`
`[
`
`7|!lllLlll\llll||||||l||||||||||||||||||||lIIHLHIIIIHI||||H|
`
`
`
`
`
`

`

`Pulse Code
`Modulation
`Techniques/
`
`with Applications
`in Communications
`
`and Data Recording
`
`Bill Waggener
`
`A Solomon Press Book
`
`VAN NOSTRAND RElHHOLD m
`1®pm A Division of International Thomson Publishing Inc. —
`
`New York 0 Albany 0 Bonn 0 Boston ° Detroit 0 London 0 Madrid ° Melbourne
`Mexico City 0 Paris 0 San Francisco 0 Singapore 0 Tokyo 0 Toronto
`
`

`

`Editing and design: Solomon Press
`
`Copyright © 1995 by Van Nostrand Reinhold
`I®P A division of International Thomson Publishing Inc.
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`
`Printed in the United States of America
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`”.5n“
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`the publisher.
`w
`
`12345678910 HAM 01009998979695
`
`Library of Congress Cataloging-in-Publication Data
`Waggener. Bill.
`Pulse code modulation techniques: with applications in
`communications and data recording I Bill Waggener.
`p.
`cm.
`Includes bibliographical references and index.
`ISBN 0-442-01436-8
`1. Digital communications.
`TK5103.7.W34
`1995
`621 .382—dc20
`
`2. Pulse-code modulation
`
`--.I
`
`:
`
`‘
`
`_;'
`
`-..
`*
`'
`
`~9’
`.-
`‘ ’/-
`
`1. Title.
`
`95-16286
`(JP
`
`1 M.I.T.. LIBRARIES
`
`

`

`Contents
`
`ACKNOWLEDGMENTS
`
`A GUIDED TOUR
`
`CHAPTER 1
`
`INTRODUCTION TO PULSE CODE MODULATION
`
`NYQUEST TO SHANNON
`
`THE PCM LINK MODEL
`
`COMMUNICATIONS CHANNELS
`
`AN OVER VIEW OF THE PCM SYSTEM
`
`DATA ACQUISITION
`
`MULTIPLEXING, FORMATTING AND ENCODING
`
`MODULATION/DEMODULATION
`
`DETECTION AND SYNCHRONIZATION
`
`FORMAT SYNCHRONIZATION AND DEMULTIPLEXING
`
`ERROR DETECTION AND CORRECTION
`
`KEY ISSUES IN PCM
`
`REFERENCES
`
`CHAPTER 2
`
`FUNDAMENTALS OF DIGITAL COMMUNICATION
`
`BACK TO BASICS
`
`LINEAR SYSTEMS
`
`SAMPLED SYSTEMS
`
`PROBABILITY, RANDOM PROCESSES AND NOISE
`
`Properties of Probability Functions
`Probability Density Functions of Interest
`Approximations
`Central Limit Theorem
`
`Principle of Minimum Prejudice
`STOCHASTlC PROCESSES
`
`Power Spectrum
`Response of Linear Systems to Stochastic Signals
`Noise Sources
`
`HYI’OTI—IESIS TESTING AND MAXIMUM LIKELIHOOD
`
`vii
`
`10
`
`13
`
`14
`
`16
`
`17
`
`18
`
`18
`
`20
`
`20
`
`21
`
`21
`
`23
`
`25
`
`26
`
`27
`
`31
`
`33
`
`37
`
`42
`
`

