Công nghệ viễn thông MIMO

In this book, I focus on WiFi IEEE 802.11n and LTE and explainhow these two popular wireless standards implement MIMO concepts in practice.Chapter 1 provides an overview of MIMO communic

the theory and implementation of MIMO techniques.

In-depth coverage of topics such as RF propagation, space-time coding, spatial tiplexing, OFDM in MIMO for broadband applications, the theoretical MIMO capacityformula, and channel estimation, will give you a deep understanding of how the resultsare obtained, while detailed descriptions of how MIMO is implemented in commercialWiFi and LTE networks will help you apply the theory to practical wireless systems.Key concepts in matrix mathematics and information theory are introduced and devel-oped as you need them, and key results are derived step by step, with no details omitted.Including numerous worked examples, and end-of-chapter exercises to reinforce andsolidify your understanding, this is the perfect introduction to MIMO for anyone new tothe field

mul-Jerry R Hampton is a research engineer with over 30 years’ experience in

communi-cations systems engineering He is a member of the principal professional staff in theApplied Physics Laboratory, and an Adjunct Professor in the Whiting School of Engi-neering, at The Johns Hopkins University, where he teaches a graduate course in MIMOwireless communications

propagation models, channel characterizations, and applications of MIMO in cial systems adds tremendous depth and understanding to the concepts After studyingthis text, if readers have interests in topics not covered, they will very likely be able tounderstand or author for themselves advanced MIMO literature on such topics.”

commer-David Nicholson, Communications consultant

MIMO Communications

J E R RY R H A M P T O N

The Johns Hopkins University

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Preface pagexi

1.5.4 Relationship between diversity order and diversity gain 12

3 Applications of the MIMO capacity formula 42

5.5 Dependence of Rtand Rron antenna spacing and scattering angle 105

6 Alamouti coding 114

7.2.1 General pairwise error probability expression 136

7.2.2 Pairwise error probability in Rayleigh fading 140

8.3.2 Zero-forcing with interference cancellation (ZF-IC) 171

8.3.3 Linear minimum mean square detection (LMMSE) 175

8.3.4 LMMSE with interference cancellation (LMMSE-IC) 179

9.2 Strategies for coping with frequency-selective fading 198

10.3.3 Linear minimum mean square channel estimation 222

11.1.6 Channel estimation 247

This book is an outgrowth of a graduate course I have taught for the past four years onMIMO Wireless Communications in the Engineering for Professionals (EP) Programwithin the Whiting School of Engineering at The Johns Hopkins University When Ibegan to develop the course in the spring of 2006, I initially thought I would simplychoose a textbook from the collection of numerous books that had been written onMIMO communications at that time As I began studying these books, however, I foundthat, although they were each excellent in various ways, none of them was as accessible

to the average practicing communications engineer or early level electrical ing graduate student as I had hoped Many of these books were written by experts inthe field, researchers who had made seminal contributions in the area of MIMO com-munications, but the prerequisites needed to follow and understand the details in theirpresentations were often above the level of expertise of those being introduced to MIMOfor the first time

engineer-This book is my attempt to remedy this problem In developing the course and in ing this book, I have tried to make the concepts and techniques associated with MIMOcommunications accessible to an average communications engineer with an undergrad-uate degree in electrical engineering I assume that readers are familiar with digitalcommunication techniques and that they have had a formal course (or its equivalent)

writ-in digital signal processwrit-ing; however, I do not assume readers are familiar with writ-mation theory or are proficient in advanced matrix mathematics, areas of expertise thatare normally assumed in the MIMO literature and in many of the books that have beenpublished on this topic When knowledge in these areas is required to understand MIMOconcepts, I have attempted to include the necessary information on those topics in thebook so that it is not necessary to consult external resources In this sense, the book hasbeen designed to be as self-contained as possible

infor-As its name suggests, this book is intended to provide an introduction to the field

of MIMO communications, and is, therefore, by design not encyclopedic My goal hasbeen to provide readers new to MIMO communications with an understanding of thebasic concepts and methods, thereby laying a foundation for further study and providingthem with the ability to understand the vast literature on this subject

Although my goal has been to make the concepts of MIMO understandable to theaverage communications engineer, I have tried to remain rigorous at the same time One

of my initial frustrations when I began searching for a textbook was that there were oftenlarge steps or gaps in derivations that were not explained, so I have attempted to fill in

the details of as many gaps as possible in my book, in some cases relegating the details

to appendices to avoid interrupting the flow of the text

A third feature of this book that I hope will be useful to readers is that it containsdescriptions of how MIMO concepts are implemented in practical systems MIMO tech-niques have now become as commonplace in wireless communications systems as mod-ulation and error correction coding, so there is no shortage of examples of systems thatuse MIMO methods In this book, I focus on WiFi (IEEE 802.11n) and LTE and explainhow these two popular wireless standards implement MIMO concepts in practice.Chapter 1 provides an overview of MIMO communication concepts and includes

a section on key matrix properties and identities that are used throughout the book.This initial chapter explains the different types of MIMO schemes, defines fundamen-tal concepts such as spatial diversity and spatial multiplexing, and presents measuredperformance results that demonstrate the performance benefits of MIMO

Chapter2is devoted to derivation of the MIMO capacity formula, which predicts themaximum error-free data rate that can be supported by a MIMO communication sys-tem This formula is used later in Chapter3to provide useful conceptual insights intohow multiple antennas enable increased spectral efficiency Although the MIMO capac-ity formula is derived using concepts from information theory, the chapter introducesconcepts as necessary to derive the final result and does not assume the reader has abackground in that subject

Chapter3explores the implications of the MIMO capacity formula and uses it to pute the communications capacities of MIMO systems under various assumptions Theconcepts of eigenmodes and channel rank are examined, and the spatial multiplexingtechnique called eigenbeamforming is derived and explained in this chapter

com-Chapter 4 discusses RF propagation in general and develops the terminology andconcepts used in characterizing multipath propagation in particular

Chapter 5 presents several theoretical MIMO propagation models that have beendeveloped based on theory and empirical results Expressions for the channel modelwhen both Rayleigh fading and line-of-sight propagation exist are also presented Thesemodels are used to derive expressions for the dependence of the MIMO capacity onantenna correlation as well as on the amount of scattering in the channel

