B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

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6.4 DIGITAL MULTIPLEXING6.4 Digital Multiplexing 285Several low-bit-rate signals can be multiplexed, or combined, to form one high-bit-rate signal,to be transmitted over a high-frequency medium. Because the medium is time-shared by variousincoming signals, this is a case of TDM (time division multiplexing). The signals from variousincoming channels, or tributaries, may be as diverse as a digitized voice signal (PCM), acomputer output, telemetry data, and a digital facsimile. The bit rates of various tributariesneed not be the same.To begin with, consider the case of all tributaries with identical bit rates. Multiplexing canbe done on a bit-by-bit basis (known as bit or digit interleaving) as shown in Fig. 6.22a, or on aword-by-word basis (known as byte or word interleaving). Figure 6.22b shows the interleavingof words, formed by four bits. The North American digital hierarchy uses bit interleaving(except at the lowest level), where bits are taken one at a time from the various signals to bemultiplexed. Byte interleaving, used in building the DS 1 signal and SONET-formatted signals,involves inserting bytes in succession from the channels to be multiplexed.The Tl carrier, discussed in Sec. 6.3, uses eight-bit word interleaving. When the bit ratesof incoming channels are not identical, the high-bit-rate channel is allocated proportionatelymore slots. Four-channel multiplexing consists of three channels B, C, and D of identical bitrate R and one channel ( channel A) with a bit rate of 3R. (Fig. 6.22c,d). Similar results can beattained by combining words of different lengths. It is evident that the minimum length of themultiplex frame must be a multiple of the lowest common multiple of the incoming channelbit rates, and, hence, this type of scheme is practical only when some fairly simple relationshipexists among these rates. The case of completely asynchronous channels is discussedlater.At the receiving terminal, the incoming digit stream must be divided and distributed to theappropriate output channel. For this purpose, the receiving terminal must be able to correctlyidentify each bit. This requires the receiving system to uniquely synchronize in time with thebeginning of each frame, with each slot in a frame, and with each bit within a slot. This isaccomplished by adding framing and synchronization bits to the data bits. These bits are partof the so-called overhead bits.6.4.1 Signal FormatFigure 6.23 illustrates a typical format, that of the DMl/2 multiplexer. We have here bit-by-bitinterleaving of four channels each at a rate of 1.544 Mbit/s. The main frame (multiframe)consists of four subframes. Each subframe has six overhead bits: for example the subframe1 (first line in Fig. 6.23) has overhead bits Mo, CA, Fo, CA, CA, and F1 . In between theseoverhead bits are 48 interleaved data bits from the four channels (12 data bits from eachchannel). We begin with overhead bit Mo, followed by 48 multiplexed data bits, then adda second overhead bit CA followed by the next 48 multiplexed bits, and so on. Thus, thereare a total of 48 x 6 x 4 = 1152 data bits and 6 x 4 = 24 overhead bits making a total1176 bits/frame. The efficiency is 1152/1 176 98%. The overhead bits with subscript 0are always O and those with subscript 1 are always 1. Thus, Mo, Fo are all Os and M1 andF1 are all ls. The F digits are periodic 010101 . .. and provide the main framing pattern,which the multiplexer uses to synchronize on the frame. After locking onto this pattern, thedemultiplexer searches for the 0111 pattern formed by overhead bits MoM 1 M 1 M 1 . This furtheridentifies the four subframes, each corresponding to a line in Fig. 6.23. It is possible, althoughunlikely, that signal bits will also have a pattern 101010 . ... The receiver could lock onto this
286 SAMPLING AND ANALOG-TO-DIGITAL CONVERSIONFigure 6.22Time divisionmultiplexing ofdigital signals:(a) digitinterleaving;(b) word (or byte)interleaving;(c) interleavingchannel havingdifferent bit rate;(d) alternatescheme for (c).ChannelA n n nn n nB CD D D DD D DD□ --- - ln nChannelA n n □n noB 0D, f,I/( /\-------{JL __ I,--1(b)/( /\non □ n\, / D n D n DD DC n--"---r A, B , A, c, A, D, A. B, A, c, A0 D,D0A DD DD DDB Dn(c)D0(d)
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INTERNATIONAL FOURTH EDITIONModern
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Oxford University Press, Inc., publ
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CONTENTSPREFACE xvii1INTRODUCTION1
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Contents1x3 .6 SIGNAL DISTORTION OV
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7PRINCIPLES OF DIGITAL DATATRANSMIS
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Contentsxiii1 0.3 COHERENT RECEIVER
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Contentsxv13.3 ERROR-FREE COMMUNICA
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PREFACE (INTERNATIONALEDITION)The c
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Preface (International Edition)xixM
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Preface (International Edition)xx,m
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l INTRODUCTIONOver the past decade,
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1 . 1 Communication Systems 3Figure
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1 .2 Analog and Di gital Messag es
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l .2 Analog and Digital Messages 7H
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1 .3 Channel Effect, Signal-to-Nois
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1 .4 Modulation and Detection 11In
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1.5 Digital Source Coding and Error
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1.6 A Brief Historical Review of Mo
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1.6 A Brief Historical Review of Mo
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References 19to transmit the tones
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2.1 Size of a Signal 21Figure 2.1Ex
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2.2 Classification of Signals 233.