`

`viii
`
`CONTENTS
`
`THE COMMUNICATION MODEL
`
`SIGNAL REPRESENTATION AND DESIGN CONCEPTS
`
`COMMUNICATING OVER NOISY CHANNELS
`
`BASEBAND SIGNALING
`
`MODULATED CARRIER SIGNALING
`
`OPTIMUM DETECTION
`
`MATCHED FILTERS
`
`DETECTION WITH INTERSYMBOL INTERFERENCE
`
`DETECTION IN NON-GAUSSIAN NOISE
`
`OPTIMUM ESTIMATION
`
`MAXIMUM LIKELIHOOD ESTIMATION APPLIED
`
`TO SYNCHRONIZATION
`
`MAXIMUM LIKELIHOOD SEQUENCE ESTIMATION
`
`S UMMAR Y
`
`REFERENCES
`
`CHAPTER 3
`
`CHANNEL CHARACTERISTICS
`
`CHANNEL TRANSFER FUNCTION MODEL
`
`LOWI’ASS AND BANDPASS CHANNELS
`
`A Discrete Channel Model
`
`CHANNEL SIGNAL DISTORTION
`
`Amplitude Distortion
`Ph use Distortion
`
`CABLE CHANNELS
`
`WIRELINE CHANNELS
`
`FIBRE OPTIC CHANNELS
`
`RADIO CHANNELS
`
`FREE SPACE LINKS
`
`MULTIPATH LINKS
`
`RECORDING MEDIA
`
`MAGNETIC RECORDING
`
`OPTICAL RECORDING
`
`OTHER CHANNELS
`
`ACOUSTIC CHANNELS
`
`SUMMARY
`
`REFERENCES
`
`47
`
`51
`
`55
`
`55
`
`56
`
`56
`
`62
`
`63
`
`64
`
`65
`
`65
`
`67
`
`69
`
`71
`
`71
`
`73
`
`78
`
`80
`
`8 1
`
`89
`
`93
`
`93
`
`94
`
`96
`
`96
`
`102
`
`104
`
`104
`
`105
`
`106
`
`

`

`x
`
`CONTENTS
`
`GROUP CODING
`
`ERROR CORRECTING CODING
`Block Codes
`
`Polynomial Addition
`Polynomial Multiplication
`Nonblnary Cyclic Codes
`Convolutional Codes
`
`OPTIMUM DETECTION IN GAUSSIAN NOISE
`
`MATCHED FILTERS AND BINARY SYMBOLS
`
`NYQUIST SIGNALS
`PARTIAL RESPONSE SIGNALS
`
`DETECTION WITH INTERSYMBOL INTERFERENCE
`
`EQUALIZATION
`BIT DECISION FEEDBACK
`
`MAXIMUM LIKELII—IOOD SEQUENCE ESTIMATION
`
`DETECTION IN NON-GAUSSIAN NOISE
`
`AD HOC DETECTORS
`
`OPTIMUM DETECTORS USING APPROXIMATION METHODS
`
`OPTIMUM DETECTION USING
`
`THE GENERALIZED LIKELIHOOD RATIO
`
`MATCHED FILTER DESIGN FOR FUN AND PROFIT
`
`PCM BASEBAND SIGNALS
`
`NRZ Symbols
`RZ Symbols
`BlPhase Symbols
`DM Codes
`
`RESET INTEGRATION IMPLEMENTATION
`
`DIGITAL IMPLEMENTATIONS
`
`SYMBOL DESIGN FOR QUADRATURE MODULATION
`TRELLIS CODE MODULATION
`
`SUMMARY
`
`REFERENCES
`
`CHAPTER 6
`
`SYMBOL SYNCHROI‘IIZATIOH
`
`TIMING EXTRACTION FROM RANDOM SIGNALS
`
`DESIGN APPROACHES
`
`TRANSITION DETECTORS AND TUNED CIRCUITS
`
`PHASE-LOCKED LOOPS
`
`176
`
`176
`
`197
`
`199
`
`210
`
`212
`
`217
`
`218
`
`223
`
`224
`
`23 1
`
`232
`
`233
`
`237
`
`240
`
`240
`
`245
`
`249
`
`254
`
`256
`
`258
`
`259
`
`261
`
`262
`
`265
`
`265
`
`273
`
`

`

`CONTENTS
`
`Acquisition Time
`Loss of Lock
`False Locking
`
`OPTIMUM DESIGN NETHODS
`
`ESTIMATION THEORY
`
`Maximum Likelihood Estimation
`Minimum Likelihood Estimator
`
`Multilevel PAM Signals
`Other Estimators
`
`MINIMUM TIME DESIGN
`
`Adaptive Synchronizers
`
`SYMBOL SYNCHRONIZER PERFORMANCE COMPARISON
`
`SUMMARY
`
`REFERENCES
`
`CHAPTER 7
`
`.
`
`FORMAT SYNCHRONIZATION
`
`FRAME AND WORD SYNCHRONIZATION
`
`SYNCHRONOUS FORMATS
`
`SYNCHRONIZATION PATTERN DETECTION
`
`One-Shot Correlators
`
`Integrating Correlators
`SYNCHRONIZATION STRATEGIES
`
`Search, Check and Lock
`Sequential
`Adaptive
`OPTIMUM FRAME SYNCHRONIZATION
`
`EMBEDDED FORMATS
`
`Synchronous
`Asynchronous Embedded Formats
`ASYNCHRONOUS FORMATS
`
`DISTRIBUTED SYNCHRONIZATION
`
`FRAME S YNCHRONIZER PERFORMANCE
`
`BINARY SYMMETRIC CHANNEL
`
`SYNCHRONIZATION MODEL
`
`ACQUISITION
`
`LOSS OF LOCK
`
`FRAME SYNCHRONIZATION IN NON-GAUSSIAN NOISE
`
`SUMMARY
`
`REFERENCES
`
`xi
`
`285
`
`286
`
`302
`
`306
`
`309
`
`310
`
`313
`
`313
`
`315
`
`316
`
`318
`
`326
`
`328
`
`330
`
`333
`
`339
`
`339
`
`340
`
`341
`
`349
`
`351
`
`352
`
`353
`
`