Chapter 6 describes Alamouti coding, which is an important practical MIMOtechnique used to achieve transmit diversity This chapter begins by examining theperformance of ideal maximal ratio receive combining and then shows how Alamouticoding achieves diversity gain equal to a maximal ratio receive combiner

Chapter7broadens the discussion begun in Chapter6to consider other types of ing techniques, called space-time codes, that can be used to achieve transmit spatialdiversity This chapter focuses on space-time block codes, but also introduces the reader

cod-to space-time trellis coding concepts The chapter describes how cod-to perform decoding,concluding with a presentation of representative performance results

Chapter8addresses spatial multiplexing, which comprises the second major class ofMIMO techniques These techniques, which exploit multipath, enable MIMO systems

to transmit higher data rates than can be achieved with conventional communicationsystems

Chapter9discusses MIMO over broadband channels Up to this point in the book, theassumption is that the bandwidth of the transmitted signal is smaller than the coherencebandwidth of the channel; however, in modern wireless communication systems this isseldom the case In practice, broadband systems operate by employing OFDM signaling,

so this chapter reviews OFDM and then shows how OFDM is used with the narrowbandMIMO techniques developed earlier to support broadband service

Chapter10discusses an important practical aspect of MIMO communications – theestimation of the properties of the communications channel Since most MIMO tech-niques require that either the transmitter or the receiver (or both) have knowledge of thechannel, channel estimation techniques are an essential aspect of any MIMO communi-cation system This chapter discusses the fundamental concepts used in MIMO channelestimation and describes how practical MIMO systems perform this function

The book concludes with Chapter11, which describes how MIMO is implemented inWiFi and LTE wireless communication systems

I would like to conclude by acknowledging and thanking some key people that helpedmake this book possible First, I want to thank the various students who have taken

my course on MIMO Wireless Communications at Johns Hopkins over the past severalyears Their penetrating questions have helped me improve both the course as well asthis book To the extent that this book succeeds in helping others understand MIMOconcepts, I am indebted to these students

In addition to my students in the EP program at Johns Hopkins, I would like toacknowledge Dennis Ryan at The Johns Hopkins University Applied Physics Labo-ratory who chairs the Janney Publication Program, which funds, on a competitive basis,sabbaticals for employees to write books and journal papers I would like to thankDennis and the Janney committee for granting me a sabbatical during the summer of

2012 to finish writing this book Thanks also go to Rob Nichols for his ment and willingness to accommodate my absence from normal work duties during thissabbatical

encourage-I would also like to express my gratitude to two colleagues who have providedinvaluable support during the preparation of this book Eric Yang shared his extensiveknowledge of cellular wireless standards and guided me through the labyrinth of LTEand IEEE 802.11n standards documents that I used to write Chapter11 Thanks Eric! Iwould also like to offer special thanks to Feng Ouyang, another colleague, who served

as a sounding board for my interminable discussions on many aspects of MIMO ory during the lengthy gestation period of this book Feng was incredibly patient andgenerous with his time while sharing his insights and mathematical expertise with me.Thanks Feng! This book would not have come about without Feng’s and Eric’s help.Finally, I would like to thank my wife, Dorothy, for her support and patience duringthis project, which has consumed far too many of my weekends and nights over the pastseveral years I dedicate this book to her, to our two wonderful children, Jessica and

the-Joshua, and finally, and ultimately, to God Soli Deo Gloria

Jerry R Hampton

This chapter lays the foundations for the remainder of the book by presenting anoverview of MIMO communications Fundamental concepts and key terminology areintroduced, and a summary of important matrix properties is provided, which will bereferred to throughout the book Some experimental results showing the benefits ofMIMO are also presented.

Multiple Input Multiple Output communications, abbreviated MIMO, and normally nounced like “My-Moe,” refers to a collection of signal processing techniques thathave been developed to enhance the performance of wireless communication systemsusing multiple antennas at the transmitter, receiver, or both MIMO techniques improve

pro-communications performance by either combating or exploiting multipath scattering in

the communications channel between a transmitter and receiver MIMO techniques in

the first category combat multipath by creating what is called spatial diversity, and those techniques that exploit multipath do so by performing spatial multiplexing These two

concepts are introduced in this chapter, and we will have much more to say about themthroughout the remainder of the book The subject of MIMO communications is thestudy of spatial diversity and spatial multiplexing techniques

Figures1.1and1.2show block diagrams of generic MIMO communication systems

As indicated, the characteristics of the system depend on whether the focus of the MIMOprocessing is on creating spatial diversity, which improves reliability by combating fad-ing, or if the purpose is to maximize throughput by performing spatial multiplexing Ifthe focus is on spatial diversity, information bits are normally encoded and modulatedusing conventional error correction coding and modulation techniques prior to under-

going some form of space-time coding (STC) At the receiver, space-time decoding

is performed followed by demodulation and error decoding If the focus is on spatialmultiplexing, as illustrated in Figure1.2, the information error encoded bits are passedthrough a serial-to-parallel converter and the individual output streams are modulatedbefore being transmitted over separate antennas At the receiver, each antenna receives

a signal that consists of the sum of the signals from all of the transmit antennas; fore, it is necessary to strip off each of the transmitted streams{s i} before demodulatingthem The block that strips off each of the transmitted streams is often referred to as

there-Space-time encoder

Space-time decoder

Demod

Demod

P/S .

Figure 1.2 A MIMO system for spatial multiplexing.

an SM decoder or demultiplexer There are different types of spatial demultiplexing

schemes based on zero-forcing or linear minimum mean square error based methods,which we discuss in detail in Chapter8

Table1.1summarizes the relationship between a variety of different terms that areused in the MIMO literature At this point, there are two main concepts to be clear

about The first concept is that spatial diversity refers to techniques that are used to improve the reliability on a communications link by combating fading and that space-

time coding is the means by which this is accomplished The second concept is that

spatial multiplexing refers to techniques that are used to increase throughput without

increasing the required bandwidth by exploiting multipath This is done by transmittingseparate data streams on each of the transmit antennas and by separating those streams atthe receiver using some form of spatial demultiplexing The details of space-time codingare the subject of Chapters6and7, and spatial multiplexing is covered in Chapters3

and8

Strictly speaking, MIMO refers to communication systems that have multiple nas at both the transmitter and receiver; however, the nomenclature can be a bit

anten-Table 1.1 Relationships of key MIMO concepts.

