Document Sample

TCOM 551 DIGITAL COMMUNICATIONS FALL 2009 IN 134 Tuesdays 4:30 – 7:10 p.m. Dr. Jeremy Allnutt jallnutt@gmu.edu TCOM 551 Lecture number 1 1 Fall 2009 General Information - 2 • Course Outline – Go to http://telecom.gmu.edu and click on course schedule or go to http://ece.gmu.edu/ and go to “courses” and “Course web pages”; select TCOM 551 • Bad weather days: call (703) 993-1000 • Textbook: no mandatory requirement. The Kolimbiris book is very useful. The Bateman book provides additional information • Mathematical Calculator – simple ones only TCOM 551 Lecture number 1 2 Fall 2009 General Information - 3 • Homework Assignments – Feel free to work together on these, BUT – All submitted work must be your own work • Web and other sources of information – You may use any and all resources, BUT – You must acknowledge all sources – You must enclose in quotation marks all parts copied directly – and you must give the full source information TCOM 551 Lecture number 1 3 Fall 2009 No double jeopardy General Information - 4 • Exam and Homework Answers – For problems set, most marks will be given for the solution procedure used, not the answer – So: please give as much information as you can when answering questions: partial credit cannot be given if there is nothing to go on – If something appears to be missing from the question set, make – and spell out clearly – assumptions used to find the solution TCOM 551 Lecture number 1 4 Fall 2009 Double-line space, Times New Roman, 12 font size, default margins. References: must be with source information – listed either as footnotes or tabulated at the end General Information - 5 • Term Paper – Any topic in field of Digital Communications – About 10 pages long + about 4 figures – Can work alone or in small groups (length of paper grows with number in group – with permission only) – There will be no specific points given for the paper, but it can help (or ruin) your grade Possible Topics? TCOM 551 Lecture number 1 5 Fall 2009 General Information – 6A • Examples of Term Paper Topics – TDMA vs. CDMA in various situations – LD-CELP: what is it and how does it help? – What is net-centric communications? – Digital Imaging and its impact on sports casting – DBS: why did digital succeed where analog failed – What is a smart antenna and how will it help? – UWB applications – Bluetooth vs. IEEE 802.11B And TCOM 551 Lecture number 1 6 Fall 2009 General Information – 6B • Examples of Term Paper Topics (Contd.) – MPEG2: what is it and how does it help? – Why has MPEG-4 taken the lead in video streaming? – Where to next with DVD‟s? – Consequences of combining RFID with GPS – Is free-space optical communications for real? – What are the comparative merits of different large screen displays (LCD, DLP, Plasma, etc.)? – Talking appliances? Etc.!!! TCOM 551 Lecture number 1 7 Fall 2009 General Information - 7 • Class Grades • Emphasis is on overall effort and results • Balance between homework, tests, final exam; plus term paper: – Homework - 15% – Tests - 30 + 30% – Final exam - 25% – Term Paper - 0% TCOM 551 Lecture number 1 8 Fall 2009 Term Paper Grade Percentage – 1 • Contribution of paper to final grade (a) – No mark will be allocated towards the paper. The paper will be graded as quintuple plus (5+), through dot (·), to quintuple minus (5–). A student with a final grade close to the borderline between two grades may be moved up across the borderline if his/her paper is ≥ +++ A soft copy and a hard copy shall be submitted TCOM 551 Lecture number 1 9 Fall 2009 Term Paper Grade Percentage – 2 • Contribution of paper to final grade (b) – (i) A student who does not hand in an adequate paper by the final exam without prior permission will have his/her final exam score reduced