`

`xii
`
`APPENDIX A
`
`CONTENTS
`
`COMPUTING SYMBOL ERROR PROBABILITY
`
`PCM SYMBOL ERROR PROBABILITY
`
`APPROXIMATING THE COMPLIMENTARY ERROR FUNCTION
`
`SYMBOL ERROR PROBABILITY WITH INTERSYMBOL INTERFERENCE
`
`REFERENCES
`
`APPENDIX B
`
`MAXIMUM LIKELIHOOD SEQUENCE ESTIMATION
`
`THE PROBLEM
`
`KEY CONCEPTS
`
`STATE SEQUENCE ESTIMATION
`
`MLSE PERFORMANCE
`
`REFERENCES
`
`INDEX
`
`355
`
`355
`
`356
`
`357
`
`358
`
`359
`
`359
`
`360
`
`362
`
`363
`
`363
`
`365
`
`

`

`
`
`Introduction to Pulse
`Code Modulation
`
`
`
`The idea of communicating information from one place to an-
`other by the presence, or absence, of pulses is quite old with
`many historical examples. Pulse code modulation (PCM) embod-
`ies the basic concepts of transmitting a sequence of symbols, i.e.,
`pulses, to represent information. Examples of early PCM systems are illus-
`trated in Figure 1.1. In the telegraph system, for example, messages were
`transmitted from one station to the other as pulses of current with two widths,
`“dots” and "dashes," with groups of pulses representing letters of the al-
`phabet.
`Pulse code modulation applies two basic concepts; time-division multi-
`plexing (TDM) and amplitude quantization. Continuously varying signals are
`sampled and quantized into discrete symbols for transmission. At the receiv-
`ing end, the symbols are recovered and the original signal is recovered. Early
`theoretical work by Nyquistl'2 established the principles of sampling while
`the work of Shannon3 and others‘”5 laid the foundation for communication
`
`theory which revealed the advantages of PCM communication.
`The practical beginning of PCM technology can probably be dated back
`to the late 1940’s and work performed at Bell Laboratories on PCM telephony
`systems.6'7'8 Since then, PCM has been applied to a variety of applications.
`This book is directed toward the underlying technologies of PCM including
`symbol encoding, symbol detection, symbol synchronization, format syn-
`chronization, modulation, demodulation, error detection and correction. Ap-
`plications are taken from telecommunications, telemetry and magnetic re-
`cording.
`A variety of applications such as telecommunications, telemetry and
`data storage share a common PCM technology. A number of data communi-
`
`7
`
`

`

`8
`
`INTRODUCTION TO PULSE CODE MODULATION
`
`“ma-2»«we
`
`‘ «9
`”We’re”
`
`Is that a
`"1 1 01...‘ or
`a "1 10 0...“ ?
`
`4'
`
`sis-9....a‘nxv
`.w...:.:.:r;.-;.";;.‘:
`
`..
`
`FIGURE 1.1 Early Pulse CodeModulation systems
`
`cations applications share both the common PCM technology and communi-
`cation media as illustrated in Figure 1.2. Telemetry applications, for example,
`tend to be a one-way communication between many data sources and one
`data sink. Telecommunications, on the other hand, deals with two-way com-
`munications between many sources and many sinks. When looked at in this
`fashion, it becomes obvious that one major distinction between the telemetry
`and telecommunication applications is an emphasis on switching technology
`in a telecommunication system. Indeed, many telecommunications organiza-
`
`
`Data Communlcatlons
`
`
`
`
`
`Telemetry I “"3232?“
`Telecommunicatlone
` Cable Links
`
` FIGURE 1 .2
`
`,
`Fiber Opllc
`
`W'r"
`
`Surface-to-
`Surface
`
`Surface-to-
`Alt
`
`communicatons
`hierarchy
`
`The data
`
`10
`
`