Spatial diversity improve reliability combat fading space-time codingSpatial multiplexing increase throughput exploit fading spatial demultiplexing

(a) SISO (Single-Input Single-Output) (b) MISO (Multiple-Input Single-Output)

(c) SIMO (Single-Input Multiple-Output) (d) MIMO (Multiple-Input Multiple-Output)

Figure 1.3 Antenna configurations and their nomenclatures used in this book

confusing on this point and there is not always agreement on the use of terminology

In this book, we use the term MIMO in two different ways: in a broad sense to refer to acommunication system that has multiple antennas at either the transmitter, the receiver,

or both, and in a particular way when referring to systems that have multiple antennas atboth ends of the link When there are multiple antennas at the transmitter and only onereceiver, as may occur, for example, on a cellular forward link between the base stationand a single mobile user, we call that type of system a Multiple Input Single Output(MISO) system When the opposite is true and there are multiple receive antennas butonly one transmit antenna, that system is called a Single Input Multiple Output (SIMO)system When using the term in the broad sense, we often refer to MISO and SIMOsystems as particular types of MIMO configurations Conventional communication sys-tems that only have a single transmit antenna and a single receive antenna are calledSingle Input Single Output (SISO) communication systems Figure1.3illustrates thefour types of antenna configurations and the nomenclature used in this book

MIMO systems with N t transmit antennas and N rreceive antennas are referred to as

N t × N r MIMO systems Thus, for example, a 2× 4 MIMO system implies that thereare two transmit antennas and four receive antennas

The phrase “Multiple Input Multiple Output” has an interesting history Although now

it is used to describe the communication techniques that are the subject of this book, itwas originally used in electric circuit and filter theory as far back as the 1950s [23]

In that original context, “MIMO” referred to circuits that had multiple input and tiple output ports In the 1990s, however, information theorists and communication sys-tem researchers adopted this term to refer to new signal processing techniques that theywere developing for communication systems having multiple antennas In this newer

use of the term, the communications channel was the reference point, and the term tiple input referred to the signals from multiple transmit antennas that were“entering”

mul-or “being input” to the communications channel Similarly, the term multiple output

referred to signals arriving at multiple receiver antennas, which were viewed as ing” or “being output” from the channel The first reference to the term MIMO in thisnewer communications sense was in a paper by Peter Driessen and Gerry Foschini in

“exit-1999 where they published an analysis on the theoretical communications capacity of acommunication system with multiple transmit and multiple receive antennas [20].Although MIMO communications requires the use of multiple antennas, it is not thefirst multi-antenna technique to be developed So what’s new or unique about MIMO? Tohelp answer that question, it is useful to place MIMO in its proper historical context Webegin by recognizing that the idea of using multiple antennas to improve aspects of com-munications and radar performance goes back to the beginning of the 1900s The firstuse of multiple antennas was for the purpose of creating phased array antennas, whichwere first proposed and then demonstrated in 1905 by Karl Braun [12] During WW II,phased array technology was used to enable rapidly-steerable radar [7], and later, phasedarrays were used in AM broadcast radio to switch from groundwave propagation duringthe day to skywave propagation at night This was accomplished by switching the phaseand power levels supplied to the individual antenna elements daily at sunrise and sun-set so that the elevation angle of the radiation pattern was towards the horizon duringdaylight hours and pointed slightly upward at night This had the obvious advantage ofenabling the transmitter to change the direction that it emitted energy without having

to mechanically point the antenna, a challenging feat with large antennas such as thoseused in AM radio Phased array technology has also long been used to perform adaptivenulling for interference and jamming avoidance

In addition to phased array applications, multi-antenna technology has been used formore than 70 years to reduce the impact of fading on communication systems throughthe use of receive diversity An early paper on the concept of receive diversity waspublished by H Beverage and H Peterson [11] in 1931 In the 1950s, receive diversitycombining found extensive application on troposcatter links for military applications

in which radio waves are scattered within the troposphere layer of the atmosphere [2],[84] The scattering that occurs on troposcatter links enables communications beyondthe horizon, which, other than HF, was the only way to communicate beyond the horizonprior to the advent of satellite communications Troposcatter links were found to sufferfrom significant fading effects, so multiple antennas at the receiver were used to createreceive diversity, which was helpful in reducing the impact of the fading

Beginning in the 1990s, two new types of multi-antenna techniques were developed,which are the subject of this book One of these techniques uses multiple antennas to

achieve transmit diversity, which, like receive diversity, reduces the effect of fading Two

early papers on this technique were published in 1991 and 1993 by A Wittneben [81]

and N Seshadri, C Sundberg, and V Weerackody [68], respectively Later, Alamouti[6] published a landmark paper that described another way to achieve transmit diversitythat required less processing at the receiver Alamouti’s technique has since become one

of the most popular MIMO schemes in use today by nearly all wireless systems Hispaper described a simple space-time coding technique for achieving transmit diversityand spurred research into other space-time coding techniques

At about the same time that research was being conducted on transmit diversity,another class of multi-antenna techniques was being developed Unlike those who wereresearching ways to use multiple antennas to combat the effects of fading, this secondgroup of researchers was interested in developing ways of exploiting fading to supportincreased throughput capacity In 1996, Gerry Foschini at AT&T Research Labs pub-lished his landmark paper on layered space-time communications, which described theunderlying concept for the class of spatial multiplexing techniques that would eventually

be called the Bell-Labs Layered Space-Time (BLAST) schemes [30] In 1998 Foschiniand a team from AT&T Research Labs were the first to demonstrate a laboratory pro-totype system that implemented a particular type of BLAST technique called verticalBLAST (i.e., V-BLAST) [31]

Since these initial breakthroughs in spatial diversity and spatial multiplexing in thelate 1990s, a large body of a research has been conducted, and MIMO techniques usingthe spatial diversity and spatial multiplexing methods emerging from this research havebeen adopted in an increasing number of commercial wireless standards The first com-mercial MIMO technology was introduced by Iospan Wireless Inc in 2001 Since 2005,when the WiMAX standard first included MIMO technology, most wireless standardsnow include MIMO