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2.2 Classification of Signals 25Fig
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2.3 Unit Impulse Signal 27Figure 2.
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2.4 Signals Versus Vectors 29Fi gur
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2 .4 Signals Versus Vectors 31andf/
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2.4 Signals Versus Vectors 33functi
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2 .5 Correlation of Signals 35Thus,
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2.6 Orthogonal Signal Set 37orthogo
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2 .7 The Exponential Fourier Series
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2 .7 The Exponential Fourier Series
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2.7 The Exponential Fourier Series
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2.7 The Exponential Fourier Series
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2.8 MATLAB Exercises 47Basic Signal
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2.8 MATLAB Exercises 49% (file name
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2.8 MATLAB Exercises 51subplot (231
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2.8 MATLAB Exercises53Figure 2.22Ex
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Problems 55Figure P.2. 1-2x(t)y(t):
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Problems 57Figure P.2.3-3g(t)t -han
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Problems 592.5-1 Find the correlati
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Problems 61(b) Determine the odd an
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3 .1 Aperiodic Signal Representatio
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3.1 Aperiodic Signal Representation
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3 .1 Aperiodic Signal Representatio
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3.2 Transforms of Some Useful Funct
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3.3 Some Properties of the Fourier
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3 .3 .5 Frequency-Shifting Property
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3 .3 Some Properties of the Fourier
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Here D n = I/To. Therefore, from Eq
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TABLE 3.2Properties of Fourier Tran
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3.4 Signal Transmission Through a L
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3.5 Ideal versus Practical Filters
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3.6 Signal Distortion Over a Commun
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3 .7 Signal Energy and Energy Spect
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Figure 3.32Interpretation ofthe ene
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3.7 Signal Energy and Energy Spectr
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3.7 Signal Energy and Energy Spectr
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3.8 Signal Power and Power Spectral
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3.9 Numerical Computation of Fourie
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3.9 Numerical Computation of Fourie
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3.10 MATLAB Exercises 123Using the
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3 . 10 MATLAB Exercises 125In this
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3. 10 MATLAB Exercises 127Observe t
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3.10 MATLAB Exercises 129We multipl
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This is the trigonometric form of t
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3.3-2 The Fourier transform of the
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Problems 1353.3-7 Use the frequency
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Problems 137(b) Discuss how this ch
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Problems 139the autocorrelation fun
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4.1 Baseband Ve rsus Carrier Commun
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4.2 Double-Sideband Amplitude Modul
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4.3 Amplitude Modulation (AM) 151Th
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4.3 Amplitude Modulation (AM) 153Fi
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4.3 Amplitude Modulation (AM) 155In