`

`Nyquist to Shannon
`
`9
`
`tions and technical references divide telecommunications into transmission
`and switching.
`In the telemetry system, although there may be many users of the data,
`the data is usually combined and gathered at one location. Although switch-
`ing and data distribution is implicit in most telemetry systems, the switching
`aspects are not a major focus of the system.
`The transmission aspects of the telecommunication and telemetry sys-
`tems clearly overlap using common communication technologies. The emer-
`gence of PCM as the dominant communication technology brings the two
`applications even closer as techniques developed in the larger telecommuni-
`cations market find application in the more specialized telemetry market.
`Within the last decade, data storage applications have used PCM tech-
`nology for recording data on both magnetic and optical media. Indeed, data
`recording applications have been fertile areas for new developments in PCM
`symbol encoding and the use of complex error correction techniques.
`The trend toward the use of PCM is pervasive, being driven by the rapidly
`advancing semiconductor technology and the principles of efficient commu-
`nications. There are many facets to PCM communication and the emphasis
`placed in this book are on those aspects which are prime determinants of
`overall system performance. As a consequence of this philosophy, a consider-
`able amount of attention is paid to the problems of synchronizing and detect-
`ing PCM signals in the presence of noise and interference. At the same time,
`more pragmatic issues must also be addressed such as the efficient use of
`allocated bandwidth and ease of implementation.
`A measure of the technology trend in PCM systems is shown in Figure
`1.3, showing the composite data rate of a variety of PCM systems over the
`past several decades. The trend line for PCM telemetry systems parallels the
`trend of PCM telecommunication systems increasing approximately an order
`of magnitude per decade. The ever increasing rates are driven by increasing
`numbers of data channels in both the telemetry and telecommunication areas
`as well as increasing sampling rates for wider bandwidth signals. This trend
`
`BitRateinMbps
`
`1960
`
`1965
`
`1970
`
`1975
`Year
`
`1980
`
`1985
`
`1990
`
`Figure 1.3 PCM Data Rate Trend.
`
`11
`
`

`

`10
`INTRODUCTION TO PULSE CODE MODULATION
`is expected to continue unabated. Limitations on communication bandwidth
`are placing severe constraints on the ability to achieve the higher rates and
`are driving the PCM technology to more efficient signaling methods as well
`as toward fiber optic and wideband satellite communication channels.
`It is impossible to cover all of the aspects of PCM in a single book without
`being superficial. I have elected to concentrate on key areas associated with
`the generation, transmission, synchronization and detection of PCM. At the
`risk of offending the mathematical purists, I use a ”mathematics of modest
`rigor" approach, preferring to leave detailed proofs and developments to
`more specialized texts. Many excellent texts"'1"'11'12 devoted to statistical
`communications and specialized topics are available for the reader wishing
`to pursue in depth more advanced topics.
`
`NYQUIST TO SHANNON
`
`Many of the key aspects to a PCM system can be identified by looking
`at a simplistic example shown in Figure 1.4. A signal source producing a
`continuous time waveform is sampled and each sample quantized into a dis-
`crete number of levels by an analog-to-digital converter (ADC). Typically, the
`number of levels is a power of Z and a given sample can be represented by a
`set of binary digits, i.e., “bits,” such that:
`
`L = 2'"
`
`[1.1]
`
`where m = the number of bits and L = the number of levels in the sample.
`Each sample can be considered to be a "word" and the individual bits
`in a word are sequentially transmitted from the data source via a transmission
`channel to the data sink, or user. The user identifies the bits in each word,
`reconstructs the word, and, if desired, converts the digital word back to analog
`form using a digital-to-analog converter (DAC).
`In the telecommunications world, the data source could be the output
`of a caller’s telephone and the data sink could be the telephone of the person
`being called or it could be one computer on a local area network (LAN) send-
`
`Time-Division
`
`lfififiu
`
`
`
`Other Channels
`
`m-blt word
`
`
`
`
`Analog-
`
`to-Dlgltal
`Convener
`
`
`
`
`SamplesOther Channe :
`
`
`
`llme
`
`time
`
`FIGURE 1.4
`
`Typical PCM data
`acqulslllon system
`
`12
`
`

