【正文】 考慮在長度為 N 的碼元時(shí)間塊內(nèi)的通信，長度為 nrN 的接收矢量一高概率位于體積與下式成比例的橢圓體內(nèi)： 該公式是與并行信道相對應(yīng)的體積公式的直接推廣，并在習(xí)題 82中加以證明。 采用 VBLAST 結(jié)構(gòu)能夠達(dá)到該上界嗎？注意到獨(dú)立數(shù)據(jù)流在 VBLAST 結(jié)構(gòu)中多路復(fù)用，是否可能需要對數(shù)據(jù)流進(jìn)行編碼才能達(dá)到上界式？為了解決這個(gè)問題，考慮 MISO 信道的特殊情況（ nt=1），并在該結(jié)構(gòu)中設(shè) Q=Int，即獨(dú)立數(shù)據(jù)流由各發(fā)射天線發(fā)送。因此，數(shù)據(jù)流獨(dú)立的 VBLAST 結(jié)構(gòu)完全能夠達(dá)到上界式。這種上行鏈路信道的詳細(xì)研究見第 10 章。為了恰當(dāng)?shù)囟x容量（由隨時(shí)間變化的信道衰落取平均獲得的）的概念，現(xiàn)做出如下（與前幾章相同的）假定，即假定 {H[m]}為平穩(wěn)遍歷過程，作為歸一化處理，設(shè) E[|hij|2=1，與前面的研究方法一樣，考慮相干通信：接收機(jī)準(zhǔn)確地跟蹤信道衰落過程。 9 附件 2：外文原文 7. MIMO I: spatial multiplexing and channel modeling In this book, we have seen several different uses of multiple antennas in wireless munication. In Chapter 3, multiple antennas were used to provide diversity gain and increase the reliability of wireless links. Both receive and transmit diversity were 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 induce channel variations, which can then be exploited by opportunistic munication 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 suitable channel fading conditions, having both multiple transmit and multiple receive antennas (., a MIMO channel) provides an additional spatial dimension for munication and yields a degreeof freedom gain. These additional degrees of freedom can be exploited by spatially multiplexing several 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 basestation allows several users to simultaneously municate with the basestation. 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 pointtopoint channel with multiple transmit and receive antennas, ., even 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. We have already seen how channel fading can be exploited by opportunistic munication techniques. Here, we see yet another example where channel fading is beneficial to munication. It is insightful to pare and contrast the nature of the performance gains offered by opportunistic munication and by MIMO techniques， Opportunistic munication techniques primarily provide a power power gain is very significant in the low SNR regime where systems are powerlimited but less so in the high SNR regime where they are bandwidthlimited. As we will see, MIMO techniques can provide both a power gain and a degreeoffreedom gain. Thus, MIMO techniques bee the primary tool to increase capacity significantly in the high SNR regime. 10 MIMO munication 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 and show how these properties can be succinctly captured in a statistical MIMO channel 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 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 statistical model based on that approach. Our approach here parallels that in Chapter 2, where we started 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 munication schemes. We will in fact see a lot of parallelism in the specific channel modeling technique as well. Our focus throughout is on flat fading MIMO channels. The extensions to frequencyselective MIMO channels are straightforward and are developed in the exercises. 7． 1 Multiplexing capability of deterministic MIMO channels A narrowband timeinvariant wireless channel with nt transmit and nr receive 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. Capacity via singular value deposition The timeinvariant channel is described by y = Hx