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Principles of Digital Communications Prof. Zesong Fei School of Information and Electronics Beijing Institute of Technology 1 Staff  Lecturer of Class Teaching (48 Hr.)  Dr. Zesong Fei  Office: Room 609, Building No.10  Email: feizesong@bit.edu.cn  Lecturer of Lab. Work Teaching (16Hr.)  Dr. Zesong Fei  Office: Room 609, Building No.10  Email: feizesong@bit.edu.cn 2 Course Description  The course is designed to provide students with a sound fundamental education in the areas of digital communications.  The main contents include spectral analysis; random signal theory; information theory; digital transmission through AWGN channels; digital carrier-modulation schemes; error control coding; optimum receivers; carrier and symbol synchronization; spread spectrum and multiuser communications.  The laboratory work will help students understand the fundamental concepts in digital communication systems, and enhance the comprehensive apprehension ability as well. 3 Course Description  Prerequisite:  Random signal analysis  Signals and Systems  Assessment:  Homework: 30%  Final Exam: 70% 4 Text & Reference Book  通信原理: Principles of Communications(英文版) 樊 昌信 电子工业出版社  John G. Proakis, Digital Communications , 5th ed., 2009, ISBN 9787121086205.  Simon Haykin, Communication Systems, 4th ed., John Wiley & Sons 5 Syllabus  Introduction  Deterministic and Random Signal Analysis  Information Theory  Digital Communication Through Band-Limited Channels  Digital Modulation Schemes  Optimum Receivers for AWGN Channel  Linear Block Codes  Trellis and Graph Based Codes  Carrier and Symbol Synchronization  Spread Spectrum and Multiuser Communications 6 Chapter 1 Introduction 1.1 Historical Review of Communication  Origin of ancient communication  Two modes of communication  Development of modern communication 7 What is communications?  Communications  The systems and processes that are used to convey information from a source to a destination, especially by means of electricity or radio waves.  Telecommunications  “tele” = distance  The technology of sending signals and message over a distance using electronic equipment, for example, telegraph, telephone, radio, television and cellphone 8 Historical Review  2000 years ago … Smoke Signals  Signal-fire  A very primitive type of optical communication  The simplest binary digital communication 9 Historical Review  1838: telegraph (S. Morse)  1876: telephone (A. Bell)  1895: radio by Marconi  1901: trans-Atlantic communication  Early 20thcentury:  Most communication systems are analog.  Engineering designs are ad-hoc, tailored for each specific application 10  Is there a general methodology for designing communication systems?  Is there a limit to how fast one can communicate? 11 Harry Nyquist (1928)  Analog signals of bandwidth W can be represented by 2W samples/second  Channels of bandwidth W support transmission of 2W symbols/second  Nyquist transformed a continuous time problem to a discrete-time problem.  But did he really solve the communication problems? 12 Claude Shannon (1948)  Shannon’s information theory solves all the big questions  Shannon describes information source and channel with probability  There exists an entropy rate H bits/sec for each source  There exists a capacity C bits/sec for each channel  If and only if H<=C,the information can be transmitted over the channel almost error-free 13 1.2 Message, information & signal  Message:speech, letters, figures, images…  Information:effective content of message. Different types of messages may contain the same information  Signal:the carrier of message What transmitted in a communication system is signal. 14  Measurement of information: # “quantity of message”  information content # Ex: “Rainfall will be 1 mm tomorrow” – information content small “Rainfall will be 1 m tomorrow” – information content large “The sun will rise in the east tomorrow morning” – information content equals zero # Information content I = I [ P(x) ],P(x) – Occurrence probability # Definition:I = loga [1/P(x)] = -logaP(x) # Usually, set a = 2, the unit of the information content will be called a bit. # For an equal probability binary symbol: I = log2 [1/P(x)] = log2 [1/(1/2)] = 1 bit 15 # For an equal probability M-ary symbol: I = log2 [1/P(x)] = log2 [1/(1/M)] = log2 M bit If M = 2k ,then I = k bit 16 1.3 Digital Communication 1.3.1 Basic concept Two categories of signals  Analog signal:Its voltage or current can be expressed by a continuous function of time. For example, speech signal.  