TCOM 551 DIGITAL COMMUNICATIONS

1
TCOM 551DIGITAL COMMUNICATIONS

• FALL 2003
• IN 204 Tuesday 430 710 p.m.
• Dr. Tuna Alper tuna.alper_at_verizon.n
  et

2
General Information - 1

• Contact Information
• - Email tuna.alper_at_verizon.net
• Consultation Hours
• Tuesdays 300 400 p.m. In Room ST2-235, by
  appointment

3
General Information - 2

• Course Outline
• Go to http//telecom.gmu.edu
• Scroll down to TCOM 551
• Snow Days Call [phone]
• You MUST Have The Following
• Both Textbooks
• A Mathematical Calculator

4
General Information - 3

• Homework Assignments
• Feel free to work together on these, BUT
• All submitted work must be your own work

5
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 give assumptions used
  to find the solution

6
General Information 5__________________________
___

• Term Paper
• Any topic in the field of Digital Communications
• About 10 pages long
• Can work alone or in small groups
• Get topic cleared by COB September 16th
• Paper due by COB November 18th

7
General Information - 6

• Possible examples of term paper topics
• TDMA vs. CDMA in various applications
• What is LD-CELP and how does it help?
• MPEG-2 and its applications
• Digital imaging and its impact on sports casting
• DBS Analog to Digital and its progression
• What is a smart antenna and its applications
• Spectrum congestion in telecom and its impact
• Wireless technology Bluetooth and IEEE 802.11b
• Etc.

8
General Information - 7

• Class Grades
• Emphasis on overall effort and results
• Final grade will be based on a balance between
  homework, tests, final exam
• Homework - 15
• Tests - 25 25
• Paper Final exam - 35

9
TCOM 551 Course Plan

• Go to web site http//telecom.gmu.edu and
  scroll down to TCOM 551
• In-Class Tests scheduled for - September 30th
  - November 11th
• In-Class Final exam scheduled for - December
  2nd

10
TCOM 551 Lecture 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

11
Sine Wave Review - 1
We all know that the Sine of an angle is the
opposite side divided by the hypotenuse, i.e.
B
Sine (a) A/B
A
Angle a
But what happens if line B rotates about Point P?
Point P
12
Sine Wave Review - 2
Line B now describes a circle about Point P
B
a
What happens if we shine a light from the left
and project the shadow of B onto a screen?
Point P
13
Sine Wave Review - 3
End of B projected onto the screen
B
a
Point P
Light from the left
Screen on the right
14
Sine Wave Review - 4
End of B projected onto the screen
As line B rotates about the center point, P,
the projected end of B oscillates up and down
on the screen. If we move the screen to the
right at a steady speed, we generate a sine wave.
Screen on the right
15
Sine Wave Review - 5
Locus of B end-point
We have a Sine Wave!
One oscillation One wavelength, ?
ScreenPosition 1
ScreenPosition 2
16
Sine Wave Review - 5
RememberSine 0 0 Sine 90 1 Sine 180 0
Since 270 -1 Sine 360 Sine 0 0
1
0 90 180 270 360
Degrees
-1
17
Sine and Cosine Waves - 1
SineWave
Sine Wave Cosine Wave shifted by 90o
0o 90o 180o 270o 0 360o
90o 180o
CosineWave
18
Sine and Cosine Waves - 2
Sine and Cosine waves can therefore be considered
to be at right angles, i.e. orthogonal, to each
other
Cosine Wave
Sine Wave
19
Sine and Cosine Waves - 3

• A Radio Signal consists of an in-phase component
  and an out-of-phase (orthogonal) component
• Signal, S, is often written in the generic
  formS A cos ? j B sin ?

Where j ?( -1 )
In-phase component
Orthogonal component
We will only consider Real signals
Real
Imaginary
20
Sine and Cosine Waves - 4

• 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 ?)

21
Sine and Cosine Waves - 5
Vary these to Modulate the signal

• Time varying signal V(t) A cos (?t ?)

Phase PM PSK
Instantaneous value of the signal
Frequency FM FSK
Amplitude AM ASK
Note ? 2 ? f
22
Back to our Sine Wave 1Defining the Wavelength
The wavelength is usually defined at the zero
crossings
?
?
23
Back to our Sine Wave - 2
One revolution 360oOne 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
24
Back to our Sine Wave 3Two useful equations
The time taken to complete one cycle, or
wavelength, is the period, T.Frequency is the
reciprocal of the period, that isf 1/T
?
Phase has changed by ?The rate-of-change of the
phase, d?/dt, is the frequency, f.
25
d?/dt Digression - 1
Person walks 16 km in 4 hours. Velocity
(distance)/(time)Therefore, Velocity 16/4 4
km/h Velocity is really the rate-of-change of
distance with time.What if the velocity is not
constant?
kilometers
1612840
0 1 2 3 4 5
6 7 8 9Time, hours
26
d?/dt Digression - 2
kilometers
You can compute the Average Velocity using
distance/time,(i.e. 16/8 2 km/h), but how do
you get the persons speed at any particular
point?
1612840
0 1 2 3 4 5
6 7 8 9Time, hours
Answer you differentiate, which means you find
the slope of the line.
27
d?/dt Digression - 3
kilometers
To differentiate means to find the slope at any
instant.The slope of a curve is given by the
tangent at that point, i.e., A/BIn this case, A
is in km and B is in hours. It could equally
well be phase, ?, and time, t.
1612840
A
B
0 1 2 3 4 5
6 7 8 9Time, hours
28
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