Figure1.4shows a time line of some key breakthroughs in multi-antenna technologyover the past century This diagram and the discussion above indicate that MIMO can

be viewed as the latest in a long line of advances in multi-antenna technology

1.3 Smart antennas vs MIMO

In recent years, another multi-antenna term, smart antennas, has become popular in the

literature What are smart antennas and what is the difference between MIMO and smartantenna technology? There is not unanimous agreement on the answer to this question.One of the first researchers to use the term smart antennas was Jack Winters at AT&TLabs [80] In his 1998 paper, he focuses on describing ways to dynamically generatebeams at a cellular base station that point in the desired direction of mobile users, andways to create nulls that point in directions of interference In another paper by AngelikiAlexiou and Martin Haardt in 2004 [4], however, the term smart antennas is used in amuch broader sense to include not only dynamic beamforming and antenna nulling, butalso spatial multiplexing and spatial diversity techniques such as Alamouti’s scheme Intheir use of the term, MIMO is a subset of smart antenna technology

In this book, we use the older original concept to delineate between MIMO andsmart antennas For our purposes, smart antennas are defined as systems that employ

Time 2000

1950 1900

1905 First phased array

demonstration

WW II Phased arrays used

in rapidly-steerable radar

1956 First receive diversity demonstration for troposcatter communication

1998 Alamouti publishes his transmit diversity method & BLAST technique is demonstrated

2001 First introduction of MIMO techniques in cellular system by Iospan, Inc.

MIMO Era

Figure 1.4 Time line of key multi-antenna advances

techniques that are primarily designed to form beams and nulls in desired directionsbased on feedback from the environment MIMO techniques, in contrast, are defined

as communication systems that involve baseband signal processing techniques such asspace-time coding and spatial multiplexing schemes that are not focused on pointingbeams or creating nulls in space In summary, we distinguish between smart antennasand MIMO as follows:

Smart antennas focus on:

• Conventional beamforming – directing energy in a desired physical direction;

• Adaptive nulling – creating nulls in desired directions to reduce interference

MIMO focuses on:

• Spatial diversity – combating fading effects by creating spatial diversity through theuse of baseband space-time coding techniques;

• Spatial multiplexing – using spatial multiplexing techniques to exploit multipath inorder to achieve higher data rates than are possible with conventional systems havingthe same bandwidth

1.4 Single-user and multi-user MIMO

Before proceeding further, a few comments should be made regarding the terms user MIMO and multi-user MIMO, which have been coined to describe two classes of

single-MIMO communications that are used in wireless systems, such as LTE and WiMAX.Single-user MIMO (SU-MIMO) refers to conventional MIMO where there is a onetransmitting node and one receiving node, and the transmitter node has multipleantennas, as illustrated in Figure1.3(b) and (d).

In multi-user MIMO (MU-MIMO), mobile cellular users, each with a single antenna,transmit to a base station, and the base station processes the signals from each of theindividual mobiles as if they were coming from multiple transmit antennas on a singlenode In this case, the base station performs the same operations as the receiver in Fig-ure1.2, so multiple mobile users can transmit data over the same bandwidth, and thebase station is able to decouple the individual data streams using spatial decoding tech-niques In MU-MIMO, the individual users will not experience increased throughput;however, the overall system will That is, MU-MIMO allows more cellular users to trans-

mit simultaneously on the uplink path over the same bandwidth than would otherwise

be possible

The focus of this book is on SU-MIMO; however, with the exception of forming, which is a spatial multiplexing technique described in Chapter3, the spatialmultiplexing techniques we describe can be used with both SU- and MU-MIMO

eigenbeam-1.5 Introduction to spatial diversity

As we have just explained, one of the key purposes of MIMO communications is toimprove communications reliability by combating multipath fading, which is achievedthrough the creation of spatial diversity In this section, we review the concept of diver-sity, describe the difference between receive and transmit spatial diversity, and define

three important performance metrics: diversity order, diversity gain, and array gain.

In most environments where wireless communication systems operate, the strength of

the received signal varies with time, which is called fading Unfortunately, fading

sig-nificantly degrades communications performance by causing the probability of bit error

to increase compared to what it would be if only white noise were present Figure1.5

shows the probability of bit error as a function of bit-energy-to-noise power spectral

density, E b /N0, for different types of modulation in both fading and non-fading ronments The results in this figure demonstrate two important characteristics The first

envi-is simply that fading causes the error probability to increase dramatically for a given

value of E b /N0 The second observation is that for Rayleigh fading, which is the type

of fading assumed in this figure and that often occurs in practice, the error probability

decreases linearly when plotted on a logarithmic scale against E b /N0plotted in dB This

is an important observation, and we use it later in this chapter

In order to reduce the impact of fading, the concept of diversity is often employed.Diversity refers to transmitting replicas of the same signal over a fading channel insuch a way that each replica fades independently of the others When this happens,each replica tends to fade at a different time, so the probability that all the replicas

10 −4

Mean of Eb /N0 (dB)

Figure 1.5 Performance of binary signaling on a Rayleigh fading channel

fade simultaneously decreases as the number of replicas gets larger By combining thereplicas, however, the depths of the fades, and, so too, their adverse effects, can besignificantly reduced because the fades do not tend to occur at the same time

Reducing the impact of fading through diversity, therefore, involves two steps:a) creating independent replicas of the signal; and

b) combining the replicas

There are various ways to generate replicas of a signal for diversity purposes One is totransmit the signal on different RF frequencies that are spaced far enough apart that the

fading occurs independently on each carrier This is called frequency diversity Another diversity technique, called time diversity, involves transmitting the same signal at dif-

ferent times In a multipath environment, this occurs naturally because the same signalarrives at the receiver by traveling over multiple physical paths, which tend to experi-ence independent fading Rake receivers are used to process such signals A third way

to create diversity is to transmit the same information on signals having different

polar-izations, called polarization diversity Normally, fading is independent of signals having different polarizations A fourth type of diversity is called spatial diversity, which refers

to transmitting the same information over different physical paths between the mitter and receiver One way to create spatial diversity is to transmit a signal from one

trans-transmit antenna and receive it using multiple receive antennas If the receive nas are far enough apart, the fading on each path will be independent This is the type

anten-of diversity that was originally used in the 1950s to reduce the impact anten-of fading ontroposcatter links discussed earlier