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4.3 Amplitude Modulation (AM) 157Fi
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either utilize or remove the 100% s
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4.4 Bandwidth-Efficient Amplitude M
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4.5 Amplitude Modulations: Vestigia
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4.5 Amplitude Modulations: Vestigia
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4.6 Local Carrier Synchronization 1
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4.8 Phase-locked Loop and Some Appl
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4. 9 MATLAB Exercises 181whereE(t)
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4. 9 MATLAB Exercises 183Fi g ure 4
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4. 9 MATLAB Exercises 185s_dem=s_ds
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4. 9 MATLAB Exercises187Figure 4.35
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4.9 MATLAB Exercises189Figure 4.36
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4. 9 MATLAB Exercises 191subplot (2
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Figure 4.41Frequencydomain signalsd
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title ('second demodulator output '
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Problems 1974.2-5 You are asked to
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Problems 1994.3-3 For the AM signal
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Problems 201Figure P.4.4·6'PL5B (t
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5.1 Nonlinear Modulation 203the AM
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Figure 5.2Phase andfrequencymodulat
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5.1 Nonlinear Modulation 207Dividin
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5.2 Bandwidth of Angle-Modulated Wa
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Alternately, the deviation ratio f3
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5.3 Generating FM Waves 223Figure 5
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5.3 Generating FM Waves 225Indirect
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5.3 Generating FM Waves 227Amplitud
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5.3 Generating FM Waves 229We may a
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5.4 Demodulation of FM Signals 23 1
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5.4 Demodulation of FM Signals 233B
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Page 262 and 263: 5.6 Superheterodyne Analog AM/FM Re
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Page 266 and 267: 5.8 MATLAB Exercises 243Figure 5.19
Page 268 and 269: 5.8 MATLAB Exercises 245title ('PM
Page 270 and 271: Problems 2476. H. R. Slotten, '"Rai
Page 272 and 273: Problems 249Figure P.5.4-15.4-1 (a)
Page 274 and 275: 6SAMPLING ANDANALOG-TO-DIGITALCONVE
Page 276 and 277: 6. 1 Sampling Theorem 253by nfs . T
Page 278 and 279: 6.1 Sampling Theorem 255identical t
Page 280 and 281: 6. 1 Sampling Theorem 257Figure 6.5
Page 282 and 283: 6.1 Sampling Theorem 259Figure 6.7S
Page 284 and 285: 6. 1 Sampling Theorem 261known as s
Page 286 and 287: 6.1 Sampling Theorem 263Figure 6.9(
Page 288 and 289: 6. l Sampling Theorem 265whereq T s
Page 290 and 291: 6.1 Sampling Theorem 267Moreover, t
Page 292 and 293: 6.2 Pulse Code Modulation (PCM) 269
Page 296 and 297: 6.2 Pulse Code Modulation {PCM) 273
Page 304 and 305: 6.3 Digital Telephony: PCM in Tl Ca
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Page 310 and 311: 6.4 Digital Multiplexing 287Figure
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Page 314 and 315: 6.5 Differential Pulse Code Modulat
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Page 318 and 319: 6.7 Delta Modulation 295deploy. Unl
Page 320 and 321: 6.7 Delta Modulation 297Figure 6.31
Page 322 and 323: 6.7 Delta Modulation 299Figure 6.32
Page 324 and 325: 6.8 Vocoders and Video Compression
Page 334 and 335: 6.9 MATLAB Exercises 31 1Fi gure 6.
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Page 344 and 345: PROBLEMSFigure P.6. 1 - 1Problems 3
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Page 348 and 349: Problems 325the transmission bandwi
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Page 352 and 353: 7.2 Line Coding 329Figure 7.3An on-
Page 354 and 355: 7.2 Line Coding 33 1in Fig. 7 .4b,
Page 356 and 357: 7.2 Line Coding 333and from Eq. (7.
