Introductionto Digital

Transmission

What is digital communication? How did it come about? Why did it come about?The answers to these questions are the motivation for this book.

Modern telecommunication is the confluence of three great trends over the lasttwo centuries: first, the invention of an electromagnetic signaling technology in theform of the telegraph, the telephone, and radio; second, the development of a scien-tific and mathematical theory that made these inventions practical and efficient; andfinally, the advent of microcircuitry, the "chip," which made these inventions small,fast, reliable, and very cheap.

To these must be added an intangible that has no explanation and is perhapssimply an absolute: the need of people to communicate with each other. Time andagain this urge has financed a new communication service, whether it be telegraphingacross London in the nineteenth century or cellular telephones in the 1990s. Anaxiom of investing said that American Telephone and Telegraph was always agood investment: When times are good, all stocks go up; when times are bad, peoplecall each other and complain. There is no shortage of clever inventions, but only afew fields—transport and health care come to mind—attract the investment andeager public support that communication does. This fact is the economic basis fordigital communication.

We start with some history and then turn to the question of why analog hasgiven way to digital communication. The plan of the book concludes the chapter.

1.1 SOME HISTORY AND SOME THEMES

Some major events in the long and fascinating history of electrical communicationare listed in Table 1.1. A listing of dates can be misleading, since trends and inven-tions are most often born in confusion and in many places at once. For this reason,

1

Introduction to Digital Transmission • Chapter 1

TABLE 1.1 Important Milestones in History of Digital Communication

Year Event

ca. 1820 Oersted shows electric currents create magnetic fields1830-1840 Henry discovers induction; Faraday and others show changing magnetic fields produce electric

fields1834-1842 Various telegraphs demonstrated1844 Morse commercial telegraph, Baltimore to Washington1864 Maxwell publishes his theory of electromagnetism1866 First permanent transatlantic telegraph1860-1876 Various telephone demonstrations by Bell and others1878 First telephone exchange installed by Bell, Brantford, Canada1887 Experiments by Hertz verify Maxwell1894-1898 Marconi and others demonstrate radio over significant distances1901 First transatlantic radio message by Marconi, United Kingdom to Canada1904, 1906 Fleming announces diode tube; DeForest announces triode1907 Fessenden transmits speech 320 kmca. 1918 Armstrong devises superheterodyne receiver1920 First modern radio broadcast by KDKA, Pittsburgh, PAca. 1925 Mechanical TV system demonstrations by Baird, London1928 Gaussian thermal noise papers of Johnson and Nyquist1929 Zworykin demonstrates electronic TV systemca. 1933 Armstrong devises FM1936 Commercial TV broadcasting by British Broadcasting Company, Londonca. 1940 First use of radarca. 1945 Matched filter devised, for radar1945-1950 Early computers constructed; proofs of sampling theorem appear; signal space theory applied to

communication1948 Transistor demonstrated by Brattain, Bardeen, and Schockley, United States; Shannon publishes

his theory of information1950-1955 Beginnings of computer software; beginnings of microwave long-haul transmission1953 First transatlantic telephone cableca. 1958 Matched filter applied to communication; first chips demonstratedca. 1960 Error-correcting codes begin rapid developmentca. 1960 Laser announced, United States,ca. 1965 Communication satellites using active transponders; long-distance communication to space

probes begins1967 Forney proposes the trellis; Viterbi proposes his algorithm1970 Low-loss optical fibers demonstrated1970-1975 Microprocessors appear; large-scale integrated circuits appear; speech and image digitization

begins rapid developmentca. 1976 Bandwidth-efficient coded modulations begin to appear; digital telephone trunks first installed1979 Images received from Jupiterca. 1980 Digital optical fiber telephone trunks begin to be installed1985-1990 Cellular mobile telephones become widespread in Europeca. 1990 Use of the Internet accelerates1992 First digital mobile telephone system, GSM, begins in Europe

Note: Most dates are approximate.

2

Section 1.1 • Some History and Some Themes 3

many dates must be approximate, and it is especially difficult to define recent in-novations. Some innovations, such as the writing of what we now call softwarealgorithms, evolved only slowly over time. A particularly readable study of thishistory, its less tangible side, and its human consequences has been published byI. Lebow [1].