Digital signal: Its voltage or current can only take finite number of discrete values. For example, digital computer data signal. 17 Analog Signal & Digital Signal s(t) s(t) t t Analog signals s(t) s(t) Symbol t t Digital signals 18 Two kinds of communication systems  Analog communication system Requirement - High fidelity Criterion - Signal to noise ratio Basic issue - parameter estimation  Digital communication system Requirement - correct decision Criterion - Error probability Basic issur - statistical decision theory 19 1.3.2 Advantages of Digital Communication  Finite number of possible values of signals  Correct decision may be achieved (a) Waveforms of distored digital signal (b) Waveforms of digital signal after shaping Fig. 1.3.2 Distortion and restoration of digital signal waveforms 20  Error correcting techniques can be used.  Digital encryption can be used.  Different kinds of analog & digital message can be integrated to transmit  Digital communication equipment: Design and manufacture are easier Weight & volume are smaller  Digital signal can be compressed by source coding to reduce redundency.  Out put S/N increases with bandwidth according to exponential law. 21 Digital communication system model 22 Receiver Source decoding Synchronization Noise 1.3.3 Digital Communication System Model Information destination Compression decoding Encryption decoding Channel decoding Demodulation Channel Modulation Channel coding Encryption coding Compression coding Information source Transmitter Source coding 23 Analog communication system model Receiver Noise Information destination Demodulation Channel Modulation Information source Transmitter Elements of digital communication system  Functional diagram of a digital communication system 24 Basic Blocks  Source coding-efficiency  Compression coding  A/D conversion  Encryption coding  Channel coding-reliability Redundant symbols Detect or correct errors 25 Basic Blocks  Modulation Coded signal match to the channel Baseband signal Channel property Baseband modulation & bandpass modulation  multiplexing 26 Basic Blocks  Channel  Transmission characteristics  Additive noise  Synchronization Carrier synchronization Symbol synchronization Frame/Codeword synchronization Network synchronization 27 1.3.4 Specifications of Digital Communication Systems  Relationship between efficiency & reliability (rate ~ accuracy)  Transmission rate: Symbol rate: RB -Baud Information rate: Rb - bit/second For M-ary system:Rb = RB log2 M Message rate: RM  Error probability: Symbol error probability Pe = number of received symbols in error/total number of transmitted symbols 28 Bit error probability Pb = number of received bits in error/total number of transmitted bits Word error probability Pw =number of received words in error/total number of transmitted words Relationship between symbol error probability and bit error probability Pb = Pe x M / [2(M-1)]  Pe /2 29 Relationship between word error probability and bit error probability For binary system, If a word is consisted of k bits, then Pw=1 – (1 – Pe)k  Utilization factor of frequency band  Utilizaition factor of energy 30 What are the Features of a Good Communication System? 31 Tradeoff (1): Data Rate vs. Bandwidth 32 Tradeoff (2): Fidelity vs. Signal Power 33 Tradeoff (3): Bandwidth Efficiency vs. Energy Efficiency 34 1.4 Channel 1.4.1 Wireless channel  Origin of wireless communication  Requirement of electromagnetic wave emission on wavelength  Division of frequency band (wavelength) 35 Division of frequency band Frequency Name band (kHz) Typical application 3 – 30 Very low frequency Long-distance navigation, (VLF) Underwater comm. Sonar 30 – 300 Low frequency (LF) Navigation, underwater comm. radio beaconing 300 – 3000 Medium frequency Broadcasting, maritime comm. (MF) direction-finding, distress calling, coast guard 36 Division of frequency band Frequency band (MHz) 3 – 30 30 – 300 300 – 3000 Name Typical application High frequency (HF) Long-distance broadcasting, telegraph, telephone, fax, search and lifesaving, comm. between aircrafts & ships, and between ship & coast, amateur radio Very high frequency (VHF) Ultra high frequency (UHF) TV, FM broadcasting, land traffic, air traffic, control, taxi, police, navigation, aircraft communication TV, cellular phone network, microwave link, , radio sounding, navigation, satellite communication, GPS, surveillance radar, radio altimeter 37 Division of frequency band Frequency Name Typical application band (GHz) 3 – 30 Super high frequency