Just as there are multiple ways to generate independent replicas of a signal, there arealso different ways to combine the replicas at the receiver The simplest type of combin-

ing is called selective combining, which involves comparing the replicas at each sample

time and choosing the largest value for the output of the combiner A second

combin-ing technique, called equal gain combincombin-ing, involves addcombin-ing the replicas together The third, and most common type of combining scheme, is called maximal ratio combin- ing (MRC) In MRC, the replicas are added together in the same way as they are in

equal gain combining, but prior to being added they are first scaled in proportion to thesignal-to-noise ratio of each replica In Chapter6, we discuss MRC in greater detail.Figure1.6illustrates the benefits of diversity combining by plotting the output ampli-tude of a selective combiner in the presence of Rayleigh fading for two cases: whenthere is no combining (i.e., the number of signals being combined is 1), and when thereare five replicas being combined The curve associated with no combining has the deep-est fades and the curve associated with five combined signals has noticeably less fading.Similar improvements occur with the other combining techniques

As we discussed earlier, troposcatter was one of the first types of communications niques to use diversity combining From that time until the 1990s, diversity techniquesinvolved transmitting a single version of a signal and extracting replicas of the trans-mitted signal at the receiver and then combining those replicas Diversity of this type is

tech-called receive diversity because extraction of the replicas is performed at the receiver.

Figure1.7illustrates the architecture of a communication system that implements spatial

receive diversity As shown in this figure, the transmitted signal is denoted by s, and the

communications channel has the effect of multiplying the transmitted signal by a

com-plex value, which we call the channel response, and denote by h i , i = 1, , N r, where

N r represents the number of receive antennas The inputs to the combiner, therefore,consist of the set of signals{r i = h i s} If the receive antennas are spaced far enoughapart, the random variables{h i} are independent, so the receiver is able to reduce theeffect of fading by combining multiple independently fading signals

In the late 1980s and early 1990s with the growing use of cellular communications,

a desire for a different type of diversity architecture arose, called transmit diversity.

The motivation for developing transmit diversity was the fact that the mobile unit inmost cellular systems is small and, as a result, is often not capable of having multipleantennas As a result, receive diversity on the forward link of cellular systems may not

be possible This led to the desire to find a spatially-based method of creating replicas

of the transmitted signal at a receiver having only one antenna

A little thought shows that this is not trivial For example, if the base station is

assumed to have multiple antennas, and if a signal, s, is simply transmitted from each of

5 0

Combined signal

Figure 1.7 Architecture of a communication system with receive diversity combining

these antennas, then the received signal, r, at the single receive antenna on the mobile

trans-is necessary to perform some type of space-time coding at the transmitter The ture of a system with transmit diversity is depicted in Figure1.8 One simple space-timecode is the Alamouti code, which is used in most MIMO systems today We discuss theAlamouti and other space-time codes in Chapters6and7and show how these schemes

architec-Space-time coding

Combined signal

h1

h2

h N

t

Figure 1.8 Architecture of a communication system with transmit diversity combining

enable diversity combining on the forward link of a cellular system For now, it is cient to introduce the concept and terminology of transmit diversity and to indicate thatspace-time coding is the means by which it is made possible

There are two common metrics that are used to characterize the amount of spatial

diver-sity in a MIMO system They are: diverdiver-sity order and diverdiver-sity gain Diverdiver-sity order, which we will denote by N d, is simply the number of independent replicas of a trans-

mitted signal that are available at the receiver for combining Since an N t × N rMIMO

system has up to N t N r independent paths between the transmitter and the receiver, itfollows that spatial diversity is capable of achieving

Intuitively, we would expect the performance of a communication system to improve

as the diversity order increases To confirm this, Figure1.9shows the theoretical

prob-ability of bit error plotted as a function of average E b /N0 for three different types of

binary modulation in Rayleigh fading, where N d = 1, 2, and 4 These results assumethe use of maximal ratio combining As anticipated, for a given signal-to-noise ratio,

the probability of bit error decreases as N dincreases Furthermore, as we saw earlier inFigure1.5, this plot also demonstrates that as E b /N0becomes large, the curves approachstraight lines, and that the slopes of these lines increase as the diversity order getslarger

A common means of quantifying the benefits of diversity is to use the slope of thecurve obtained by plotting bit error probability on a logarithmic scale versus mean

E b /N0in dB, when E b /N0gets large (i.e., in the region where the curve is linear) The

resulting slope is defined as the diversity gain of the system, which we denote by G d Itfollows that in the linear region, we can express the bit error probability mathematically

as follows:

P b = ζG c (E b /N0)−G d

where ζ is a constant that depends on the type of modulation, G c is a constant,

sometimes called the coding gain of the system, and the bar over E b /N0 denotes themean

Figure 1.9 Performance of binary signals in Rayleigh fading with maximal ratio receive combining for three

different diversity order values

Example 1.1 How to compute the diversity gain: Assume that the bit error probability

is 10−4at E

b /N0= 30 dB and that it is 3.5 × 10−4at E

b /N0= 27.5 dB Assume that

we are in the linear region of the curve What is the diversity gain of this system?

Answer Start by taking 10 log10 of both sides of Eq.1.3 This results in P b[dB] =

10 log10(ζ ) − G d G c[db]− G d(¯ρ[dB]), where we have used ¯ρ to represent E b /N0 fornotational convenience It follows that

P b1 − P b2 = −G d(¯ρ1− ¯ρ2) (1.4)

For the values in this example, P b1 = −40, P b2 = 10 log10(3.5× 10−4) = −34.6,

¯ρ1= 30, and ¯ρ2= 27.5 Therefore, G d = −(−40 + 34.6)/(30 − 27.5) = 2.1.

The two parameters that we have defined for characterizing spatial diversity may appearfundamentally different – one refers to the number of signal replicas being combined

and the other to the slope of the bit error probability versus E /N curve – but it can be

Table 1.2 Parameter values for selected modulation schemes.