`

`Nyquist to Shannon
`
`11
`
`mg files to another computer on another network. In the telemetry world,
`the data source could be the output of a strain gage and the data sink could
`be a strip chart display. In either case, once the signal has been sampled,
`other signals could be interleaved and transmitted with the original signal
`provided the transmission bandwidth will allow it. This is called multiplexing
`and the interleaving of samples in time leads to the notion of a time-division
`multiplexed (TDM) system.
`Sampling is obviously a key feature of the PCM system. What sampling
`rate must be used for a given signal? The sampling theorem answers that
`question; the sampling rate must be at least twice the highest frequency of
`the input signal. If, in our example, the signal is bandlimited to 4 kilohertz,
`a minimum sampling rate of 8 kilosamples per second would be required.
`This is typical of a voice channel in a telecommunication channel. If the
`same signal sample is quantized to 8 bits (28 = 128 levels), the PCM bit rate
`would be 64 kilobits per second (8 bits per sample times 8 kilosamples per
`second).
`
`f—E—fi
`
`Bits per Second, Symbols per Second and Bauds
`
`Information rate is normally expressed in “bits per second” where a bit
`represents a binary choice, i.e., the information Is either a “one" or a
`“zero." When the binary information is transmitted over a
`communication channel, one, or more, bits are encoded into “symbols”
`which are transmitted and the transmission rate is expressed in terms of
`“symbols per second." The unit “baud” is used interchangeably with
`symbol rate. it is incorrect to refer to “baud rate" since baud is defined
`as a measure of rate. Note that symbol rate ls only equal to bit rate
`when only one bit is represented by a symbol. It Is not uncommon for a
`transmission symbol to represent several bits. For example, a 4800 bit
`per second data modem typically transmits at 1200 baud, or 1200
`symbols per second, each symbol representing 4 bits of information.
`
`The quantization of the sample clearly limits the resolution of each sam-
`ple to 2"" of the maximum sample amplitude. While this is a consideration
`in the design of the overall system, this book will assume the data sources
`are encoded bit streams without regard for the individual data sampling rates
`or quantizations.
`In order to appreciate some of the rationale for the use of PCM, compare
`the direct transmission of the signal in the presence of noise with transmis-
`sion using PCM. Suppose the quantization of a signal sample is chosen to be
`comparable to the transmission channel signal-to- noise ratio so that
`
`If the signal is sampled at the minimum rate, the PCM bit rate is then
`
`SNR = 2'"
`
`Rb = ZmB
`
`[1.2]
`
`[1.3]
`
`where B = signal bandwidth in Hertz, m = number of quantization bits,
`and Rb = PCM bit rate in bits per second.
`
`13
`
`

`

`12
`
`INTRODUCTION TO PULSE CODE MODUIATIOH
`
`Intuitively, the PCM transmission bandwidth must be about 2m greater
`than the signal bandwidth in order to transmit the PCM bits with minimum
`distortion. Noise increases with the square root of the bandwidth so that the
`PCM signal-to-noise ratio (SNR) would be less than the direct transmission
`SNR by a factor of V(2m). However, the PCM signal is composed only of
`binary pulses and the receiver need only decide if a “one” or a ”zero" was
`transmitted. The SNR needed for a reliable decision is relatively small, typi-
`cally about 4: 1 is sufficient. If 8 bit quantization were used, a direct transmis-
`sion channel SNR of greater than 100:1 would be required to maintain the
`8 bit signal precision. Using PCM, a bandwidth increase of about 16:1 would
`be required, increasing the transmission noise by about 4 : 1, however, a chan-
`nel SNR of only 4:1 or 5:1 would be required. Thus, the PCM transmission
`would require about a 20:1 SNR defined in a bandwidth equal to the signal
`bandwidth for the PCM system compared to over 100:1 SNR for direct trans-
`mission. Thus PCM has exchanged bandwidth for signal-to-noise ratio, a fun-
`damental principle established by Shannon.
`The sampling theorem establishes the minimum permissible rate re-
`quired to sample a bandlimited signal. Conversely, Nyquist established the
`maximum signaling rate required for a bandlimited channel. Nyquist proves
`that signaling at a rate of twice the bandwidth of a bandlimited channel
`is possible without intersymbol interference (that is, energy from adjacent
`symbols overlapping). Nyquist further proved that the channel does not have
`to have "brickwall" bandlimiting to be free from intersymbol interference.
`Nyquist signaling will be an important concept in the analysis and design of
`the PCM system.
`In 1959, CE. Shannon13 published a key development in communica-
`tions theory in which he proposed a theoretical bound for communication
`over a noisy analog channel. Shannon developed the channel capacity
`bound:
`
`0 = Wlog2(1 + SNR)
`
`[1.4]
`
`where C = the channel capacity in bits per second, W = the channel band—
`width in Hertz, and SNR = the channel signal-to-noise ratio.
`Shannon's bound is very interesting because it asserts that there exist
`coding schemes which will allow the channel capacity to be reached with
`arbitrarily small error rate. Further, the theorem suggests that capacity
`can be traded for signal-to-noise ratio. Shannon's channel capacity theorem
`and the implicit trade-off between bandwidth and required signal-to-noise
`ratio will provide a valuable performance bound for comparing the perfor-
`mance of PCM systems. In Chapter 2 we will take a detailed look at Shannon’s
`results and the implications to PCM systems.
`
`r—————__———_——_—fi
`
`Signal-to-Noise Ratio
`
`Signal-to-noise ratio, or SNR, may be defined in a number of ways.
`Typically, SNR is defined as ratio of signal power to noise power fora
`given bandwidth, W. The noise power depends on the type of noise and
`
`14
`
`

