multiple antennas allow spatial separation of the signals from the different users. It was observed in the mid 1990s that a similar effect can occur for a point-to-point channel with multiple transmit and receive antennas, i.e., ev

26、en when the transmit antennas are not geographically far apart. This holds provided that the scattering environment is rich enough to allow the receive antennas to separate out the signals from the different transmit antennas. Weh ave already seen how channel fading can be exploited by opportunistic

27、 communication techniques. Here, we see yet another example where channel fading is beneficial to communication.It is insightful to compare and contrast the nature of the performance gains offered by opportunistic communication and by MIMO techniques，Opportunisticcommunication techniques primarily p

28、rovide a power gain.This power gain is very significant in the low SNR regime where systems are power-limited but less so in the high SNRr egime where they are bandwidthlimited. As we will see, MIMOt echniques can provide both a power gain and a degree-of-freedom gain. Thus, MIMOt echniques become t

29、he primary tool to increase capacity significantly in the high SNRr egime.MIMO communication is a rich subject, and its study will span the remaining chapters of the book. The focus of the present chapter is to investigate the properties of the physical environment which enable spatial multiplexing

30、and show how these properties can be succinctly captured in a statisticalMIMOc hannel model.We proceed as follows. Through a capacity analysis, we first identify key parameters that determine the multiplexing capability of a deterministic MIMO channel. We then go through a sequence of physical MIMO

31、channels to assess their spatial multiplexing capabilities. Building on the insights from these examples, we argue that it is most natural to model the MIMO channel in the angular domain and discuss a statisticalmodel based on that approach. Our approach here parallelsthat in Chapter 2, where we sta

32、rted with a few idealized examples of multipath wireless channels to gain insights into the underlying physical phenomena, and proceeded to statistical fading models, which are more appropriate for the design and performance analysis of communication schemes. We will in fact see a lot of parallelism

33、 in the specific channel modeling technique as well.Our focus throughout is on flat fading MIMO channels. The extensions to frequency-selective MIMO channels are straightforward and are developed in the exercises.7 1 Multiplexing capability of deterministic MIMO channelstransmit and nr receiveA narr

34、owband time-invariant wireless channel with n antennas is described by an nr by nt deterministic matrix H. What are the key properties of H that determine how much spatial multiplexing it can support? We answer this question by looking at the capacity of the channel.7.1.1 Capacity via singular value

35、 decompositionThe time-invariant channel is described by where x,yand wdenote the transmitted signal,received signal and white Gaussian noise respectively at a symbol time (the time index is dropped for simplicity).The channel matrix H is deterministic and assumedto be constant at all times and know

36、n to both the transmitter and the receiver.Here, hij is the channel gain from transmit antenna j to receive antenna i. There is a total power constraint, P, on the signals from the transmit antennas.This is a vector Gaussian channel. The capacity can be computed by decomposing the vector channel int

37、o a set of parallel, independent scalar Gaussian sub-channels. From basic linear algebra, every linear transformation can be represented as a composition of three operations: a rotation operation, a scaling operation, and another rotation operation. In the notation of matrices, the matrix H has a si

38、ngular value decomposition (SVD):10Where and are (rotation) unitary matrices1 andis a rectangular matrix whose diagonal elements are non-negative real numbers and whose off-diagonal elements are zero.2 The diagonal elementsare the ordered singular values of the matrix H, where nmin： =min( nt ，nr ).

39、Since*the squared singular values _2i are the eigenvalues of the matrix HHand also of*HH. Note that there are nmin singular values. We can rewrite the SVD asThe SVD decomposition can be interpreted as twocoordinate transformations:it says that if the input is expressed in terms of a coordinate syste

40、m defined by the columns of V and the output is expressed in terms of a coordinate system defined by the columns ofU, then the input/output relationship is very simple.Equation (7.8) is a representation of the original channel (7.1) with the input and output expressed in terms of these new coordinat

41、es.We have already seen examples of Gaussian parallel channels in Chapter 5, when we talked about capacities of time-invariant frequency-selective channels and about time-varying fading channels with full CSI. The time-invariantMIMOc hannelis yet another example. Here, the spatial dimension plays th

42、e same role as the time and frequency dimensions in those other problems. The capacity is by now familiar:where P1 , ,P nmin are the waterfilling power allocations:corresponds towith chosen to satisfy the total power constraint an eigenmode of the channel (also called an eigenchannel ). Each eigench