Satellite comm., radio altimeter, (SHF) microwave link, aircraft radar, meteorological radar, public land vehicle communication 30 – 300 Extremely high Radar landing system, satellite frequency (EHF) comm., vehicle comm., railway traffic 300 – 3000 Submillimeter wave Experiment, not designated (0.1 – 1 mm) 38 Division of frequency band Frequency band (THz) Name Typical application 43 – 430 Infrared (7 – 0.7 m) Optical communication 430 – 750 Visible light (0.7 – 0.4 m) 750 – 3000 Ultraviolet (0.4 – 0.1 m) Note: kHz = 103 Hz, MHz = 106 Hz, THz = 1012 Hz, mm = 10-3 m, Optical communication Optical communication GHz = 109 Hz, m = 10-6 m 39 Ground wave Frequency:below 2MHz Diffraction: Propagation distance:hundreds to thousands of km Ground surface 40 Ionosphere Structure D layer: 60 ~ 80 km E layer: 100 ~ 120 km F layer: 150 ~ 400 km F1 layer: 140 ~ 200 km F F2 layer: 250 ~ 400 km  At night: D layer: disappears F1 layer: disappears (Or, F1 and F2 are combined as F layer) F2 F1 E D Ground surface 41 Sky-wave Ionosphere Height :60 ~ 400 km One hop max. propagation distance:4000 km Propagation distance by multi-hops: >10000 km Frequency:2 ~ 30 MHz Ionosphere Propagation path of signal Transmitting antenna Ground Receivng antenna Figure 1.4.2 Sky-wave propagation 42 Line-of -sight propagation  Frequency:> 30 MHz  Propagation distance: d 2 + r 2 =(h+r)2, or d  h2  2rh h  D 2/50 (m) Signal Propagation where D - km Transmitting antenna h d d D Receiving antenna Ground r Figure 1.4.3 Line-of-sight propagation 43 Radio relay Transmitting antenna Figure 1.4.4 Radio relay Receiving antenna 44 Geostationary satellite equator 45 Stratosphere communication  HAPS(High Altitude Platform Station) 46 Attenuation (dB/km) Atmosphere attenuation Vapor Oxygen Frequency (GHz) (a) Attenuation of oxygen & vapor(concentration 7.5 g/m3) Rainfall rate Frequency (GHz) (b) Attenuation of rainfall 47 Figure 1.4.5 Atmosphere attenuation Attenuation (dB/km) Scatter communication  Ionosphere scattering  Frequency: 30 ~ 60 MHz  Troposphere scattering  Frequency: 100 ~ 4000 MHz  Meteor-tail scattering  Frequency: 30 ~ 100 MHz Transmitting antenna Effective scattering region Earth Receiving antenna Figure 1.4.6 Troposphere scattering communication Ground Figure 1.4.7 Meteor-tail scattering communication 48 1.4.2 Wired channel  Open wires  Symmetrical cables  Coaxial cables Fig. 1.4.8 49 Table 1.4.3 General electrical characteristics of wired channels Kinds of channel Open wire Open wire Symmetrical cable Symmetrical cable Small coaxial cable Small coaxial cable Medium coaxial cable Medium coaxial cable Medium coaxial cable Communication capacity (channels) 1+3 1+3+12 24 60 300 960 1800 2700 10800 Frequency range (kHz) 03.~27 0.3~150 12~108 12~252 60~1300 60~4100 300~9,000 300~12,000 300~60,000 Transmission distance (km) 300 120 35 12~18 8 4 6 4.5 1.5 50  Optical fiber  Structure n2 n1 Reflection index (Cladding) (Core) n2 n1 Reflection index Multimode step-index optical fiber (Cladding) 2a (Core) Multimode graded-index optical fiber Figure 1.4.9 Sketch of the structure of multimode optical fibers 51 Transmission loss 1.31 m 1.55 m Loss (dB/km) 0.7 0,9 1.1 1.3 1.5 1.7 Wavelength of light waves(m) Figure 1.4.10 Relationship between loss and wavelength 52 53 1.4.3 Channel models •Modulation channel model: ei(t) Time-variant linear network eo(t) eo(t) = f [ei(t)] + n(t) 式中 ei(t) - input signal eo(t) - output signal n(t) - additive noise f [ei(t) ] -function relating input and output signals 54 Usually, assume f [ei(t) ] can be expressed as k(t) ei(t) So, eo(t) = k(t) ei(t) + n(t) where k(t) is called multiplicative interference, and is a complicated function which reflects the characteristics of the channel. In the simplest condition: k(t) = const., expressing attenuation. When k(t) = const., it is a constant parameter channel. For example, coaxial cable. When k(t)  const., it is called a random parameter channel. For example, vehical cellular network communication channel. 