29
Sine Wave Continued

• Can think of a Sine Wave as a Carrier
  Signal,i.e. the signal onto which the
  information is incorporated 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

30
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
31
Carrier signals - 2

• Example
• An FM radio station transmits at a carrier
  frequency of 90.9 MHz
• What is the wavelength of the carrier signal?
• Answer
• c (3108) m/s f ? (90.9 ? 106) (?)
• Which gives ? 3.3 m

Remember Make sure you are using the correct
units
32
Digression - UNITS

• 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

So do not mix feet with meters and pounds with
kilograms
33
Carrier signals - 3

• A Carrier Signal can
• carry just one channel of information (this is
  often called Single Channel Per Carrier or SCPC)
• Or carry many channels of information at the same
  time by using a Multiplexer

Single Channel
Note The modulator has been omitted in these
drawings
Tx
SCPC
Multiplexer
Multiplexed Carrier
Multi-channel carrier
Tx
34
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

35
Logarithms - 2

• 1, 2, 3, 4, 5, 6, 7, 8, 9, 10To be easier to
  see, this should be written as the series00, 01,
  02, 03, 04, 05, . 09, 10
• 11, 12, 13, 14, 15 ..
• ..
• 91, , 97, 98, 99, 100
• 991, .., 997, 998, 999, 1000

We actually count from 1 to 10 but the numbering
goes from 0 to 9, then we change the first digit
and go from 0 to 9 again, and so on
36
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

37
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

38
Logarithms 4B

• 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

Do you detect any logic here?
39
Logarithms 4C

• 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

The number of zeroes is the same as the value of
the exponent
40
Logarithms - 5

• Lets look at these again
• 100 1
• 101 10
• 102 100
• 103 1,000
• 104 10,000

The exponent is called the logarithm of the number
That isThe logarithm of 1 0The logarithm of
10 1The logarithm of 100 2, etc.
41
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

Example
42
Logarithms - 7

• Question
• What is the logarithm of 5?
• Answer
• We want log105
• Let log105 x
• Transposing, we have 10x 5
• And 100.69897 5, giving x 0.69897
• Thus log105 0.69897

43
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?

44
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 lt 1 so the answer must be below 0
45
Logarithms - 10

• Question
• What if I want to have a logarithm of the value
  x with a different base?
• Answer
• Lets 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
46
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

47
Logarithms - 12

• Lets 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?
48
Logarithms - 13

• 20 1 log2 1 0
• 21 2 log2 2 1
• 22 4 log2 4 2
• 23 8 log2 8 3
• 24 16 log2 16 4
• 25 32 log2 32 5
• 26 64 log2 64 6

This is the Binary System Log2 is fundamental to
Information Theory
49
Logarithms - 14

• Note you can go forwards (log) and backwards
  (anti-logarithm), thus
• If log 10 (number) x
• Then
• The anti-logarithm of a (value x) is given
  by10x
• So the calculator button log gives the
  logarithm and the calculator button 10x gives
  the anti-logarithm

50
Logarithms - 15

• Standard notations
• A log10 (number) is normally written as log
  (number) - i.e. leave off the 10 e.g. log 10 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)

51
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

52
Logarithms - 17
2 3 5

• Example
• 100 ? 1,000 102 ? 103 105
• 297 ? 4735 102.4728 ? 103.6753
  106.1481 1,406,295
• 3879 ? 193 103.5887 ? 102.2856 101.3031
  20.0984

53
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)

54
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

55
Decibel (dB) Notation - 1

• 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
56
Decibel (dB) Notation - 2

• 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)
• 1 mW (unit would be dBm)

Some examples
57
Decibel (dB) Notation - 3

• Question
• An amplifier increases power by a ratio of 251,
  what is the dB gain?
• Answer
• 10 log10 25 14 dB
• Question
• The amplifier is fed with 1W input power, how
  many watts are at the output?
• Answer
• 25 Watts which is equivalent to 14 dBW