by half – (ii) A student who hands in their paper late, even with permission, will not have their paper considered for a “grade shift” TCOM 551 Lecture number 1 10 Fall 2009 Term Paper Grade Percentage – 3 • PLAGIARISM I plan on using search software on the term papers, so please: – No more than 40% by content directly from the web – All quoted content should be inside quotation marks – Every source should be acknowledged in the paper at the point of usage. TCOM 551 Lecture number 1 11 Fall 2009 Another alternative http://ece.gmu.edu/coursepages.htm TCOM 551 & ECE 463 Course Plan -Go to http://telecom.gmu.edu, click on course schedule, scroll down to TCOM 551 - In-Class Tests scheduled for - October 6th - November 17th - In-Class Final exam scheduled for - December 15th TCOM 551 Lecture number 1 12 Fall 2009 TCOM 551 GTA Information • The TA is TBD • Email address is: TBD • Office Hours in room TBD of the new engineering building are: – TBD; TBD p.m. • Please Email the TA if you would like to meet with him/her. TCOM 551 Lecture number 1 13 Fall 2009 TCOM 551 & ECE 463 Lect. 1 Outline • Sine Wave Review • Frequency, Phase, & Wavelength • Logarithms and dB (decibel) notation • Core Concepts of Digital Communications – Source info., Carrier Signal, Modulation – C/N, S/N, and BER – Performance & Availability TCOM 551 Lecture number 1 14 Fall 2009 TCOM 551 & ECE 463 Lect. 1 Outline • Sine Wave Review • Frequency, Phase, & Wavelength • Logarithms and dB (decibel) notation • Core Concepts of Digital Communications – Source info., Carrier Signal, Modulation – C/N, S/N, and BER – Performance & Availability TCOM 551 Lecture number 1 15 Fall 2009 Sine Wave Review – 1A We all know that the Sine of an angle is the side opposite to the angle divided by the hypotenuse, i.e. A Sine (a) = A/B Angle a Point P TCOM 551 Lecture number 1 16 Fall 2009 Sine Wave Review – 1B We all know that the Sine of an angle is the side opposite to the angle divided by the hypotenuse, i.e. A Sine (a) = A/B Angle a But what happens if line B rotates about Point P? Point P TCOM 551 Lecture number 1 17 Fall 2009 Sine Wave Review – 2A The end of Line B will describe a circle about Point P a Point P TCOM 551 Lecture number 1 18 Fall 2009 Sine Wave Review – 2B The end of Line B will describe a circle about Point P a Point P What happens if we now shine a light from the left and project the shadow of the end of line B onto a screen? TCOM 551 Lecture number 1 19 Fall 2009 Sine Wave Review - 3 End of “B” projected onto the a screen Point P Light from Screen on the left the right TCOM 551 Lecture number 1 20 Fall 2009 Sine Wave Review – 4A End of “B” As line “B” rotates about projected the center point, P, the projected end of line “B” onto the oscillates up and down on screen the screen. The end of line “B” moves up and down with what is called Screen on Simple Harmonic Motion, the right TCOM 551 Lecture number 1 21 Fall 2009 Sine Wave Review – 4B End of “B” Simple Harmonic Motion projected is an oscillation, or a rotational movement, onto the about a mean value screen (center) that is periodic. What happens if we move the screen to the right and „remember‟ where the Screen on projected end of “B” was? the right TCOM 551 Lecture number 1 22 Fall 2009 Sine Wave Review – 5A Locus of “B” end-point We have a Sine Wave! One oscillation = One wavelength, a.k.a. SHM Screen Screen Position TCOM 551 1 Lecture number 1 Position 223 Fall 2009 Sine Wave Review – 5B Remember: Sine 0 = 0; Sine 90 = 1; Sine 180 = 0; Since 270 = -1; Sine 360 = Sine 0 = 0 +1 0 90 180 270 360 Degrees -1 TCOM 551 Lecture number 1 24 Fall 2009 Sine and Cosine Waves – 1 Sine Wave Sine Wave = Cosine Wave shifted by 90o 0o 90o 180o 270o 0 = 360o 90o 180o Cosine TCOM 551 Wave Lecture number 