551 TCOM & ECE 463 DIGITAL COMMUNICATIONS
SPRING 2007 IN 206 Tuesdays 4:30 7:10 p.m. Dr. Jeremy Allnutt [e-mail]
TCOM 551 & ECE 463 Spring 2007
Lecture number 1
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General Information - 1
Contact Information
Room: Science & Technology II, Room 269 Telephone [phone] Email: [e-mail] Office Manager: TBD [phone] Email: TBD
Office Hours
Mondays and Wednesdays 3:00 6:00 p.m. Please, by appointment only
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General Information - 2
Course Outline
Go to http://telecom.gmu.edu and click on course schedule Scroll down to TCOM 551
Bad weather days: call [phone] You MUST Have The Following
Bateman Textbook, preferably also Kolimbiris A Mathematical Calculator please, simple ones only
TCOM 551 & ECE 463 Spring 2007 Lecture number 1 3
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 & ECE 463 Spring 2007 Lecture number 1 4
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 give assumptions used to find the solution
TCOM 551 & ECE 463 Spring 2007 Lecture number 1 5
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 & ECE 463 Spring 2007 Lecture number 1 6
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
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TCOM 551 & ECE 463 Spring 2007
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, etc.)? Talking appliances?
Etc.!!!
TCOM 551 & ECE 463 Spring 2007
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General Information - 7
Class Grades Emphasis is on overall effort and results Balance between homework, tests, paper + final exam:
Homework Tests Final exam Term Paper
Lecture number 1
-
15% 30 + 30% 25% 0%
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TCOM 551 & ECE 463 Spring 2007
Term Paper Grade Percentage
No mark will be allocated towards the paper. The paper will be graded as triple plus (3+), through dot (), to triple minus (3). A student with a final grade on the borderline between two grades may be moved up across the borderline if his/her paper is more than a plus (+). 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 in half
TCOM 551 & ECE 463 Spring 2007 Lecture number 1 10
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 - February 27th - April 10th - In-Class Final exam scheduled for - May 8th (very exceptionally, May 15th)
TCOM 551 & ECE 463 Spring 2007 Lecture number 1 11
TCOM 551 & ECE 463 Course Plan
Please remember:
If there is a snow day before Spring Break (March 11th through 18th), we will have a makeup class during the spring break (*) If there is a "snow day" after the Spring Break, we will probably only have a make-up class if we lose more than one lecture (see slide 11)
(*) Undergraduates taking ECE 463 who have made plans for spring break should let me know if we do require a make-up lecture during spring break
TCOM 551 & ECE 463 Spring 2007 Lecture number 1 12
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 & ECE 463 Spring 2007 Lecture number 1 13
Sine Wave Review - 1
We all know that the Sine of an angle is the opposite side divided by the hypotenuse, i.e.
B
A
Sine (a) = A/B
But what happens if line B rotates about Point P?
Angle a Point P
TCOM 551 & ECE 463 Spring 2007
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Sine Wave Review - 2
Line B now describes a circle about Point P
B
a
Point P
What happens if we shine a light from the left and project the shadow of B onto a screen?
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TCOM 551 & ECE 463 Spring 2007
Sine Wave Review - 3
End of "B" projected onto the screen
Point P
Light from the left
TCOM 551 & ECE 463 Spring 2007 Lecture number 1
B
a
Screen on the right
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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. What happens if we move the screen to the right and `remember' where the projected end of "B" was?
Screen on the right
TCOM 551 & ECE 463 Spring 2007 Lecture number 1 17
Sine Wave Review - 5
Locus of "B" end-point
We have a Sine Wave!
One oscillation = One wavelength,
a.k.a. SHM
Screen Position 1 TCOM 551 & ECE 463 Spring 2007
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Screen Position 218
Sine Wave Review - 5
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 & ECE 463 Spring 2007 Lecture number 1 19
Sine and Cosine Waves 1
Sine Wave
Sine Wave = Cosine Wave shifted by 90o
0o
90o
180o
270o
0 = 360o
90o
180o
Cosine Wave TCOM 551 & ECE 463 Spring 2007
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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.ht m
It is very slow to load: have patience!
TCOM 551 & ECE 463 Spring 2007 Lecture number 1 21
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
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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 Wave TCOM 551 & ECE 463 Spring 2007
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http://en.wikipedia.org/wiki/Image:Sine_Cosine_Graph.png
Sine and Cosine Waves 5
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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 & ECE 463 Spring 2007 Lecture number 1 25
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").