`

`The PCM Link Model
`
`13
`
`'how it is measured. It the noise is “white” (that is. has a uniform
`distribution of power with frequency) the noise power is:
`
`m=mw
`
`where N0 = the noise spectral density. a constant, and W = the
`equivalent noise bandwidth.
`If the equivalent noise bandwidth is expressed in terms of the
`symbol rate, SNR is frequently expressed in terms of the symbol
`energy-to-noise spectral density:
`
`
`SNR — N0 k
`
`with, k = the ratio of the noise equivalent bandwidth to the symbol
`
`rate.
`K———E_J
`
`THE PCM LINK MODEL
`
`A generalized PCM system can be represented as shown in Figure 1.5.
`An information source produces a sequence of information bits which are
`then encoded into channel symbols. The channel symbols, in turn, modulate
`a transmitter. The transmitted signal is propagated over a communication
`channel which may distort the signal and add noise. The receiver must re-
`cover the channel symbol sequence from the modulated signal. In order to
`recover the symbols, timing information must be extracted (synchronization)
`and symbol decisions (detection) made on the noisy signal. Finally, the re-
`covered symbols are mapped back into information bits. In the practical PCM
`system, information sources may be multiplexed into a composite PCM
`stream. The composite data stream may have a complex format which must
`be demultiplexed at the receiving end.
`A major effort has been expended over the last ten years, or so, defining
`
`
`
`Iniorrnatlon
`
`
` Transmitter
`Source
`
`Channel
`
` Comrmnlcatlons
`
`
`S Sgnboll
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`'0" 29'
`Y"
`
`
`FIGURE 1.5
`General PCM system
`block diagram
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`
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`15
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`

`14
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`Application
`Services
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`
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`
`
`
`
`m
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`End-lo
`End
`Services
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`INTRODUCTION TO PULSE CODE MODULATION
`
`
`
`
`
`
`
`
`
`FIGURE 1.6
`08! reference model
`
`communication protocol standards for data links and, specifically, local area
`networks. The Open Network Interconnect (081) standard describes commu-
`nication systems in terms of a seven layer protocol "stack" as shown in Figure
`1.6. The bottom of the stack is the physical layer (PHY) which is responsible
`for the electrical (or optical) interface to the communications media. The
`next higher layer in the stack, the Data Link Layer (DLL), is responsible for
`the transmission, framing (formatting) and error control. The Network Layer
`(NL) is responsible for network data transfer independent of the type of media
`and the network topology. The Transport Layer (TL) is responsible for reliabil-
`ity and multiplexing of data transfer over the network. These four layers are
`normally provided by the data service provider. The three layers above these
`are typically associated with the applications.
`In 081, the services provided by a layer are either connection-oriented
`or connection-less. A connection-oriented service establishes a connection
`between source and destination using a calling method. Connection-less ser-
`vices have only one mode, data transfer. Routing of data from source to desti-
`nation must take place within the data transfer itself. Many data services are
`based on the 051 model although considerable liberty is taken with regard
`to the number, names and functions of the protocol stack. One view of the
`protocol stack is that it provides a logical “block diagram” of the system.
`Each layer sends and receives information from the layers above and below
`it. This book deals with the lowest levels in the data communications hier-
`archy - the physical layer which deals with the intimate details of the PCM
`signaling and reconstruction and, to a limited extent, the Data Link Layer
`which deals with the format and framing of data.
`
`COMMUNICATION CHANNELS
`
`PCM systems use a variety of communication channels ranging from
`radio systems to fiber optic cable systems. Each communication media has
`
`16
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`