A reason to study history is to identify its trends, which lead to the structure ofthe present day. We will look now at the table and see what it says about trends indigital communication. Parts of the following will be obvious to those with somebackground, but we discuss them to avoid a greater danger, which is that we miss thesubtleties among the commonplace.

Communication as we know it today began in the nineteenth century. It isinteresting that except for light fibers, the electromagnetic transmission technologiesthat we use today, namely radio and wireline telegraph and telephone, all appearedin the nineteenth century. So also did the scientific understanding of electricity andelectromagnetism, without which the inventions would have made little sense. Thecontribution of the twentieth century was of another, no less important character.Radio found immediate use on board ships, but at first it was not at all the channel-ized medium that we use today. A major contribution to the Titanic disaster of 1912was the fact that all radio operators used the same spectrum space. Since the Titanichad the strongest transmitter, and constantly used it, other nearby operators wereoverwhelmed and shut down their radio sets. Consequently, the early distress signalsfrom the sinking ship went unheard.

Here arises a theme that plays a major role in the book, the fact that radiotransmission uses a carrier. It is often said that only by conversion to electromagneticform can an audio signal be made strong enough for transmission. This may havebeen true in 1912, but kilowatt audio "transmitters," in the form of car stereos, areall too common today. The critical point is rather that electromagnetic transmissioncan be translated in spectrum, by shifting its carrier, to whatever frequency is mostconvenient. For communication with submarines, the physics of salt water implythat the best frequencies lie almost in the audio range. Efficient antennas here arehundreds of kilometers long, and so any radio service subject to ordinary economicsuses a much higher frequency. Transmissions that need to follow Earth for a fewhundred kilometers need medium-wave frequencies (these terms are defined in Table1.2); for a few thousand kilometers they need short-wave frequencies, and spacecommunication must take place in the micro- and millimeter-wave spectrum. Allthis derives from physical laws, and some concept of translation by carrier is whatmakes radio work. A second important reason for carrier transmission was drama-tized by the Titanic. Now many users can share the same spectrum if each is trans-lated by a different carrier.

Considerable technology had to be invented before the idea of narrowbandradio, which we take for granted today, became practical. New transmitters weredeveloped that radiated a true amplitude-modulated (AM) signal. Receivers thatcould effectively reject all but one narrow frequency range had to await the intro-duction of Armstrong's superheterodyne concept in the 1920s.

Another invention by Armstrong in the 1930s, frequency modulation (FM),was the first inkling of another major theme in electromagnetic communication: thebandwidth and energy trade-off. Armstrong found that FM had a better signal-to-noise ratio at the same transmitter power than AM, apparently in proportion to its

4 Introduction to Digital Transmission • Chapter 1

TABLE 1.2 Frequency Bands in Radio Spectrum

Frequency Band Band Name Comments

< 100 kHz Extra low frequency (ELF) Submarine communication100-500 kHz Low frequency (LF) Follows Earth surface500-3000 kHz Medium wave (MW) AM broadcasting; follows Earth with

loss3-30 MHz High frequency (HF)* Reflected by ionosphere30-300 MHz Very high frequency (VHF) TV and FM broadcasting300-1000 MHz Ultrahigh frequency (UHF) Mobile radio1-10 GHz Microwave Wideband links, Earth and space10-100 GHz Millimeter wave Space links> 200,000 GHz Infrared Optical fiber links

*Also called short wave.

bandwidth expansion. Armstrong found it frustrating to convince his colleagues ofthis fact, but today we know that the same trade-off appears in many other places.The pulse-code-modulated (PCM) digitization of speech, for example, essentiallyfreezes its signal-to-noise ratio, no matter how many retransmissions it passesthrough, but PCM also increases the transmission bandwidth.

An even more radical idea was to appear in Shannon's 1948 paper, "AMathematical Theory of Communication." Shannon showed that error could notonly be traded for bandwidth but could in principle be reduced to zero by the use ofcoded signals. In a parallel development during the 1940s and 1950s, Kotelnikov,Shannon, Wiener, and others developed a new theory of optimal communication, atheory that worked best with symbolic, or "digital," transmission.

