TCOM 551 DIGITAL COMMUNICATIONS_1_

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					          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

				
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