58
Decibel (dB) Notation - 4

• Examples of dB notations of power, etc.
• 500 W ? 27 dBW
• 500 W 500,000 mW ? 57 dBm
• 0.4 W ? -4 dBW
• 0.4W 400 mW ? 26 dBm
• 27,000 K ? 44.3 dBK
• -273 K ? Error you cannot take logarithm of a
  negative number

59
Core Concepts of Digital Communications - 1
Frequency
Frequency
Amplification and transmission
Reception and amplification
Transmission medium
RFtoIF
RFtoIF
Modulation
Demodulation
Channel coding
Channel decoding
Multiplexing
Demultiplexing
Source encodingSource
SinkInformation user
Distance
60
Core Concepts of Digital Communications - 2
Frequency
Frequency
Amplification and transmission
Reception and amplification
Transmission medium
RFtoIF
RFtoIF
Lectures 2, 6, 7, 11, 12, 14Lectures 3, 4, 8
Lectures 9 10Lecture 13Lecture 4Lectures 3
5
Modulation
Demodulation
Channel coding
Channel decoding
Multiplexing
Demultiplexing
Source encodingSource
SinkInformation user
Distance
61
Key Design Issues - 1

• S/N
• Signal-to-Noise Ratio (Analog)
• Need to be above users threshold for Required
  QoS
• C/N
• Carrier-to-Noise Ratio (Analog and Digital)
• Need to be above demodulation thresholdfor
  useful transfer of information
• BER
• Bit Error Rate (Sometimes Bit Error Ratio) ? S/N
• Need to satisfy the Performance and Availability
  Specifications

We will look at each of these
62
Signal-to-Noise Ratio - 1

• Signal-to-Noise, written as S/N, is mainly used
  for Analog Systems
• S/N is specified at theBaseband of the
  Information Channel

Baseband is a range of frequencies close to zero
Information is what is sent to the user and the
channel over which it is sent is the Information
Channel
63
Signal-to-Noise Ratio - 2

• What S/N value gives a good reception?
• Telephone and TV channels require a minimum of 50
  dB
• Analog signals have graceful degradation
  characteristics

50 dB ? ratio of 100,000IEthe Signal power is
100,000 gt the Noise power
64
Signal-to-Noise Ratio - 3
Analog Reception
S/NLevel
A
B
Good Marginal Bad
100 80 60 40
20 0Percentage Time above
Threshold
65
Signal-to-Noise Ratio - 4

• The S/N is what the user perceives, but it is
  usually measured at the demodulator output
• The C/N at the demodulator input will determine
  the output S/N

Users Application Device
Received signal
Output S/N
Demodulator
66
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

as
67
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 the
key design point in any communications system
RF
RF
Mixer
Mixer
IF
IF
Information to be sent
Information received
Modulator
Demodulator
68
Carrier-to-Noise Ratio - 3
Input C/N
Useful output?
Demodulator
C/N121086420
Conservative design Level (10 dB) with no coding
Can use these C/N levels with Coding, etc.
69
Carrier-to-Noise Ratio - 4

• Useful design reference for QPSKBER 10-6 at
  10.6 dB input C/N to Demodulator

BER?
10.6 dB
BER10-310-410-510-610-710-8
BER Voice Maximum
BER Data Maximum
Goal is 10-10
0 10 20
30 C/N
70
BER - 1

• BER is acronym for 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

71
BER - 2

• A BER of 10-6 means on the order of one error in
  a transmission of one million bits
• 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

72
BER - 3

• Performance
• Generally specified as a BER to be maintained for
  a very high percentage of the time (usually set
  between 96 and 99.999 of the time)
• Availability
• Generally specified as a minimum BER below which
  no information can be transmitted successfully -
  i.e. an outage occurs

73
BER - 4

• 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
• Attenuation of signal
• Changes in N (i.e. noise power level)
• Interference
• Enhanced noise input

We will look at this one
74
BER - 5
Attenuation, dB
99.999 0.001 outage is a typical single-hop
specification
201612840
? 19 dB
99.99 0.01 outage is a typical high
availability spec.
99.7 0.03 outage is a typical VSAT spec.
? 6 dB
?3 dB
100 10 1
0.1 0.01 0.001
Percentage of the Time
75
BER - 6_____________________________

• Example BER Requirements and Availability for
  QPSK Transmission with rate ¾ FEC Coding
• Minimum
• BER
  Availability
• Clear Sky 10-7 95.9
• Degraded 10-6 99.36
• Degraded 10-3 99.96

76
BER 7Performance Availability
BER
Exceeds Performance Spec.
10-10
Exceeds Availability Spec.
10-8
10-6
Does not meetPerformance orAvailability Specs.
10-4
10-2
100 10 1
0.1 0.01 0.001
Percentage of the Time
77
BER 8Performance 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