These latter ideas involved all sorts of complex processing and coding, andwere it not for another evolving trend, they would have remained for the most part acuriosity. This was the idea of written processing algorithms on the one hand andever cheaper hardware to run them with on the other. An algorithm is a step-by-stepprocedure to attain an end. Some algorithms, like long division, are ancient, but amajor change in the algorithm concept took place in the mid-twentieth century. Withthe ideas of von Neumann and the perfecting of computer languages and the storedprogram computer, algorithms took a mighty jump upward in complexity. What hasevolved today is a technology in which various functions in a system can all bestandard processor chips, each taking its function from the algorithm loaded intoit. It seems likely that the algorithm concept will continue to evolve beyond thesequential programs that dominate today, but the 1950s concept has been morethan enough to implement the new theory of communication.

Everyone knows the story of the large-scale integrated circuit, one of the majortechnology drivers of the last 30 years. It is perhaps worth reviewing how revolu-tionary the chip really is. A single vacuum tube active circuit element in the 1950scost about five 1990 U.S. dollars. Transistor technology soon reduced this costmanifold and at the same time made the element more efficient and reliable. Butthe technique of photolithography and successive waves of miniaturization were tocome, until the cost of this single device had dropped a millionfold and more.Further drops are still to come. It is interesting to imagine what would happen ifsome other part of the economy, say the cost of energy or of cars, were to drop this

Section 1.2 • Why Digital? 5

much. The upheaval would be hard to imagine and hard to plan for. Just such arevolution is in progress in communication, because it is based on a key commodity,processing, whose price has collapsed. What is cheap today is the processor chip—auniversal computing machine—whose function is set by an algorithm. Consider thedetector, a part of every receiver. With Fleming's 1904 diode, a great advance in itstime, a detector was a vacuum tube that cost at least $100. By the 1950s, a detectorwas a vastly more reliable and cheaper solid state diode. By the 1970s, this detector,and considerably more sophisticated ones, was a part of a larger integrated circuitchip. Today the detector and much of the rest of the radio can be a processor chip onwhich runs a stored program, whose identity as a "radio" can be changed at will.

What has happened here is a move away from communication as the study ofphysics and devices and toward algorithms, information as symbols, and complexprocessing. Just as energy and bandwidth were found to trade off, now we see athree-way trade-off, among energy, bandwidth, and processing complexity. Anincrease in any one means the other two can be reduced, more or less, for thesame performance. A PCM digitizer can be replaced by a more complex digitizer,which puts out fewer bits, which consume less transmission bandwidth. Shannon'sconcept of coded communication, which originally was a mathematical theory, nowhas a practical meaning: Transmission error may be driven down by more complexcoding, which in effect reduces transmission energy. With modern coded modula-tion, coding complexity can even be exchanged for bandwidth. The cheapest of thesethree is now processor complexity. Digital communication is so full of concepts,processes, algorithms, and complexity because this is the route to lower cost.

Although the processor revolution dominates our story, it should not be for-gotten that many analog components have seen large cost declines. Perhaps the mostsignificant of these is the optical fiber and its codevice, the laser. The much lower per-bit transmission cost of fibers is probably driving us to a two-choice world, in whichfixed channels of any length are fibers and mobile channels are radio. Aside fromfiber technology, radio frequency (RF) components have been miniaturized andreduced in cost, a prime example being the analog RF chips in cellular telephones.Still, digital processor technology is steadily working its way toward the front ofradios and eliminating more and more of the RF technology.

While the book takes its structure from these evolving trends, we should admitin closing that predicting the future and its cousin, characterizing the present, arehazardous, even pointless exercises. One needs to learn with caution and prepare forthe unexpected. Historians of technology tell us that a major innovation is not feltcompletely for 50 years, and if so, it is chastening to look at Fig. 1.1 and realize howmuch of it is not yet 50 years old.

1.2 WHY DIGITAL?

Why indeed is communication more and more digitally based? When the stereo shopsays its products are digital ready for digital quality, is this an advertising slogan, oris digital really better? Let us look at the slogans and the reality and see why thisrevolution is really occurring. There are many solid reasons, and we have listed themin rough order of importance.

Data source

Introduction to Digital Transmission • Chapter 1

Data sink

Figure 1.1 Plan of a communication link (and plan of the book).