1 25 Fall 2009 Sine and Cosine Waves – 2 • There is a useful java applet that will show you a sine wave derived from circular motion (simple harmonic motion) • The applet is found at: http://home.covad.net/alcoat/sinewav.htm It is very slow to load: have patience! TCOM 551 Lecture number 1 26 Fall 2009 Sine and Cosine Waves – 3 • Another applet that lets you „play‟ with two sine waves to see the combined waveform is: http://www.udel.edu/idsardi/sinewave/sinewave.html TCOM 551 Lecture number 1 27 Fall 2009 For more details on Sine Waves Sine and Cosine Waves – 4 Sine Wave Sine Wave = Cosine Wave shifted by 90o 0o 90o 180o 270o 0 = 360o 90o 180o Cosine TCOM 551 Wave Lecture number 1 28 Fall 2009 http://en.wikipedia.org/wiki/Image:Sine_Cosine_Graph.png Sine and Cosine Waves – 5 TCOM 551 Lecture number 1 29 Fall 2009 Sine and Cosine Waves – 6 • Any wave that is periodic (i.e. it repeats itself exactly over succeeding intervals) can be resolved into a number of simple sine waves, each with its own frequency • This analysis of complex waveforms is part of the Fourier Theorem • You can build up a complex waveform with harmonics of the fundamental frequency TCOM 551 Lecture number 1 30 Fall 2009 http://www.sfu.ca/sonic-studio/handbook/Harmonic_Series.html Harmonics – 1 A harmonic is a multiple of a fundamental frequency. In the figure below, a fundamental frequency of 100 Hz is shown with 31 harmonics (total of 32 “lines”). TCOM 551 Lecture number 1 31 Fall 2009 http://www.sfu.ca/sonic-studio/handbook/Law_of_Superposition.html Harmonics – 2 In this example, 20 harmonics are mixed together to form a saw-tooth waveform TCOM 551 Lecture number 1 32 Fall 2009 Sine and Cosine Waves - 7 Sine and Cosine “Cosine waves can Wave” therefore be Sine Wave considered to be at right angles, i.e. orthogonal, to each other TCOM 551 Lecture number 1 33 Fall 2009 Sine and Cosine Waves - 8 • A Radio Signal consists of an in-phase component and an out-of-phase (orthogonal) component • Signal, S, is often written in the generic form S = A cos + j B sin Where j = ( -1 ) In-phase Orthogonal We will only component component consider Real Real Imaginary signals TCOM 551 Lecture number 1 34 Fall 2009 Sine and Cosine Waves - 9 • Two concepts – The signal may be thought of as a time varying voltage, V(t) – The angle, , is made up of a time varying component, t, and a supplementary value, , which may be fixed or varying • Thus we have a signal V(t) = A cos (t + ) TCOM 551 Lecture number 1 35 Fall 2009 Sine and Cosine Waves - 10 Vary these • Time varying signal to Modulate the signal V(t) = A cos (t + ) Phase: PM; PSK Instantaneous value of the Frequency: FM; FSK signal Amplitude: AM; ASK Note: = 2 f TCOM 551 Lecture number 1 36 Fall 2009 Back to our Sine Wave – 1A Defining the Wavelength The wavelength is calculated between any two points on the wave where it repeats itself TCOM 551 Lecture number 1 37 Fall 2009 Back to our Sine Wave – 1B Defining the Wavelength Measuring between the peaks or the “zero crossings” is often used: However: TCOM 551 Lecture number 1 38 Fall 2009 Back to our Sine Wave – 1C Defining the Wavelength The wavelength is usually defined at the “zero crossings” since these points are more precise than anywhere else TCOM 551 Lecture number 1 39 Fall 2009 Back to our Sine Wave - 2 One revolution = 360o One revolution also completes one cycle (or wavelength) of the wave. So the “phase” of the wave has moved from 0o to 360o (i.e. back to 0o ) in one cycle. The faster the phase changes, the shorter the time one cycle (one wavelength) takes TCOM 551 Lecture number 1 40 Fall 2009 Back to our Sine Wave – 3 Two useful equations The time taken to complete one cycle, or wavelength, is the period, T. Frequency is the reciprocal of the period, that is f = 1/T Phase has changed by The rate-of-change of the phase, d/dt, is the frequency, f. TCOM 551 Lecture number 1 41 Fall 2009 Before we look at d/dt, lets look at rate-of-change of phase Sine Wave – 4 • What do we mean “Rate-of-change of phase is frequency”? One revolution = 360o = 2 radians One revolution = 1 cycle One revolution/s = 1 cycle/s = 1 Hz Examples: 1. 