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

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Problems 871FigureP. 14.5-2(b) Use Viterbi's algorithm to decode the following received sequences:(i) 100 110 111 101 001 101 001 010(ii) 010 110 111 101 101 101 001 010(iii) 111 110 111 111 001 101 001 101s 314.5-3 A systematic recursive convolution encoder (Fig. P14.5-3) generates a rate 1/2 code. Unlikeearlier examples, this encoder is recursive with feedback branches. It turns out that we canstill use a simple trellis and state transition diagram to represent this encoder. The maximumlikelihood Viterbi decoder also applies. Denote the state value as (d k - 1 , d k -2).(a) Illustrate the state transition diagram of this encoder.(b) Find the corresponding trellis diagram.(c) For an input data sequence of 0100110100, determine the corresponding codeword.FigureP.14.5-3dk ---------- vk, I1 014.6-1 A block code has parity check matrix01100]
872 ERROR CORRECTING CODES(a) Find the code-generating matrix of this code.(b) Find the minimum distance.( c) Find the trellis diagram.14.6-2 For the block code in Prob. 14.2-9,(a) Find the code-generating matrix.(b) Find the minimum distance.( c) Find the trellis diagram.
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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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5.5 Effects of Nonlinear Distortion
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5.5 Effects of Nonlinear Distortion
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5.6 Superheterodyne Analog AM/FM Re
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5.7 FM BROADCASTING SYSTEM5.7 FM Br
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5.8 MATLAB Exercises 243Figure 5.19
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5.8 MATLAB Exercises 245title ('PM
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Problems 2476. H. R. Slotten, '"Rai
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Problems 249Figure P.5.4-15.4-1 (a)
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6SAMPLING ANDANALOG-TO-DIGITALCONVE
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6. 1 Sampling Theorem 253by nfs . T
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6.1 Sampling Theorem 255identical t
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6. 1 Sampling Theorem 257Figure 6.5
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6.1 Sampling Theorem 259Figure 6.7S
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6. 1 Sampling Theorem 261known as s
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6.1 Sampling Theorem 263Figure 6.9(
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6. l Sampling Theorem 265whereq T s
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6.1 Sampling Theorem 267Moreover, t
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6.2 Pulse Code Modulation (PCM) 269
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6.2 Pulse Code Modulation {PCM) 273
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6.3 Digital Telephony: PCM in Tl Ca
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6.3 Digital Telephony: PCM in Tl Ca
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6.4 DIGITAL MULTIPLEXING6.4 Digital
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6.4 Digital Multiplexing 287Figure
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6.4 Digital Multiplexing 289Figure
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6.5 Differential Pulse Code Modulat
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6.5 Differential Pulse Code Modulat
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6.7 Delta Modulation 295deploy. Unl
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6.7 Delta Modulation 297Figure 6.31
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6.7 Delta Modulation 299Figure 6.32
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6.8 Vocoders and Video Compression
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6.9 MATLAB Exercises 31 1Fi gure 6.
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6. 9 MATLAB Exercises 315% ts new s
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t= [O:td :1.]; %time interval of 1
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PROBLEMSFigure P.6. 1 - 1Problems 3
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Problems 323(c) This filter, being
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Problems 325the transmission bandwi
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7. 1 Digital Communication Systems
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7.2 Line Coding 329Figure 7.3An on-
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7.2 Line Coding 33 1in Fig. 7 .4b,
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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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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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Page 848 and 849: Figure 14.3Performancecomparison of
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Page 856 and 857: Figure 14, 10 !Iii! Received bits:
Page 858 and 859: Figure 14. 1 1Convolutionalencoder.
Page 860 and 861: 14.7 Trellis Diagram of Block Codes
Page 862 and 863: 14.8 CODE COMBINING AND INTERLEAVIN
Page 864 and 865: 14.9 Soft Decoding 841Figure 14. 1
Page 866 and 867: 14.9 Soft Decoding 843modify the ha
Page 868 and 869: 14. 10 Soft-Output Viterbi Algorith
Page 870 and 871: 14.1 1 Turbo Codes 847following sim
Page 872 and 873: 14.1 1 Turbo Codes 849derived from
Page 874 and 875: 14.1 1 Turbo Codes 851Figure 14.20
Page 876 and 877: 14. 1 1 Turbo Codes 853whereas from
Page 878 and 879: 14. 1 2 Low-Density Parity Check (L
Page 880 and 881: 14. 12 Low-Density Parity Check (LD
Page 882 and 883: 14. 12 Low-Density Parity Check (LD
Page 884 and 885: 14. 13 MATLAB EXERCISES14. 1 3 MATL
Page 886 and 887: 14.13 MATLAB Exercises 863Exl4 3r =
Page 888 and 889: References 865rig_l= (l+sign ( xig_
Page 890 and 891: Problems 867generates a ( 4,2) code
Page 892 and 893: Problems 869Hint: A third-order pol
Page 896 and 897: APPENDIX AORTHOGONALITY OF SOME SIG
Page 898 and 899: APPENDIX BCAUCHY-SCHWARZ INEQUALITY
Page 900 and 901: APPENDIX CGRAM-SCHMIDT ORTHOGONALIZ
Page 902 and 903: Appendix C: Gram-Schmidt Orthogonal
Page 904 and 905: Appendix D: Basic Matrix Properties
Page 906 and 907: Appendix D: Basic Matrix Properties
Page 908 and 909: APPENDIX EMISCELLANEOUSE.1 L'Hopita
Page 910 and 911: 1cos 3 x = (3 cosx4 + cos 3x)1sin 3
Page 912 and 913: IND EXAdaptive delta modulation (AD
Page 914 and 915: Index 891of discrete memoryless cha
Page 916 and 917: Index 893Energyof modulated signals
Page 918 and 919: Index 895Ideal vs. practical filter
Page 920 and 921: Index 897discrete multitone (DMT),
Page 922 and 923: Index 899of digital carrier modulat
Page 924 and 925: 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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