1. Cheap hardware. First and foremost, digital hardware has become verycheap, as we have just stressed. This makes all the other advantages cheap to buy.

2. New services. We live in an age of e-mail, airline booking systems, computermodems, and electronic banking. Whereas voice and images are originally analogand may be transmitted either way, all these newer services are fundamentally digitaland must be transmitted symbolically. Whether or not there is a new thirst for databy the human psyche is debatable, but it is clear that widely distributed enterprisesand the "virtual workplace" and telephones that work "anytime, anywhere" are keyto the way many of us choose to live. These new ways of life are more difficult toimagine in an analog world.

3. Control of quality; error control. Here the digital story becomes more subtle.For high-quality music and television, digital format is not necessarily better per se.It is easily demonstrated that any reasonable frequency response, signal-to-noiseratio, and dynamic range may be achieved by analog recording and broadcasting.Where the digital format has a major advantage is in systems that are a chain ofmany transmission links. These systems appear in many places, and two importantones are worth summarizing here. First, long-distance voice channels are usuallychains of many repeaters. In former times, the links were microwave and nowadaysthey are more likely fiber-optic, but in either case a transcontinental channel canrequire 50-100 links. We will see in the chapters that follow that with analog linksthe noises add, while with digital links the symbol error probabilities add. What thismeans is that a given signal-to-noise ratio over 100 analog links requires a ratio ineach link that is 101og10100, or 20 dB, better; we will see that an error probability pover 100 digital links instead of just 1 needs only 1-2 dB more energy in each. "Fiber-optic quality," as the advertising slogan calls it, is not so much a matter of fibers butrather a matter of digital transmission by whatever means when there are repeaters.

A second, perhaps more subtle example of a repeater chain is music recording.Now the chain is a microphone, amplifiers, mixing, more mixing, conversion to amedium, storage, conversion back, amplification, and speakers. While this is not a

6

Source/channelencoding

C-6

ModulatorC-2,3

ChannelC-5

DemodulatorC-2, 3, 7

Source/channeldecoding

C-6

Phase synchronization& symbol synchronization

C-4

Network synchronization& control

C-4

Section 1.3 • Contents of This Book 7

sequence of similar links, there are still many troublesome points where distortioncan enter. Again, digital signal handling has a major advantage. Once a quality isagreed upon and set in the initial analog-to-digital conversion, the digital chain canbe designed to carry the music essentially error free to the speaker.

4. Compatibility and flexibility. Once signals are digitized, it is possible, at leastin principle, to think about transmitting them all by a similar shared medium.Network functions such as switching and multiplexing are much easier. New net-work topologies and modes of multiple access become possible. Control and servi-cing information can be combined with revenue-producing signals. All sorts offeatures, from telephone voice mail to disc-player music search, become economic.

5. Cost of transmission. In certain channels, the cost of digital transmission canbe less. We have already seen this in the channel with repeaters. Another case wheredigital transmission wins is a channel with very low power, such as the deep-spacechannel. Since AM schemes cannot have better signal-to-noise ratios than the under-lying channel, a bandwidth-expanding modulation such as FM is necessary at theleast. This is the energy-bandwidth trade-off. Another alternative is digital transmis-sion combined with coding: This is trading energy for both complexity and band-width. Communication theory shows, in fact, that the most effective use of a weakchannel is binary modulation combined with coding. Yet another case where digitalmodulation can win is a channel with a lot of nearby interferers, such as happens incellular radio.

6. Message security. With the growth of mobile telephony, message securityhas attracted more attention. Older mobile systems are analog FM, which has littlesecurity. Analog encryption is fundamentally difficult, but the encryption of symbolsis just as fundamentally not difficult.

1.3 CONTENTS OF THIS BOOK

Figure 1.1 shows the overall plan of a digital communication link, and this is theplan of the book as well. To make the plan a little more concrete, the rough para-meters of some common data sources are given in Table 1.3. These sources play a

TABLE 1.3 Parameters of Some Representative Digital Signal Sources

Signal Source

PacketVoice, simpleVoice, complex codingPhone modem

Phone trunk

Video, simpleVideo, complex coding

Analog Bandwidth

4 kHz4 kHz3.4 kHz

100 kHz

4.5 MHz4.5 MHz

Bits

50-1000b64kb/s4-6kb/s2.4^28.8 kb/s

1.5Mb/s

>40Mb/s< 1 Mb/s

Comments

Not real time; retransmission allowedPCM telephoneLatest cellular speech codingQuadrature amplitude modulation

(QAM)Lowest level line concentrator; 24 one-

way linesPCM videoAdvanced coding; real time

Introduction to Digital Transmission • Chapter 1

role in the examples of the succeeding chapters. Some additional orientation can beobtained from the spectral bands in Table 1.2.