Binary, coherent orthogonal 1/2 1/2

shown that they are normally numerically equivalent in a Rayleigh fading environment.Although it is difficult to prove this in the most general case, it can be shown to betrue for specific modulation types when maximal ratio combining (MRC) is used Thissection provides such a proof

We begin with a well-known property of MRC, which states that the signal-to-noiseratio at the combiner output,ρ, is equal to the sum of the SNRs associated with the

individual diversity channels,ρ i , i = 1, , N d[14] That is,

modulation are listed in Table1.2

We next express the complementary error function in the following alternativeform [16]:

erfc(x)= 2

π

π/20exp

⎫

⎬

Assuming Rayleigh fading, it can be shown that the SNR on each diversity channel

is exponentially distributed Therefore, the probability density function (pdf) ofρ i isgiven by

f (ρ i)= 1

¯ρ i

where ¯ρ i is the mean value of the SNR on the ith diversity channel If the diversity

channels are independent, it follows that

¯P b=2α π

π/20

N d



i=1

 ∞0

N d



i=1

 ∞0

where the last step follows from performing simple integration

Since G d is defined in the limit as the signal-to-noise ratio becomes large, we areinterested in examining the expression for ¯P bwhen the average SNR values on each ofthe diversity paths approach infinity (i.e., as ¯ρ i → ∞, i = 1, , N d) For simplicity,

we assume that the average signal-to-noise ratio on each diversity channel is the sameand denote ¯ρ i = ρ ∀i Therefore,

lim

¯ρ→∞ ¯P b(¯ρ) = lim

¯ρ→∞

2α π

π/20

sin2θ



We note that the equation above has the same form as Eq.1.3forζ = 1, where G c

and G dhave the following forms:

said to achieve full diversity when N d = G d = N t N r MIMO systems achieve diversitythrough the use of space-time coding, which we describe in later chapters

1.6 Introduction to spatial multiplexing

The second class of MIMO techniques that we study in this book is called spatialmultiplexing This section provides a brief introduction to that topic

Spatial multiplexing (SM) refers to transmitting multiple data streams over a multipathchannel by exploiting multipath By so doing, multiple data channels are able to betransmitted simultaneously over the same frequency band, enabling potentially largenumbers of bits per second to be transmitted per Hertz of spectrum Spatial multiplexing

is analogous to other more common types of multiplexing schemes such as division multiplexing (FDM) and time-division multiplexing (TDM) In those schemes,multiple signals are assigned to either frequency slots in the case of FDM or time slots

frequency-in TDM In SM, multiple signals are assigned to different spatial channels frequency-instead oftime or frequency slots, so the signals are transmitted at the same time over the samebandwidth As a result, SM does not suffer from bandwidth expansion the way thatTDM and FDM do

Figure1.10shows a high-level block diagram of a SM MIMO system As illustrated,there are three main components to an SM system The first component is referred to in

the diagram as a precoder Its purpose is to map the multiple input streams of data that

are to be transmitted onto the set of transmit antennas The simplest form of precodersimply maps each data stream to a single unique antenna This, of course, can only occurwhen the number of data streams is equal to the number of antennas In general, thenumber of data streams may be less than or equal to the number of transmit antennas Inthe general case, the role of the precoder may be more complex One type of precodingthat we study in Chapter3is called eigenbeamforming In that scheme, the operations

of the precoder depend on the characteristics of the communications channel

The second component of an SM system is the postcoder, which processes the

sig-nals from the receive antennas and generates estimates of the original input data streamsthat originally went into the precoder at the transmitter Since the signal at each receiveantenna consists of the sum of the signals from each of the transmit antennas, the post-coder must be able to, in essence, strip off each data stream from the composite receivedsignal There are various ways to do this, which are discussed in detail in Chapter8

1

2

Data streams

Up to

min{Nt, Nr}

data streams

Received data streams

Figure 1.10 Generic diagram of a MIMO communication system that uses spatial multiplexing

The third component of an SM system is the communications channel itself In orderfor spatial multiplexing to work, the channel must have a significant amount of multi-path scattering This may seem odd since multipath is normally regarded as the enemy

by communications engineers since it degrades the performance of conventional munication systems However, since spatial multiplexing exploits multipath, its presence

com-is necessary for SM techniques to work In Chapter3, we discuss the concept of nel rank and show why it is used to characterize the scattering richness of a multipath

chan-channel

The spatial multiplexing literature uses a variety of different terms to describe thedata signals that are able to be transmitted at the same time over an SM MIMO system

Terms such as data streams, data pipes, and spatial channels are common terms used

to describe these data signals, and they mean the same thing In addition, when beamforming is used, the data signals that are transmitted in parallel are often called

eigen-eigen-channels It can be shown that the maximum number of data streams, Nstream, thatcan be supported by a MIMO system using spatial multiplexing is given by

Nstream= min (N t , N r ) (1.15)

This equation shows that for an N × N MIMO system, the throughput increases

lin-early with the number of antennas Since the increase in the number of data streamsdoes not require a wider bandwidth, this equation shows that the spectral efficiency

of a MIMO system also increases linearly with the number of antennas Figure1.11

shows the theoretical average communications capacity (in bits-per-second-per-Hertz)1

in Rayleigh fading plotted as a function of the number of antennas (when N t = N r) fordifferent signal-to-noise ratios,ρ This plot illustrates the linear dependence of the aver-

age capacity on the number of antennas, which is one of the key properties that has ledthe wireless industry to enthusiastically adopt MIMO techniques in its modern wirelessstandards These results show that even at modest SNR values, it is theoretically possi-ble to achieve spectral efficiencies of 15 to 30 bps/Hz It is evident from this plot that

the capacity is proportional to the number of antennas, i.e., C(N) = a(ρ)N; where, a is

the slope of the curve, which is a function ofρ It follows that the capacity of an N × N MIMO system, CMIMO(N), is N times the capacity of a SISO system That is,

It should be emphasized that these results are theoretical and assume ideal scattering

in the channel In practice, maximum spectral efficiencies are significantly lower thanthese values due to the combination of implementation limitations and the presence

of ill-conditioned channels (which we define in Chapter 3) Nevertheless, the utility

of the theoretical results in Figure1.11, like any theoretical communication capacitypredictions, is that they show what can be achieved in the ideal limit and they provide areference to judge how much room there is for improvement in practical systems

1 Although communication engineers often use the term capacity in such a way that it has units of

bits-per-second, it is also common to define it to have units of bits-per-second-per-Hertz In that case, theoretical capacity is equivalent to theoretical spectral efficiency For this discussion, we have made this assumption and use the terms interchangeably These distinctions are clarified in Chapter 2.