55 •Coding channel model: Binary coding channel model P(0/0) 0 0 P(0/1) P(1/0) 1 1 P(1/1) where, P(0/0), P(1/1) -corrrect transfer probabilities P(0/1), P(1/0) -error transfer probabilities P(0/0) = 1 - P(1/0) P(1/1) = 1 - P(0/1) 56  4-ary coding channel model 0 0 1 Transmitting end 2 1 Receiving end 2 3 3 Figure 1.4.12 4-ary coding channel model 57 1.4.4 Influence of channel characteristics on signal transmission  Constant parameter channel ~ time-invariant linear network Link:a segment of physical line where no exchange exists Amplitude ~ frequency characteristics: Attenuation (dB) Typical characteristic of a telephone channel Ideal characteristic 0 300 f (Hz) 3000 58  Compensation of frequency distortion A A A 0 f0 f0 f (a) Channel characteristic (b) Characteristic of (c) Channel characteristic with frequency distortion linear compensation after compensation network 59 Phase ~ frequency characteristics:  ()  () Ideal characteristic 0 ω 0 Ideal characteristic  Ideal characteristic: phase ---  () = k  ; group delay ---  () = d()/d = k Influence of distortion: waveform distortion, inter-symbol interference Linear distortion including frequency distortion & phase distortion can be corrected by linear compensation network. Nonlinear distortion: nonlinear amplitude characteristic, frequency deviation, phase jittering, … 60  Random parameter channel  Common characteristics - attenuation: varying with time transmission delay: varying with time multi-path propagation: fast fading  Characteristics of received signal: Let transmitting signal be A cos 0t,after transmission through n paths, the received signal R(t) can be expressed as: n n   R ( t )  ri ( t ) cos  0 [ t   i ( t )]  ri ( t ) cos[  0 t   i ( t )] i 1 i 1 where ri (t) - amplitude of received signal passing over i-th path i (t) - delay of the received signal passing over i-th path  i (t) = - 0 i (t) n n   R ( t )  ri ( t ) cos  i ( t ) cos  0 t  ri ( t ) sin  i ( t ) sin  0 t i 1 i 1 X c (t) X s (t) 61 R(t)  X c (t) cos 0 t  Xs (t) sin 0 t  V(t) cos[0 t  (t)] where V(t) - envelope of the received signal R(t) (t) - phase of the received signal R(t) i.e., V (t)  X 2 c (t)  X 2 s ( t )  ( t )  arctan X s ( t ) X c (t) Because ri(t) and i(t) are slowly varied, ri(t) and i(t) are also slowly varied. Hence, Xc(t), Xs(t) and V(t), (t) are also slowly varied. Hence, R(t) can be considered a narrow band signal (random process). 62 It can be seen from the following equation R (t)  V (t) cos[  0 t  (t)] After transmission, the transmitting signal A cos 0t: * amplitude A becomes slowly varied amplitude V(t); * phase 0 becomes slowly varied phase (t); * spectrum becomes narrow band spectrum from single frequency. f t f0 63 f (t)  F ( ) Frequency selective fading Assume: there are only two paths with identical attenuation and different delays, Transmitting signal is f(t),received signals are af(t - 0) and af(t - 0 - );spectrum of transmitting signal is F()。 then f(t)  F() af(t - 0)  a F() e-j0 af(t - 0 - )  a F() e-j(0 + ) af(t - 0) + af(t - 0 - )  a F() e-j0 (1+e-j)  H() = a F() e-j0 (1+e-j)/F() = ae-j0 (1+e-j) |1+e-j| = |1+cos-jsin|=|[(1+cos)2+sin2]1/2| =2|cos(/2)| 3 categories of signal: * deterministic signal * random phase signal * fluctuation signal 64 1.5 Noise in Channel  Classified according to origins:  Man-made noise:electric sparks, …  Natural noise:lightning, atmosphere noies, thermal noise,...  Classified according to characteristics:  impulse noise  narrow band noise  fluctuation noise  Main noise involved in the following discussion on communication systems is: white noise – thermal noise is a kind of typical white noise 1.6 Brief Summary 65 1.1 Elements of digital communication system  Functional diagram of a digital communication system 66 1.2 Comm. channels and their characteristics  Physical channel media  (magnetic-electrical signaled) Wireline channel  Telephone line, twisted-pair and coaxial cable, etc.  (modulated light beam) Fiber-optical channel  (antenna radiated) Wireless electromagnetic channel  ground-wave propagation, sky-wave propagation,  Line-of-sight (LOS) propagation, etc.  (multipath) Underwater acoustic channel  ...etc.  Virtual channel  Storage channel  Magnetic storage, C6D7 , DVD, etc 1.2 Comm. channels and their characteristics  Channel impairments  Thermal noise (additive noise)  Signal attenuation  Amplitude and phase distortion  Multi-path distortion  Limitations of channel usage  Transmission power  Receiver sensitivity  Bandwidth  Transmission time 68 1.3 Math models for communication channels  Additive noise channel (with attenuation) In studying these channels, a mathematical model is necessary. 69 1.3 Math models for communication channels Linear filter channel with additive 70 1.3 Math models for communication channels  Linear time-variant (LTV) filter channel with additive noise 71  Assume n(t)=0 (noise-free). 72 1.3 Math models for communication channels  LTV filter channel with additive noise 73 1.3 Math models for communication channels  Time varying multipath fading 74 1.1-1.6 Exercises 75

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