The core of a transmission link is of course its transmitter and receiver. It isconvenient to break that subject down into baseband signaling, which has no carrier,and passband, or RF, signaling, which works with a carrier. The baseband case ispresented in Chapter 2, and here we introduce the ideas of pulse forming, modula-tion by linear superposition of pulses, modulation spectrum, and modulation prob-ability of error. The last is derived via an elegant and general method called signalspace theory, a method that is one of the major achievements of communicationtheory. Chapter 3 is the extension to carrier transmission. The ideas of pulse super-position, spectrum, and error probability extend easily to the RF case; another thrustof the chapter is the parts that are unique to carrier transmission: nonlinear modula-tions like frequency-shift keying and distortions that occur in RF signaling.

Signals must pass through a channel medium. Some of the many channel typesare simple wires, coaxial cables, free space, the terrestrial surface and atmosphere,and optical fibers. Each has its own character and distortions, and these are allcollected in Chapter 5. The chapter also provides the opportunity to study a parti-cularly important and challenging medium, the fading mobile channel.

Probably the most underrated area in transmission design is synchronization.Little time is spent in most books on this subject, yet synchronization of varioustypes probably consumes half of transmission design effort. In reality there areseveral layers to the synchronization of a system: An RF system needs receivercarrier synchronization, all systems need to identify the symbol boundaries, andmost data transmissions have a frame structure that needs identifying. As well, theentire network needs to stay in synchronization. All of this is in Chapter 4. Inaddition, the chapter is a good place to introduce some of the physical side ofnetworks.

Chapters 2-5 are the core of the book. There are a great many allied topics topursue, and space allows presenting only two of these. Error correction coding and abrief introduction to information theory form Chapter 6. Some advanced receiversfor distorted and fading channels make up Chapter 7.

Communication engineering goes much further, and indeed it is a constantchallenge for the working engineer to keep up with developments. For example,digital signal processing and software play an important role in modern systemdesign; the areas of speech and of image processing are fields in their own right. Afield that evolves especially rapidly is communication devices and electronics and RFengineering. Unfortunately, it is hard to find courses—and consequently engineers—in these fields. For those with a theoretical bent, communication theory, detectiontheory, and information and coding theory are fascinating subjects. Further topicsthat are usually taught as separate subjects are antennas, cryptography, and com-munication networking.

The prerequisites for this book are good courses in probability and transformand linear system theory and some introduction to analog communication.Stochastic process theory has been kept to a minimum in order to make the bookmore accessible, but this and other advanced disciplines are sometimes referred to inthe text as a guide for the more advanced reader.

Some useful notation for the rest of the book as well as some further insightinto communication electronics is given in Fig. 1.2. This figure defines the parts of a

8

Section 1.3 • Contents of This Book

Data

Notation

Figure 1.2 Simplified transmitter and superheterodyne receiver, showing notationused in practice and throughout this book. Not all parts are present inall systems.

standard transmitter and superheterodyne receiver. The last, devised by E. Armstrongbefore 1920, is the basis of almost all receivers and is one of the great inventions ofelectrical engineering. The receiver begins with a roughly tuned amplifier, the low-noise amplifier (LNA), which is designed for moderate gain at the lowest possiblenoise contribution (for more, see Section 5.2); the LNA sets the noise level in thereceiver. Next comes a mixer, whose purpose is to move all signals from their loca-tion in the RF spectrum to a single spectrum location, called the intermediate fre-quency, or IF. The IF amplifier and bandpass filters illustrated in Fig. 1.2 achieve