1 2 3 4 5 6 7 8 9 10 0

Figure 1.11 Theoretical capacity of an N × N MIMO communication system in Rayleigh fading.

1.7 Open- and closed-loop MIMO

As we will see, MIMO techniques normally require that either the transmitter or thereceiver have knowledge of the characteristics of the communications channel As such,

MIMO techniques are often classified as either open-loop or closed-loop, depending on

whether the transmitter or the receiver uses knowledge of the communications nel MIMO techniques that require the transmitter to have knowledge of the channelare called closed-loop because they require the receiver to estimate the channel and tosend that information back to the transmitter – hence, requiring a “closed loop” MIMOtechniques that only require the receiver to have knowledge of the channel are calledopen loop These terms are used throughout the MIMO literature and in the wirelessstandards

chan-Table1.3compares the types of MIMO techniques commonly associated with and closed-loop MIMO The first thing to note is that the two basic classes of MIMO:transmit diversity and spatial multiplexing, each have separate open- and closed-loopversions For example, when operating in an open loop manner, transmit diversity isimplemented using space-time coding (STC), of which Alamouti coding is the mostcommon Similarly, an example of open loop spatial multiplexing is the BLAST tech-nique, of which there are several varieties In contrast, when operating in a closed-loop

open-Table 1.3 Comparison of open loop and closed MIMO.

Transmit diversity STC (e.g., Alamouti)

Closed loop

Spatial multiplexing eigenbeamforming

configuration, transmit diversity can be implemented using transmit selection diversity(TSD) and spatial multiplexing can be implemented using eigenbeamforming

TSD is the simplest form of closed-loop transmit diversity where the transmitter

selects one out of N t of its available transmit antennas to transmit information at anygiven instant based on channel information feedback from the receiver In general, thetransmitter will use the antenna associated with the best channel response between itand the receiver TSD was first proposed by J Winters in 1983 [78]

At this point, it sufficient for the reader to have an understanding of the basic tinction between closed and open loop MIMO and to have a growing familiarity withthe names of the various MIMO techniques We will have much more to say about thedetails of these methods in later chapters In this book, we will focus on space-timecoding, BLAST, and eigenbeamforming

dis-1.8 The practical use of MIMO

Having introduced some of the fundamental concepts and terminology in MIMOcommunications, we now briefly consider its implementation in practical wirelesssystems

The first use of MIMO techniques in a cellular system was by Iospan, Inc in 2001 Sincethen, increasing numbers of wireless commercial standards have adopted the use ofMIMO techniques Table1.4lists prominent commercial standards that support MIMOand the maximum antenna configuration that each supports (i.e., all combinations ofantennas less than those listed are supported by the standard) In general, the standardslisted in this table support the following types of multi-antenna techniques:

• Alamouti space-time coding for transmit diversity;

• Eigenbeamforming spatial multiplexing;

• BLAST spatial multiplexing architectures;

• Conventional beam and null forming;

• Conventional receive diversity

Table 1.4 Commercial wireless standards that use MIMO technology.

Wireless standard Antenna configurations

IEEE 802.11n (WiFi) 4× 4

IEEE 802.16e (WiMAX) 4× 4

HSPA+(Enhanced HSPA) 2× 2

This section describes performance measurements that empirically demonstrate theadvantages that MIMO can provide A particularly clear and compelling paper thatdemonstrates the performance benefits of MIMO was presented at the Military Com-

munications Conference (MILCOM) in 2010 by Lai et al [53] In that paper, theypresent results from demonstration tests that were performed to quantify the benefits

of a MIMO communication system called Mobile Networked MIMO (MNM) that wasdeveloped by the Defense Advanced Research Projects Agency (DARPA) for militaryapplications

The MNM MIMO radio tests were conducted at Fort Monmouth, New Jersey and

in Los Angeles, California in various environments including indoor, outdoor, space, and in dense foliage These tests measured the throughput gain of MIMO overSISO configurations and also measured the MIMO transmit power required to achievethe same throughput as a SISO system, thus demonstrating the ability of MIMO toextend battery life in a battery-powered transceiver The MNM radio used in these testsconsists of up to four transmit antennas and four receive antennas, operates at about2.4 and 5 GHz, employs bandwidths ranging from 0.625 to 20 MHz, transmits databetween 1.5 Mbps and 260 Mbps, and employs spatial multiplexing, space-time coding,eigenbeamforming, and receive diversity Table1.5lists the parameters of the MNMradio used in this demonstration

open-Two performance metrics were used in these tests to quantify the performance

improvement due to MIMO One of these metrics, called throughput gain (TPG), is

defined as the ratio of MIMO throughput over SISO throughput, given the same totaltransmit power, spectrum usage, and channel conditions That is,

Table 1.5 MNM MIMO radio system parameter values.