720o/s = 2 revolutions/s = 2 Hz 2. 18,000o/s = 18,000/360 revs/s = 50 revs/s = 50 Hz TCOM 551 Lecture number 1 42 Fall 2009 http://www.sfu.ca/sonic-studio/handbook/Simple_Harmonic_Motion.html Simple Harmonic Motion “Geometric derivation of simple harmonic motion. A point p moves at constant speed on the circumference of a circle in counter-clockwise motion. Its projection OC on the vertical axis XOY is shown at right as a function of the angle . The function described is that of a sine wave.” From the URL above TCOM 551 Lecture number 1 43 Fall 2009 d/dt Digression - 1 kilometers Person walks 16 km in 4 hours. 16 Velocity = (distance)/(time) Therefore, Velocity = 16/4 12 = 4 km/h 8 Velocity is really the rate-of-change of distance with time. 4 What if the velocity is not constant? 0 0 1 2 3 4 5 6 7 8 9 Time, hours TCOM 551 Lecture number 1 44 Fall 2009 d/dt Digression - 2 kilometers 16 You can compute the Average Velocity 12 using distance/time, (i.e. 16/8 = 2 km/h), 8 but how do you get the person‟s speed at 4 any particular point? 0 0 1 2 3 4 5 6 7 8 9 Time, hours Answer: you differentiate, which means you find the slope of the line. TCOM 551 Lecture number 1 45 Fall 2009 d/dt Digression - 3 kilometers To differentiate 16 means to find the A slope at any instant. 12 The slope of a curve is given by the B 8 tangent at that point, i.e., A/B 4 In this case, A is in km and B is in hours. 0 It could equally well 0 1 2 3 4 5 6 7 8 be phase, , and 9 Time, hours time, t. TCOM 551 Lecture number 1 46 Fall 2009 d/dt Digression - 4 -When we differentiate, we are taking the smallest increment possible of the parameter over the smallest interval of (in this case) time. - Small increments are written „d‟(unit) -Thus: the slope, or rate-of-change, of the phase, , with time, t, is written as d/dt TCOM 551 Lecture number 1 47 Fall 2009 Sine Wave Continued • Can think of a Sine Wave as a Carrier Signal, i.e. the signal onto which the information is loaded for sending to the end user • A Carrier Signal is used as the basis for sending electromagnetic signals between a transmitter and a receiver, independently of the frequency TCOM 551 Lecture number 1 48 Fall 2009 Carrier signals – 1 • A Carrier Signal may be considered to travel at the speed of light, c, whether it is in free space or in a metal wire • Travels more slowly in most substances • The velocity, frequency, and wavelength of the carrier signal are uniquely connected by c=f Wavelength Velocity of light Frequency TCOM 551 Lecture number 1 49 Fall 2009 Carrier signals – 2 • Example – WAMU (National Public Radio) transmits at a carrier frequency of 88.5 MHz – What is the wavelength of the carrier signal? • Answer – c = (3×108) m/s = f × = (88.5 106) × () – Which gives = 3.3898 m = 3.4 m Remember: Make sure you are using the correct units TCOM 551 Lecture number 1 50 Fall 2009 Digression – UNITS – 1 • Standard units to use are MKS – M = meters written as m – K = kilograms written as kgm – S = seconds written as s • Hence – the velocity of light is in m/s – The wavelength is in m – And the frequency is in Hz = hertz TCOM 551 Lecture number 1 51 Fall 2009 Digression – UNITS – 2 • Standard units to use are MKS – M = meters written as m So: do not mix feet with meters – K = kilograms written as kgm and pounds – S = seconds written as s with kilograms • Hence – the velocity of light is