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7.2 Line Coding 335Moreover, both G
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7.2 Line Coding 337Figure 7.7Split-
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7.2 Line Coding 339Fi gure 7.8Power
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7.2 Line Coding 341Figure 7.9PSD of
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7.3 Pulse Shaping 343Binary with N
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7.3 Pulse Shaping 345to be positive
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7.3 Pulse Shaping 347Fi g ure 7. 13
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7.3 Pulse Shaping 349the case of th
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TABLE 7. 1Transmitted Bits and the
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7.3 Pulse Shaping 353In fact, many
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7.4 Scrambling 355TABLE 7.2Binary D
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7.4 Scrambling 357Figure 7.20 shows
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Figure 7.21Regenerativerepeater.7.5
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7 .5 Digital Receivers and Regenera
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7.5 Digital Receivers and Regenerat
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7.5 Digital Receivers and Regenerat
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7.6 Eye Diagrams: An Important Tool
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7.7 Pam: M-Ary Baseband Signaling f
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7.7 Pam: M-Ary Baseband Signaling f
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Figure 7.30(a) The carriercos Wet.
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where 'VT (f) is the Fourier transf
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7.8 Digital Carrier Systems 377we c
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7. 8 Digital Carrier Systems 379Fi
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7.9 MAry Digital Carrier Modulation
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7.9 M-Ary Digital Carrier Modulatio
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7.9 M-Ary Digital Carrier Modulatio
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7. l O MATLAB Exercises 387The firs
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Problems 389(a) Assuming half-width
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Problems 39 1sequence T is applied
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8FUNDAMENTALS OFPROBABILITY THEORYT
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8.1 Concept of Probability 395Figur
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8.1 Concept of Probability 397Exam
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8.1 Concept of Probability 399Let t
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8.1 Concept of Probability 401But t
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8.1 Concept of Probability 403Hence
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8.1 Concept of Probability 405Figur
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8.1 Concept of Probability 407IP(F
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8.2 Random Va riables 409Figure 8.5
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8 .2 Random Variables 41 1Similarly
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8.2 Random Variables 413Because x :
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8.2 Random Va riables 415From Eq. (
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8.2 Random Variables 417This integr
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8.2 Random Variables 419TABLE 8.2Co
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8.2 Random Va riables 421Figure 8.1
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8.2 Random Variables 423Figure 8.13
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8.2 Random Va riables 425Independen
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8.3 Statistical Averages (Means) 42
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8.4 Correlation 437RVs x and y. We
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8.4 Correlation 439Thus, if x and y
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Since by definition xy = R x y and
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8.6 Sum of Random Va riables 443Fig
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Upon carrying out this convolution
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8.7 Central Limit Theorem 447is kno
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PROBLEMSProblems4498.1-1 A card is
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Problems 45 18.1-16 In a binary com
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Problems 453where M = ab - c 2 . Sh
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Problems 4558.6-3 If x(t) and y(t)
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9. 1 From Random Va riable to Rando
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9. 1 From Random Va riable to Rando
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9 .2 Classification of Random Proce
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Because pe(0) = 1/2n over (0, 2n) a
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9 .3 Power Spectral Density 465resp
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9.3 Power Spectral Density 467Figur
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9.3 Power Spectral Density 469It is
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9.3 Power Spectral Density 471Hence
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9.3 Power Spectral Density 473where
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9.3 Power Spectral Density 475Recal
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In each case we shall first determi
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9.4 MULTIPLE RANDOM PROCESSES9 .4 M
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9.5 Transmission of Random Processe
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9.6 Application: Optimum Filtering
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9.6 Application: Optimum Filtering
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9.7 Application: Performance Analys
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9.8 Application: Optimum Preemphasi
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9.9 Bandpass Random Processes 491an
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9.9 Bandpass Random Processes 493Th
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It follows from this equation and f
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9.9 Bandpass Random Processes 497Ba
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References 499Figure 9.26Rican PDF.