`

`Communications Channels
`
`15
`
`it’s own set of unique characteristics and the PCM system must be tailored
`to the link characteristics. Radio systems tend to be limited by noise, interfer-
`ence and multipath propagation distortion and signal-to-noise efficient com-
`munication techniques are essential. Systems using cable communications
`are typically limited by insufficient bandwidth and require techniques which
`maximize signaling efficiency. The recording media in a PCM data storage
`system may be regarded as a specialized communications channel requiring
`unique PCM symbol encoding methods.
`Regardless of the type of media, the communications channel can, nor-
`mally, be represented by a combination of an equivalent filter with an addi-
`tive noise source as shown in Figure 1.7. In some cases, this simplistic model
`is inadequate and a more complex model must include nonlinear effects and
`multiplicative noise sources, as well as the additive, noise sources. For the
`purposes of this book, the simpler model will suffice. Communication system
`simulation programs”15 are now available which permit the simulation of
`more complex link models, if required.
`Radio links are used in both telemetry and telecommunication systems.
`In many practical applications, radio telemetry links are used between a
`ground station and an airborne vehicle operating at significant ranges from
`the receiving site. Under these conditions, radio energy is reflected from the
`ground as well as traveling by a direct path causing a form of distortion known
`as "multipath.” Transmission power is frequently limited and radio telemetry
`links operate with small communication link margins. Detection and syn-
`chronization performance is crucial for these applications.
`Telecommunication systems use radio links both for ground microwave
`links and for satellite communication (SATCOM) systems. Although greater
`system signal-to-noise ratios are attainable in these systems through the use
`of higher signal power and more conservative design practices, fading and
`interfering signals are also cause for concern in the areas of detection and
`synchronization.
`The use of wire cable for communications is, probably, still the major
`means of communications for telecommunication networks. Fiber optic ca-
`bles are replacing both wire cable and microwave systems and will likely
`become the primary communication link for the telecommunication net-
`works in the 1990s and beyond.
`
`Noise
`
`
`
`
`
`"(0
`
`Equivalent
`Channel
`Response
`
`PCM
`Input
`
`FIGURE 1.7
`Communlcatlon
`channel model
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`17
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`16
`
`INTRODUCTION TO PULSE CODE MODULATION
`The primary limitation of cables, either wire or fiber optic, is the signal
`distortion created by the transmission line behavior in which signals of differ-
`ing frequencies are propagated with slightly differing velocities. This effect
`can be, at least partially, compensated by equalization networks. The distor-
`tion introduced by a cable communication system causes energy from one
`symbol to be spread over adjacent symbols causing "intersymbol interfer-
`ence.” The intersymbol interference degrades system performance by reduc-
`ing the symbol decision margin in the PCM receiver. Equalization techniques
`which reduce, or eliminate, intersymbol interference also tend to accentuate
`system noise, thereby making the system more sensitive to noise. Once again,
`detection and synchronization are key system functions. Since the character-
`istics of the typical cable communication channel change with time and net-
`work connection, equalization techniques should be adaptive to gain the
`greatest performance benefit. Although equalization is extremely important,
`the subject is complex and is left to several excellent books”17 which are
`devoted entirely to the subject. In this book, the effects of the equalizer on
`time (or frequency) domain performance and on equivalent noise are in-
`cluded in the equivalent communication link model.
`
`AN OVERVIEW OF THE PCM SYSTEM
`
`The typical PCM system is shown in Figure 1.8. The system begins with
`a data acquisition subsystem which acquires data from one, or more, sensors,
`samples, multiplexes and digitizes the signals. The digital data may then be
`multiplexed with other digital data and synchronization markers are embed-
`ded in the composite digital signal to permit proper data recovery. The digital
`data stream is serialized and fed to a symbol encoder which replaces one or
`
`MUX - multiplexer
`
`
`
`<- —————————————
`
`Communlcotion Link
`
`
`Receiver and
`De modulator
`
`Symbol
`Synchronizor
`
`Format
`Synchronizor
`
`
`
`and Detector
`
`
`FIGURE 1.8 Typical PCM system with a radio communication link
`
`18
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`