in m/s – The wavelength is in m – And the frequency is in Hz = hertz TCOM 551 Lecture number 1 52 Fall 2009 Carrier signals – 3 • A Carrier Signal can – carry just one channel of information (this is often called Single Channel Per Carrier = SCPC) – Or carry many channels of information at the same time, usually through a Multiplexer Single Note: The modulator Channel Tx SCPC has been omitted in these drawings Multiplexer Multi-channel Multiplexed carrier Tx Carrier TCOM 551 Lecture number 1 53 Fall 2009 TCOM 551 & ECE 463 Lect. 1 Outline • Sine Wave Review • Frequency, Phase, & Wavelength • Logarithms and dB (decibel) notation • Core Concepts of Digital Communications – Source info., Carrier Signal, Modulation – C/N, S/N, and BER – Performance & Availability TCOM 551 Lecture number 1 54 Fall 2009 Logarithms – 1 • The use of logarithms came about for two basic reasons: – A need to multiply and divide very large numbers – A need to describe specific processes (e.g. in Information Theory) that counted in different bases • Numbers are to the base 10; i.e. we count in multiples of tens TCOM 551 Lecture number 1 55 Fall 2009 Logarithms – 2 • 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 We actually count To be easier to see, this should be written as the series from 1 to 10 but 00, 01, 02, 03, 04, 05, …. 09, 10 the numbering goes from 0 to 9, • 11, 12, 13, 14, 15 ….. then we change • ….. the first digit and • 91, ……, 97, 98, 99, 100 go from 0 to 9 • … again, and so on • 991, ….., 997, 998, 999, 1000 TCOM 551 Lecture number 1 56 Fall 2009 Logarithms – 3 • Counting to base 10 is the Decimal System • We could equally well count in a Duodecimal System, which is a base 12, a Hexadecimal System, which is a base 16, a Binary System, which is a base 2, etc. • Sticking with the Decimal System TCOM 551 Lecture number 1 57 Fall 2009 Logarithms – 4A • A Decimal System can be written as a power of 10, for example – 100 = 1 – 101 = 10 – 102 = 100 – 103 = 1,000 – 104 = 10,000 TCOM 551 Lecture number 1 58 Fall 2009 Logarithms – 4B • A Decimal System can be written as a power of 10, for example – 100 = 1 Do you detect any logic here? – 101 = 10 – 102 = 100 – 103 = 1,000 – 104 = 10,000 TCOM 551 Lecture number 1 59 Fall 2009 Logarithms – 4C • A Decimal System can be written as a power of 10, for example – 100 = 1 Do you detect any logic here? – 101 = 10 – 102 = 100 The number of zeroes is the – 103 = 1,000 same as the value of the – 104 = 10,000 exponent TCOM 551 Lecture number 1 60 Fall 2009 Logarithms – 5 • Let‟s look at these again – 100 = 1 The exponent is called the – 101 = 10 logarithm of the number – 102 = 100 That is: – 103 = 1,000 The logarithm of 1 = 0 – 104 = 10,000 The logarithm of 10 = 1 The logarithm of 100 = 2, etc. TCOM 551 Lecture number 1 61 Fall 2009 Logarithms – 6 • Question: – The logarithm of 1 to the base 10 (written as log101) = 0 and log1010 = 1. What if I want the logarithm of a number between 1 and 10? • Answer: – You know the answer must lie between 0 and 1 – The answer = x, where x is the exponent of 10 – Ummmmmh???? We’ll do an example TCOM 551 Lecture number 1 62 Fall 2009 Logarithms – 7 • Question – What is the logarithm of 3? • Answer: – We want log103 – Let log103 = x – Transposing, we have 10x = 3 – And 100.4771213 = 3, giving x = 0.4771 – Thus log103 = 0.4771 TCOM 551 Lecture number 1 63 Fall 2009 Logarithms – 8 • More Examples – What is log10 4? – What is log10 7? – What is log10 7.654? – What is log10 24? – What is log10 4123.68? – What is log10 0.69? TCOM 551 Lecture number 1 64 Fall 2009 Logarithms – 9 • More Examples (Answers) – What is log10 4? = 0.6021 – What is log10 7? = 0.8451 – What is log10 7.654? = 0.8839 – What is log10 24? = 1.3802 – What is log10 4123.68? = 3.6153 – What is log10 0.69? = -0.1612 0.69 is < 1 so the answer must be below 0 TCOM 551 Lecture number 1 65 Fall 2009 Logarithms – 10 • Question – What if I want to have a logarithm of the value “x” with a different base? • Answer – Let‟s assume you want to have loga of x, i.e. the base is “a” and not 10 – Then loga x =(log10 x) / (log10 a) Example TCOM 551 Lecture number 1 66 Fall 2009 Logarithms – 11 • Question – What is log2 10? (i.e. base “a” = 2 and the number x =10) • Answer – Since loga x =(log10 x) / (log10 a) – Log210 = (log1010) / (log102) = 1/0.301 = 3.3219 TCOM 551 Lecture number 1 67 Fall 2009 Logarithms – 12 • Let‟s look at this another way: – Log2 10 = 3.3219 • Remember, if loga (number) = x, we can transpose this to ax = (number) • Thus, another way of looking at – Log2 10 = 3.3219 is to write – 23.3219 = 10 But what if the exponent is always a whole number? TCOM 551 Lecture number 1 68 Fall 2009 Logarithms – 13 • 20 = 1 log2 1 = 0 This is the • 21 = 2 log2 2 = 1 Binary • 22 = 4 log2 4 = 2 System • 23 = 8 log2 8 = 3 Log2 is • 24 = 16 log2 16 = 4 fundamental to Information • 25 = 32 log2 32 = 5 Theory • 26 = 64 log2 64 = 6 TCOM 551 Lecture number 1 69 Fall 2009 Logarithms – 14 • Note you can go forwards (logarithm) and backwards (anti-logarithm), thus – If log 10 (number) = x • Then – The anti-logarithm of a (value = x) is given by 10x • So the calculator button “log” gives the logarithm and the calculator button “10x” gives the anti-logarithm TCOM 551 Lecture number 1 70 Fall 2009 Logarithms – 15 • Standard notations – A log10 (number) is normally written as log (number) - i.e. leave off the 10; e.g. log10 = 1 – A logarithm that uses the exponential value, e, as a base, referred to as a “natural” logarithm, is written as loge (number), or ln (number) – All other bases must be included if they are not 10 or e; e.g. log2 (number) TCOM 551 Lecture number 1 71 Fall 2009 Logarithms – 16 • So how do logarithms help us? • Answer: by converting to logarithms – Instead of multiplying you can add – Instead of dividing you can subtract – [They are also an intermediate step (see later)] • How is that possible? – See example on the next slide TCOM 551 Lecture number 1 72 Fall 2009 Logarithms – 17 2+3=5 • Example – 100 1,000 = 102 103 = 105 – 297 4735 = 102.4728 103.6753 = 106.1481 = 1,406,294.998 – 3879 193 = 103.5907 102.2856 = 101.3051 = 20.1917 • Big Deal! My calculator can do that stuff in zero seconds flat! So: read on! TCOM 551 Lecture number 1 73 Fall 2009 Logarithms – 18 • What if the numbers are really large or really small? • Examples – (1,387.465 1014) (893 109) – (1.38 10-23) (10, 397) (283) • But logarithms are really an intermediate step to decibels (written as dB) TCOM 551 Lecture number 1 74 Fall 2009 Decibel (dB) Notation – 1 • Historically the Bel, named after Alexander Graham Bell, is a unit of sound • It was developed as a ratio measure: i.e., it compares the various sound levels • The Bel was found to be too large a value and so a tenth of a Bel was used, i.e., the decibel • A decibel, or 1 dB, was found to be the minimum change in sound level a human ear could detect TCOM 551 Lecture number 1 75 Fall 2009 Decibel (dB) Notation – 2 • Question – How do you get a dB value? • Answer – Take the log10 value and multiply it by 10 • Example – One number is 7 times larger than another. The dB difference = 10 log107 = 10 0.8451 = 8.5 dB NOTE: Never quote a dB number to more than one place of decimals TCOM 551 Lecture number 1 76 Fall 2009 Decibel (dB) Notation – 3 • Some things to remember – A dB value is always 10 log10 ; it is never, ever, 20 log10 , however ….. – 10 log10 (x)a = 10 a log10 (x) • e.g. 10 log10 (x)2 = 10 2 log10 (x) = 20 log 10 (x) – The dB ratio may be referenced to a given