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Problems 5019.2-1 For each of the f
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Problems 503by first finding its tr
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Problems 5059.8-1A white process of
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10.1 Optimum Linear Detector for Bi
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10. 1 Optimum Linear Detector for B
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10.1 Optimum Linear Detector for Bi
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10.2 General Binary Signaling 513Fi
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10.2 General Binary Signaling 515Th
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10.2 General Binary Signaling 517Fi
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Additionally, substituting q(t) = 0
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where the pulse energy is simplyl 0
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To compute P b from Eq. (10.25b), w
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10.4 Signal Space Analysis of Optim
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10.5 Vector Decomposition of White
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10.6 Optimum Receiver for White Gau
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l 0.6 Optimum Receiver for White Ga
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Figure 10.21Determiningoptimumdecis
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(M - 2) symbols. Hence,10.6 Optimum
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10.7 General Expression for Error P
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10.8 Equivalent Signal Sets 569and
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10.8 Equivalent Signal Sets 571Assu
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10.8 Equivalent Signal Sets 573Obse
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10.8 Equivalent Signal Sets 575As a
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10. 9 Nonwhite (Colored) Channel No
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l 0. 10 Other Useful Performance Cr
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10.1 1 Noncoherent Detection 581err
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10.1 1 Noncoherent Detection 583Bec
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10.1 1 Noncoherent Detection 585Fig
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10.1 1 Noncoherent Detection 587Sub
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Figure 10.42Error probability P Pof
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l 0.12 MATLAB Exercises 591yrect=xr
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Figure 1 0.45Power spectraldensity
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10.12 MATLAB Exercises 595set (figw
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10.12 MATLAB Exercises 597Figure 1
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10.12 MATLAB Exercises 601noiseq=ra
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Problems 603legend ('Analytical BER
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Problems 605where Am sin wet is the
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10.4-4 For the three basis signals
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FigureP. 10.6·5r--a• "v • •s
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Problems 61 110. 7-1 The vertices o
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Problems 613Hint: Use Gram-Schmidt
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11 . 1 Frequency Hopping Spread Spe
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11.1 Frequency Hopping Spread Spect
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11 .2 Multiple FHSS User Systems an
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l l .3 APPLICATIONS OF FHSS11 .3 Ap
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11.3 Applications of FHSS 623To com
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l l .4 Direct Sequence Spread Spect
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11 .4 Direct Sequence Spread Spectr
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11 .5 Resilient Features of DSSS 62
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11.6 Code Division Multiple-Access
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11 .6 Code Division Multiple-Access
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11 .6 Code Division Multiple-Access
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11 .7 Multiuser Detection (MUD) 637
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11. 8 Modern Practical DSSS CDMA Sy
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l l .8 Modern Practical DSSS CDMA S
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11.8 Modern Practical DSSS CDMA Sys
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11. 8 Modern Practical DSSS CDMA Sy
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11 . 9 MATLAB Exercises 651Figure 1
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11 . 9 MATLAB Exercises 653% can be
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11.9 MATLAB Exercises 655% Add jamm
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11.9 MATLAB Exercises 657The first
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11.9 MATLAB Exercises 659y_out=x_in
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11 . 9 MATLAB Exercises 661Eb2N_num
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References 663awgnois=signois*noise
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Problems 665(a) Find the probabilit
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12.1 Linear Distortions of Wireless
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12.1 Linear Distortions of Wireless
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12.2 Receiver Channel Equalization
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12.3 Linear T-Spaced Equalization (
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Minimum MSE and Optimum DelayBecaus
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12.4 Linear Fractionally Spaced Equ
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12.4 Linear Fractionally Spaced Equ
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12.6 Decision Feedback Equalizer 68
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12.6 Decision Feedback Equalizer 69
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12.7 OFDM (Multicarrier) Communicat
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h[0] h[l] h[L] 0 012.7 OFDM (Multic
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X __!:_ [ :Nl1H[O]H[O]=N __!:_ :H[O
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Figure 12. 13DMT transmissionof Ndi
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12.8 Discrete Multitone (DMT) Modul
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12.9 Real-Life Applications of OFDM
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Digital Broadcasting12.9 Real-Life
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12.10 Blind Equalization and Identi
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the maximum Doppler shift is bounde
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12.12 MATLAB Exercises 715is known