9

Antenna

RF IF

Mixer

Baseband

DecoderDemodulator

O)g nT

Wordsynchronizer

Receiver

Synchronizer

Narrow High-gainBPF amplifier

LNAWideBPF

LO-Rx

Baseband RF

Mixer

Exciter PA NarrowBPF

ModulatorEncoderData

Transmitter LO-Tx

Amplifier Bandpass filter (BPF)

Low-pass filter (BPF)

Mixer

PA Power amplifierLNA Low-noise amplifier

Oscillator

LO Local oscillatorIF Intermediate frequencyRF Radio frequency

10 Introduction to Digital Transmission • Chapter 1

two purposes. They hugely amplify the signal to a level suitable for detection, andthey strongly reject all neighboring signals, thus setting the narrow-bandpass char-acteristic of the receiver (a property called its "selectivity"). The genius in this circuitis subtle to appreciate because it lies buried in the lore of circuit design. The goals oflow noise, tunability, gain, and selectivity in circuit design all mildly contradict:Somehow, they should be accomplished in separate, single-purpose circuits.Armstrong was one of the first to appreciate this fact about the circuitry and topropose a solution.

The top of Fig. 1.2 shows the superheterodyne, the remaining detector syn-chronizer and decoder subsystems, and also defines some common names and sym-bols in communication circuitry. These will be used on and off throughout the book.The electronic design of tuned amplifiers and such blocks as mixers is explainedelsewhere, for example Refs. [2] and [3].

The remainder of the figure shows a simplified transmitter design and somerelevant acronyms and notation. Not all transmitters follow this chain: Many lack anexciter and of course many feed fibers or wires rather than antennas.

1.4 THE COMPUTER PROGRAMS

A major aid, both for learning and for later practice of engineering, is some sort ofcomputing engine, especially one with a vector capability. Perhaps the most commonsuch software tool at this writing is MATLAB, but there are several others. Forconcreteness, MATLAB is used in this book. As the book progresses, shortMATLAB routines are given for the special calculations that arise in each subject.These are called programs. The programs and routines for such basic operations asconvolution and the fast Fourier transform (FFT) also play a role in many of thehomework problems.

Software tools are related to the pervasive shift in communication engineeringtoward software-based signal processing and away from hardware circuitry.Filtering, for example, is increasingly time-domain convolution instead of analoghardware. The programs and related homeworks help keep a focus on this shift.

Rather than include the programs on a disk at the back of the book, we havekept them short and simply written them out. This brevity is made possible by thevector nature of MATLAB. The fact is that disks-in-the-back seldom work the firsttime: The reader's platform is wrong, the tool version is wrong, the disk is incom-patible, and so on. Murphy's law is against us here. We believe it is easier for thereader to copy out the short programs as need be, making the necessary modifica-tions. Inexpensive student editions of MATLAB are widely available.*

Experience shows that significant time must be set aside to learn these softwaretools. Not only are there the usual problems with the computer system, but many ofus lack practice with such underlying techniques as sampling, convolution, andnumerical analysis. The problem is not limited to the readers of this book but affects

f MATLAB is a trademark of The Math Works, Inc. Further information is available from TheMath Works, Inc., Cochituate Place, 24 Prime Park Way, Natick, MA 01760. The simplest availableversions of such tools are recommended.

References 11

all communication engineers. Time needs to be set aside for these techniques, inaddition to that needed for studying digital communication.

In closing, we offer some more general words of encouragement. Digital com-munication is a subtle subject, but it contains only a few methods and relatively fewcentral lessons that with a little care and patience can be discerned and mastered.This book has been designed to make that process easier. Here, as in engineering ingeneral, cleverness is not so important as resourcefulness and dedication to the job.The book is not encyclopedic and it leaves out many smaller topics, so that the largerlessons can be more often repeated. Digital communication also has its engineeringlore, its experience aspect, and we have included some of this along the way. Thereward for studying this book is entry into a fascinating subject that is welcome andthriving everywhere in the world.

REFERENCES

[1] I. Lebow, Information Highways and Byways, IEEE Press, New York, 1995.[2] K. K. Clarke and D. T. Hess, Communication Circuits: Analysis and Design,

Addison-Wesley, Reading, MA, 1971.[3] H. L. Krauss, C. W. Bostian, and F. H. Raab, Solid State Radio Engineering,

Wiley, New York, 1980.