level, for example • 1 W (unit would be dBW) Some examples • 1 mW (unit would be dBm) TCOM 551 Lecture number 1 77 Fall 2009 Decibel (dB) Notation – 4 • Question – An amplifier increases power by a ratio of 17:1, what is the dB gain? • Answer – 10 log10 17 = 12.3 dB • Question – The amplifier is fed with 1W, how many watts are output? • Answer – 17 Watts which is equivalent to 12.3 dBW TCOM 551 Lecture number 1 78 Fall 2009 Decibel (dB) Notation – 5 • NOTE: – Whenever you have just “dB” after a number, then it is merely a ratio. EG: 3dB bigger just means twice as big. It gives you no measure of the absolute amount. – Whenever you have additional letters after “dB”, this will tell you the absolute value. EG: 3dBW means 3dB bigger than a watt = 2 watts. TCOM 551 Lecture number 1 79 Fall 2009 Decibel (dB) Notation – 6 • Examples of dB notations of power, etc. – 425 W 26.3 dBW – 425 W = 425,000 mW 56.3 dBm – 0.3 W -5.2 dBW – 0.3W = 300 mW 24.8 dBm – 24,500 K 43.9 dBK – -273 K Error – you cannot take a logarithm of a negative number TCOM 551 Lecture number 1 80 Fall 2009 TCOM 551 & ECE 463 Lect. 1 Outline • Sine Wave Review • Frequency, Phase, & Wavelength • Logarithms and dB (decibel) notation • Core Concepts of Digital Communications – Source info., Carrier Signal, Modulation – C/N, S/N, and BER – Performance & Availability TCOM 551 Lecture number 1 81 Fall 2009 Core Concepts of Digital Communications – 1 Frequency Frequency Amplification Reception and and transmission Transmission medium amplification RF RF to to IF IF Modulation Demodulation Channel coding Channel decoding Multiplexing Demultiplexing Source encoding Sink; Source; Information user Distance TCOM 551 Lecture number 1 82 Fall 2009 Core Concepts of Digital Communications – 2 Frequency Frequency Amplification Reception and and transmission Transmission medium amplification RF RF to to Lectures 2, 6, 7, 11, 12, &14 IF IF Lectures 3, 4, & 8 Lectures Modulation 9 & 10 Demodulation Channel coding Lecture 13 Channel decoding Multiplexing Lecture 4 Demultiplexing Lectures 3 & 5 Source encoding Sink; Source; Information user Distance TCOM 551 Lecture number 1 83 Fall 2009 Key Design Issues – 1 • S/N – Signal-to-Noise Ratio (Analog) • Need to be above user‟s threshold for Required QoS • C/N We will – Carrier-to-Noise Ratio (Analog and Digital) look at • Need to be above demodulation threshold for useful transfer of information each of • BER these – Bit Error Rate (Sometimes Bit Error Ratio) S/N • Need to satisfy the Performance and Availability Specifications TCOM 551 Lecture number 1 84 Fall 2009 Signal-to-Noise Ratio – 1 • Signal-to-Noise, written as S/N, is mainly used for Analog Systems • S/N is specified at the Baseband of the Information Channel Baseband is a Information is what is sent range of to the user and the channel frequencies over which it is sent is the close to zero Information Channel TCOM 551 Lecture number 1 85 Fall 2009 Signal-to-Noise Ratio – 2 • What S/N value gives a good reception? – Telephone and TV channels require a minimum of 50 dB 50 dB ratio of 100,000 IE:the Signal power is 100,000 > the Noise power • Analog signals have “graceful degradation” characteristics TCOM 551 Lecture number 1 86 Fall 2009 Signal-to-Noise Ratio – 3A Digital signal Analog signal S/N Good Level Marginal or Bad Eb/N o100 80 60 40 20 0 Percentage Time above Threshold TCOM 551 Lecture number 1 87 Fall 2009 Many times you will find performance and availability curves with this perspective Signal-to-Noise Ratio – 3B Digital signal Analog signal S/N Good Level Marginal or Bad Eb/N o0 20 40 60 80 100 Percentage Time above Threshold TCOM 551 Lecture number 1 88 Fall 2009 Signal-to-Noise Ratio – 4 • The S/N is what the user perceives, but it is usually measured