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12.12 MATLAB Exercises 717% Generat
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12.12 MATLAB Exercises 719After a m
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Fi g ure 12.22Scatter plots ofsigna
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12.12 MATLAB Exercises 723% It show
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12.12 MATLAB Exercises 725Fi g ure
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References 729Figure 1 2.28Average
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PROBLEMSProblems 73 112.1-1 In a QA
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Problems 73312.7-3 Consider an FIR
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13. l Measure of Information 735The
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13. 1 Measure of Information 737Hen
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13.2 Source Encoding 739on the aver
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13.2 Source Encoding 74 1TABLE 13.1
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13.2 Source Encoding 743TABLE 13.3O
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13.3 Error-Free Communication Over
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13.3 Error-Free Communication Over
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13.4 Channel Capacity of a Discrete
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13.5 Channel Capacity of a Continuo
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subject to the following constraint
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13.5 Channel Capacity of a Conti nu
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13.5 Channel Capacity of a Conti nu
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13.6 Practical Communication System
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13.6 Practical Communication System
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13 .7 Frequency-Selective Channel C
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13.7 Frequency-Selective Channel Ca
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13.8 MULTIPLE-INPUT-MULTIPLE-OUTPUT
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13.8 Multiple-Input-Multiple-Output
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Page 810 and 811:
Page 812 and 813:
1 3. 9 MATLAB Exercises 789Fi gure
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% probabilities of each source inpu
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13.9 MATLAB Exercises 793estimate=e
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13.9 MATLAB Exercises 795% Matlab P
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Problems 7973. H. Nyquist, "Certain
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Problems 79913.2-3 A source emits o
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Problems 80113.4-5 A cascade of two
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14.2 Redundancy for Error Correctio
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14.2 Redundancy for Error Correctio
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14.3 Linear Block Codes 807codeword
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14.3 Linear Block Codes 809where th
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14.3 Linear Block Codes 81 1TABLE 1
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14.4 Cyclic Codes 813This is precis
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14.4 Cyclic Codes 815Regardless of
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14.4 Cyclic Codes 817Example 1 4.4
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Consider a Hamming (7, 4, 3) code w
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14.4 Cyclic Codes 821TABLE 14.6e100
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TABLE 14.7Commonly Used CRC Codes a
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Figure 14.3Performancecomparison of
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14.6 Convolutional Codes 827check d
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14.6 Convolutional Codes 829Figure
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14.6 Convolutional Codes 83 1Fi gur
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Figure 14, 10 !Iii! Received bits:
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Figure 14. 1 1Convolutionalencoder.
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14.7 Trellis Diagram of Block Codes
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14.8 CODE COMBINING AND INTERLEAVIN
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14.9 Soft Decoding 841Figure 14. 1
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14.9 Soft Decoding 843modify the ha
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14. 10 Soft-Output Viterbi Algorith
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14.1 1 Turbo Codes 847following sim
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14.1 1 Turbo Codes 849derived from
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14.1 1 Turbo Codes 851Figure 14.20
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14. 1 1 Turbo Codes 853whereas from
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14. 1 2 Low-Density Parity Check (L
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14. 12 Low-Density Parity Check (LD
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14. 12 Low-Density Parity Check (LD
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14. 13 MATLAB EXERCISES14. 1 3 MATL
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14.13 MATLAB Exercises 863Exl4 3r =
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References 865rig_l= (l+sign ( xig_
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Problems 867generates a ( 4,2) code
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Problems 869Hint: A third-order pol
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Problems 871FigureP. 14.5-2(b) Use
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APPENDIX AORTHOGONALITY OF SOME SIG
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APPENDIX BCAUCHY-SCHWARZ INEQUALITY
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APPENDIX CGRAM-SCHMIDT ORTHOGONALIZ
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Appendix C: Gram-Schmidt Orthogonal
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Appendix D: Basic Matrix Properties
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Appendix D: Basic Matrix Properties
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APPENDIX EMISCELLANEOUSE.1 L'Hopita
Page 910 and 911:
1cos 3 x = (3 cosx4 + cos 3x)1sin 3
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IND EXAdaptive delta modulation (AD
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Index 891of discrete memoryless cha
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Index 893Energyof modulated signals
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Index 895Ideal vs. practical filter
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Index 897discrete multitone (DMT),
Page 922 and 923:
Index 899of digital carrier modulat
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Index 90 1transmitter power loading
Page 926:
Index 903vector decomposition of ra
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B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

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