MIMO processing Spatial multiplexing, Space-time coding

Eigenbeamforming, Receive diversity

Number of data streams 1, 2, 3, 4

in the TPS columns These power savings have potentially significant implications for

battery-power transceivers

The results from this study are interesting for two reasons One: they show, asexpected, that MIMO is capable of significantly increasing throughput Two: they showthat MIMO increases throughput by more when operating in a NLOS environmentthan it does in a LOS geometry This can be explained by the fact that LOS condi-tions have less multipath scattering than NLOS geometries Since spatial multiplexing

uses multipath scattering to increase throughput, the lower LOS TPG numbers are

expected Perhaps more interesting, however, is that the throughput increase is as large

as it is in LOS conditions Conventional wisdom has assumed that MIMO would not beeffective in LOS conditions; however, these results suggest the benefits of MIMO may

be realizable in a broader range of conditions than has often been assumed

Table 1.6 Summary of measured MIMO performance improvement

from MNM radio field demonstrations (derived from [53])

LOS transmission NLOS transmission

signals applied to each of the antennas as a vector s = [s1, s2, , s N t]T Similarly,

the signals at multiple receiver antennas can be represented as a receive vector r =

[r1, r2, , r N r]T Furthermore, because there are N t × N rcombinations of transmit andreceive antennas, each of which can be viewed as a separate communication channel,

it is convenient to represent the overall communication channel in a MIMO system

as a matrix with N r × N t elements Using matrices and vectors greatly simplifies themathematics needed to describe the behavior of MIMO systems As a result, in order

to be able to read and understand the MIMO literature, it is necessary to be conversantwith matrix nomenclature and matrix properties

This section lists those definitions and matrix identities that are needed to stand the material in this book and the majority of published papers on MIMOcommunications No attempt is made to prove or elaborate on these properties; thus,this section is intended to be a reference only The reader who wants to delve intomatrix mathematics in greater detail should consult a text on that subject Two excellentreferences on matrices are those by Horn and Johnson [38] and Carl Meyer [54]

under-1.9.1 Basic definitions

(a) Identity matrix An N × N square matrix with all diagonal elements equal to unity

and all other elements equal to zero is called an identity matrix, and is denoted by

scalar A matrix is said to be orthonormal if c= 1

(e) Hermitian operation The Hermitian of a complex, square matrix A is denoted by

(f) Unitary matrix A square matrix U is said to be unitary if UUH = UHU = cI,

c > 0, where c denotes an arbitrary real scalar If c = 1, U is said to normalized

unitary In this book, as well as in most of the MIMO literature, the term unitary implies normalized unitary; hence, c= 1 The definition of unitary is analogous tothe definition for orthogonal,the former applying to complex matrices and the latter

to real matrices

(g) Frobenius norm The norm of a matrix is a generalization of the concept of vector

norm, which, in turn, is the length of a vector Similarly, the norm of a matrix isthe measure in some sense of the “size” of that matrix There are different types

of matrix norms; however, in most of the MIMO literature the Frobenius norm iscommonly used The Frobenius norm is defined in one of two ways We denote the

Frobenius norm of a matrix A using the two nomenclatures below:

k a kvk = 0 is the trivial solution a k = 0 ∀k.

(j) Rank The rank of an m × n matrix A is defined as the largest number of columns or

rows from that matrix that form a linearly independent set The maximum number

of rows is equal to the maximum number of columns We denote the rank of A by

r(A) If m ≤ n, then 1 ≤ r(A) ≤ m Similarly, if m ≥ n, then 1 ≤ r(A) ≤ n.

(k) Singular and non-singular A square matrix A is said to be singular if its nant, det(A) = 0, and is said to be non-singular if det(A) = 0 Since the concept of

determi-determinant is not defined for a non-square matrix, the concept of singularity onlyapplies to square matrices

(l) Eigenvalues and eigenvectors Given a square matrix, A, then the polynomial in the

independent variable s formed by det(sI−A) is called the characteristic polynomial,

and its roots are called the eigenvalues of A Alternatively, the eigenvalues of A are

the values ofλ that satisfy the equation Av = λv for some non-zero vector v The

vector v is said to be an eigenvector of A corresponding to the eigenvaluesλ.

(m) Determinant There are multiple ways to define the determinant of a square matrix.

For the purpose of this book, we define the determinant to be equal to the product

of the eigenvalues of the matrix The following additional comments apply:(1) The determinant is only defined for a square matrix

(2) The determinant of a matrix, A, is denoted either as det(A) or as |A| Both

notations are used in this book

(n) Null space Given an m×n matrix A, the null space of A, which we denote by N(A),

is defined as the set 1× m vectors {x|xA = 0} In other words, N(A) is the set of all

solutions{x} to xA = 0.

(o) Kronecker product Let A be an m × n matrix and B be a p × q matrix It follows

that the Kronecker product, A⊗ B, is the mp × nq block matrix:

(a) For any matrices A and B, (AB)T = BTAT

(b) For any matrices A and B, (AB)∗= A∗B∗.

(c) For any matrices A and B, (AB)H= BHAH

(d) For any square matrices A and B, (AB)−1= B−1A−1.

(e) For any matrices A and B, r(AB) ≤ min {r(A), r(B)}.

(f) The determinant of any identity matrix is 1

(g) Let Aand B denote any two matrices having the same dimensions and a denote any

scalar Then

1

a |A + B| = |A/a + B/a|.

(h) The inverse of any n × n matrix, A, exists if and only if

(1) r(A) = n (i.e., A is full rank); and

(k) Let A denote an m × n matrix Then

(1) a necessary condition for"

AAH#−1

to exist is that n ≥ m; and

(2) a necessary condition for"

AHA#−1

to exist is that m ≥ n.

(l) For any square matrices A and B, it follows that det(AB) = det(A)det(B).

(m) For any square real matrix A, det(AT)= det(A).

(n) For any square complex matrix A, det(AH)= [det(A)]∗.

(o) For any matrix A, AAHand AHA are Hermitian.

(p) Let A be an n × n matrix with eigenvalues {λ i} Then the determinant and trace of

A can be expressed as follows:

(r) Singular value decomposition For any complex m ×n matrix A of rank r, there are

unitary matrices Um ×mand Vn ×nand a diagonal matrix Dr ×r = diag(σ1,σ2, , σ r)such that

where{σ i } are called the singular values of A.

(s) Let A be any complex matrix and denote the singular values of A by{σ i} and the

eigenvalues of AAH(and AHA) by{λ i} Then

σ i=λ i , i = 1, , r(AA H

)

(t) For any Hermitian matrix A with eigenvalues{λ1,λ2, , λ r}, the non-zero singular

values of A,{σ1,σ2, , σ r}, are given by

σ i = |λ i |, i = 1, , r(A).

(u) Eigenvalue decomposition Suppose that A is a Hermitian matrix of

dimen-sion m × m and rank r It follows that there is an m × m diagonal matrix

Dm ×m = diag(λ1,λ2, , λ r, 0, , 0), r ≤ m, and a normalized unitary matrix

U dimensioned [m × m] such that

A = UDUH

,