at the demodulator output User‟s Received Output signal Demodulator S/N Application Device • The C/N at the demodulator input will determine the output S/N TCOM 551 Lecture number 1 89 Fall 2009 Carrier-to-Noise Ratio – 1 • Carrier-to-Noise, written as C/N, is used for both Analog and Digital Systems • The Carrier signal has information from the sender impressed upon it, through modulation. The carrier, plus the modulated information, will pass through the wideband portion of transmitter and receiver, and also over the transmission path ??? TCOM 551 Lecture number 1 90 Fall 2009 Carrier-to-Noise Ratio – 2 = Wideband (passband) signal with modulation = Baseband signal with raw information Transmitter Receiver The C/N at the input to the demodulator is RF RF the key design point in any Mixer Mixer communications system IF IF Information Information to be sent Modulator Demodulator received TCOM 551 Lecture number 1 91 Fall 2009 Carrier-to-Noise Ratio – 3 Input Useful output? C/N Demodulator C/N Conservative design Level 12 10 (10 dB) with no coding Can use these 8 C/N levels with 6 Coding, etc. 4 2 0 TCOM 551 Lecture number 1 92 Fall 2009 Carrier-to-Noise Ratio – 4 • Useful design reference for uncoded QPSK BER = 10-6 at 10.6 dB input C/N to Demodulator BER? 10.6 dB BER 10-3 BER Voice Maximum 10-4 10-5 10-6 BER Data Maximum 10-7 10-8 Goal is ≤ 10-10 0 10 20 30 C/N TCOM 551 Lecture number 1 93 Fall 2009 BER – 1 • BER means Bit Error Rate, however some people refer to it as the Bit Error Ratio (i.e. the ratio of bad to good bits) • Strictly speaking, it is the Probability that a single Bit Error will occur • BER is usually given as a power exponent, e.g. 10-6, which means one error in 106 bits TCOM 551 Lecture number 1 94 Fall 2009 BER – 2 • A BER of 10-6 means on the order of one error in a page of a FAX message • To improve BER, channel coding is used – FEC codes – Interleaved codes • Communications systems are specified in many ways, but the two most common are performance and availability TCOM 551 Lecture number 1 95 Fall 2009 BER – 3 • Performance – Generally specified as a BER to be maintained for a very high percentage of the time (usually set between 98% and 99% of the time) • Availability – Generally specified as a minimum BER below which no information can be transmitted successfully - i.e. an outage occurs TCOM 551 Lecture number 1 96 Fall 2009 Fig. 8.4 in Pratt et al., Satellite Communications BER – 4 TCOM 551 Lecture number 1 97 Fall 2009 BER – 5 • What causes the change in BER? • Since BER is determined by C/N, change in BER is caused either by – Changes in C (i.e. carrier power level) • Antenna loses track We will • Attenuation of signal look at – Changes in N (i.e. noise power level) this one • Interference • Enhanced noise input TCOM 551 Lecture number 1 98 Fall 2009 BER – 6 Attenuation, dB 99.999% = 0.001% outage is a 20 typical single-hop specification 19 dB 16 99.99% = 0.01% outage is a typical high availability spec. 12 99.7% = 0.03% outage 8 is a typical VSAT spec. 6 dB 4 3 dB 0 100 10 1 0.1 0.01 0.001 Percentage of the Time TCOM 551 Lecture number 1 99 Fall 2009 BER – 7 Performance & Availability BER 10-10 Exceeds Performance Spec. 10-8 10-6 Exceeds Availability Spec. Does not meet 10-4 Performance or 10-2 Availability Specs. 100 10 1 0.1 0.01 0.001 Percentage of the Time TCOM 551 Lecture number 1 100 Fall 2009 BER – 8 Performance & Availability BER 10-10 With Coding 10-8 10-6 Without Coding 10-4 10-2 100 10 1 0.1 0.01 0.001 Percentage of the Time TCOM 551 Lecture number 1 101 Fall 2009

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 18 |

posted: | 8/2/2011 |

language: | English |

pages: | 101 |

OTHER DOCS BY pptfiles

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.