`

`An Overview of the PCM System
`
`17
`
`more data stream bits with a symbol for transmission. Depending on the type
`of channel, the symbol stream may also modulate a carrier to translate the
`signal to a different frequency band. The baseband or modulated signal is
`then transmitted over the communication channel.
`At the receiving end, the signal must be demodulated to recover the
`serial stream of symbols. The symbols must be detected to recover the original
`data bits and appropriate timing clocks must be extracted, both for optimum
`symbol detection and for format synchronization. The format synchroniza-
`tion process includes locating and synchronizing the embedded synchroniza-
`tion markers and establishing the position of the data words in the bit stream.
`Decommutation, or demultiplexing, is then required to split the data stream
`back into individual data channels corresponding to each individual sensor.
`In the telecommunications system, the individual sensors may corre-
`spond to individual telephones. At the lowest level, 24 voice channels are
`digitized and multiplexed to form a single PCM data stream. The digital voice
`channels are multiplexed with data streams from other data sources. In addi-
`tion to digitized voice, the telecommunications network now provides a vari-
`ety of data services ranging from X.25 packet data to broadband multimedia
`information over ATM services. In the telemetry system, a wide variety of
`sensors may be used to measure everything from temperature to stress. The
`composite serial PCM data stream may contain hundreds or thousands of
`data channels.
`
`In addition to the basic functions described, the PCM system may in-
`clude error correcting coding and data encryption. As technology permits,
`the digitization of sensor data is moving toward sensors with digital outputs
`so that all multiplexing is performed digitally.
`
`Data Acquisition
`
`The PCM system begins with the acquisition of data which can take
`many forms. Traditionally, the telecommunication system handles voice and
`low rate data sources, although video and higher rate data are increasingly
`important. The sampling rates for data sources in the telecommunication
`system are typically limited to a relatively small range. Voice channels are
`sampled at 8 kilosamples per second with a nominal quantization of 8 bits
`resulting in each voice channel requiring 64 kilobits per second. Voice
`compression techniques reduce the rate per channel but the composite multi-
`plex rate is usually kept constant, increasing the number of channels per
`multiplex. Similarly data in the telecommunication network is acquired in
`multiples of 75 baud ranging up to 56 kilobaud.
`The telemetry system acquires data from a wide variety of sensors and
`sources ranging from individual sensors to data from aircraft buses. Whereas
`the telemetry instrumentation engineer, at one time had complete control
`over the sensor sampling rates, the PCM telemetry system must now contend
`with asynchronous data from on-board data buses and computers.
`In general, the data acquisition process consists of signal conditioning
`electronics, analog and digital multiplexers, and the analog-to-digital con-
`
`19
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`

`

`INTRODUCTION TO PULSE CODE MODULATION
`18
`verter (ADC). The signal conditioning electronics are responsible for convert-
`ing the wide variety of sensor and transducer outputs to a common electrical
`level. Analog signals are multiplexed and digitized using the ADC and com-
`bined with other digital signals to form the composite PCM signal.
`The data acquisition subsystem is generally the domain of the instru-
`mentation engineer who worries about things such as signal conditioning
`drift and noise, aliasing error and quantization errors. While these are all
`worth worrying about, this book will leave those topics to others and begin
`our story of PCM with the multiplexer.
`
`Multiplexing, Formatting and Encoding
`The PCM story really begins to get interesting when the individual data
`streams are multiplexed. While the multiplexing of the input signals may
`appear to be quite straight forward on the system block diagram, in fact, the
`multiplexing process can be quite complex. In multiplexing and sampling of
`the data, the sampling rate per sensor must be at least twice the highest signal
`frequency (Nyquist's theorem) in order to prevent the distortion known as
`aliasing. If the sensors all have an equal bandwidth, such as the voice channels
`in a telephone system, the multiplexing scheme is nearly trivial. On the other
`hand, if a system has a number of different sensors with widely va