43、annel can support a data stream; thus, the MIMO channel can support the spatial multiplexing of multiple streams. Figure 7.2 pictorially depicts the SVD-based architecture for reliable communication.11There is a clear analogy between this architecture and the OFDMs ystem introduced in Chapter 3. In

44、both cases, a transformation is applied to convert a matrix channel into a set of parallel independent sub-channels. In the OFDM setting, the matrix channel is given by the circulant matrixC in (3.139), defined by the ISI channeltogether with the cyclic prefix added onto the input symbols. The impor

45、tant difference between the ISI channel and the MIMO channel is that, for the former, the U and V matrices (DFTs) do not depend on the specific realization of the ISI channel, while for the latter, they do depend on the specific realization of the MIMO channel.7.2 Physical modeling of MIMO channelsI

46、n this section, we would like to gain some insight on how the spatial multiplexing capability of MIMO channels depends on the physical environment. We do so by looking at a sequence of idealized examples and analyzing the rank and conditioning of their channel matrices. These deterministic examples

47、will also suggest a natural approach to statistical modeling of MIMO channels, which we discuss in Section 7.3. To be concrete, we restrict ourselves touniform linearantenna arrays , where the antennas are evenly spaced on a straight line. The details of the analysis depend on the specific array str

48、ucture but the concepts we want to convey do not.7.2.1Line-of-sight SIMO channelThe simplest SIMOc hannel has a single line-of-sight (Figure 7.3(a). Here, there is only free space withoutany reflectors or scatterers, and only a direct signalpath between each antenna pair. The antenna separation iswh

49、ere is thecarrier wavelength andis the normalized receive antenna separation,normalized to the unit of the carrier wavelength. The dimension of the antenna array is much smaller than the distance between the transmitter and the receiver.The continuous-time impulse response between the transmit anten

50、na and the ith receive antenna is given by12where di is the distance between the transmit antenna and ith receive antenna,c is the speed of light and a is the attenuation of the path, which we assume tobe the same for all antenna pairs. Assuming di/c 1/W, where Wi s the transmission bandwidth, the b

51、aseband channel gain is given by (2.34) and (2.27):where fc is the carrier frequency. The SIMO channel can be written asy = hx+wwhere x is the transmitted symbol,w is the noise andy is the received vector.The vector of channel gains h=h1, hnt t is sometimes called the signal directionor the spatial

52、signature induced on the receive antenna array by the transmitted signal.Since the distance between the transmitter and the receiver is much larger than the size of the receive antenna array, the paths from the transmit antenna to each of the receive antennas are, to a first-order, parallel andiswhe

53、re d is the distance from the transmit antenna to the first receive antenna and _ is the angle of incidence of the line-of-sight onto the receive antenna array.(You are asked to verify this in Exercise 7.1.) The quantity13the displacement of receive antenna i from receive antenna1 in the direction o

54、f the line-of-sight. The quantityis often called the directional cosine with respect to the receive antenna array. The spatial signature h=h1,hntt is therefore given byi.e., the signals received at consecutive antennas differ in phase by due to the relative delay. For notational convenience, we defi

55、neas the unit spatial signature in the directional cosine .The optimal receiver simply projects the noisy received signal onto the signal direction, i.e., maximal ratio combining or receive beamforming (cf. Section 5.3.1). It adjusts for the different delays so that the received signals at the anten

56、nas can be combined constructively, yielding an nr-fold power gain. The resulting capacity isThe SIMO channel thus provides a power gain but no degree-of-freedom gain.channel, the receive antenna array is sometimesIn the context of a line-of-sight called a phased-array antenna.148. MIMO II: capacity

57、 and multiplexing architecturesIn this chapter, we will look at the capacity of MIMOf ading channels and discuss transceiver architectures that extract the promised multiplexing gains from the channel. Wep articularlyfocus on the scenario when the transmitter does not knowthe channel realization. In

58、 the fast fading MIMO channel, we show the following: ? At high SNR, the capacity of the i.i.d. Rayleigh fast fading channel scales like nminlogSNRb/s/Hz. where nmin is the minimum of the number of transmit antennas nt and the number of receive antennas nr . This is a degree-of-freedom gain.? At low SNR,t he capacity is approximately nrSNRl og2 e bits/s/