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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
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Sine and Cosine Waves - 7
"Cosine Wave" Sine Wave
Sine and Cosine waves can therefore be considered to be at right angles, i.e. orthogonal, to each other
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TCOM 551 & ECE 463 Spring 2007
Lecture number 1
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
In-phase component Orthogonal component
Where j = ( -1 ) We will only consider Real signals
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Real
Imaginary
Lecture number 1
TCOM 551 & ECE 463 Spring 2007
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 & ECE 463 Spring 2007 Lecture number 1 30
Sine and Cosine Waves - 10
Time varying signal
V(t) = A cos ( t + ) Instantaneous value of the signal Vary these to Modulate the signal
Phase: PM; PSK Frequency: FM; FSK Amplitude: AM; ASK Note: = 2 f
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TCOM 551 & ECE 463 Spring 2007
Back to our Sine Wave 1 Defining the Wavelength
The wavelength is usually defined at the "zero crossings"
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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 & ECE 463 Spring 2007 Lecture number 1 33
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 & ECE 463 Spring 2007 Lecture number 1 34
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. 2. 720o/s = 2 revolutions/s = 2 Hz 18,000o/s = 18,000/360 revs/s = 50 revs/s = 50 Hz
TCOM 551 & ECE 463 Spring 2007 Lecture number 1 35
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 & ECE 463 Spring 2007 Lecture number 1 36
d /dt Digression - 1
kilometers 16 12 8 4 0 0 1 2 3 4 5 Time, hours 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? 6 7 8 9
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d /dt Digression - 2
kilometers 16 12 8 4 0 0 1 2 3 You can compute the Average Velocity using distance/time, (i.e. 16/8 = 2 km/h), but how do you get the person's speed at any particular point? 4 5 6 7 8 9 Time, hours Answer: you differentiate, which means you find the slope of the line.
Lecture number 1 38
TCOM 551 & ECE 463 Spring 2007
d /dt Digression - 3
kilometers 16 A 12 8 4 0 0 1 2 3 4 5 6 Time, hours 7 B 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/B In this case, A is in km and B is in hours. It could 8 9 equally well be phase, , and time, t.
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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 & ECE 463 Spring 2007 Lecture number 1 40
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
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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 Frequency
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Velocity of light
TCOM 551 & ECE 463 Spring 2007 Lecture number 1
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 = (3108) 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 & ECE 463 Spring 2007 Lecture number 1 43
Digression - UNITS
Standard units to use are MKS
M = meters K = kilograms S = seconds
So: do not mix written as m feet with meters written as kgm and pounds with written as s kilograms
Hence
the velocity of light is in m/s The wavelength is in m And the frequency is in Hz = hertz
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Carrier signals - 3
A Carrier Signal can
carry just one channel of information (this is often called Single Channel Carrier Per = SCPC) Or carry many channels of information at the same time, usually through a Multiplexer
Single Channel
Tx
SCPC
Note: The modulator has been omitted in these drawings
Multiplexer
Multi-channel carrier
Tx
Multiplexed Carrier
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TCOM 551 & ECE 463 Spring 2007
Lecture number 1
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 & ECE 463 Spring 2007 Lecture number 1 46
Logarithms - 2
1, 2, 3, 4, 5, 6, 7, 8, 9, 10 We actually count To be easier to see, this should be from 1 to 10 but written as the series the numbering 00, 01, 02, 03, 04, 05, .... 09, 10 11, 12, 13, 14, 15 ..... ..... 91, ......, 97, 98, 99, 100 ... 991, ....., 997, 998, 999, 1000
TCOM 551 & ECE 463 Spring 2007 Lecture number 1
goes from 0 to 9, then we change the first digit and go from 0 to 9 again, and so on
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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 & ECE 463 Spring 2007 Lecture number 1 48
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
Lecture number 1 49
TCOM 551 & ECE 463 Spring 2007
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?
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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
Do you detect any logic here? The number of zeroes is the same as the value of the exponent
Lecture number 1 51
TCOM 551 & ECE 463 Spring 2007
Logarithms - 5
Let's 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 is: The logarithm of 1 = 0 The logarithm of 10 = 1 The logarithm of 100 = 2, etc.
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TCOM 551 & ECE 463 Spring 2007
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 & ECE 463 Spring 2007 Lecture number 1 53
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 & ECE 463 Spring 2007 Lecture number 1 54
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 & ECE 463 Spring 2007 Lecture number 1 55
Logarithms - 9
More Examples (Answers)
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 & ECE 463 Spring 2007
= = = = =
0.6021 0.8451 1.3802 3.6153 -0.1612
0.8839
0.69 is < 1 so the answer must be below 0
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Lecture number 1
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 & ECE 463 Spring 2007 Lecture number 1 57
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 & ECE 463 Spring 2007 Lecture number 1 58
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
TCOM 551 & ECE 463 Spring 2007
But what if the exponent is always a whole number?
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Logarithms - 13
20 = 1 21 = 2 22 = 4 23 = 8 24 = 16 25 = 32 64 26 = ECE 463 Spring 2007 TCOM 551 & log2 1 = 0 log2 2 = 1 log2 4 = 2 log2 8 = 3
This is the
Binary System
Log2 is fundamental to
log2 16 = 4 Information log2 32 = 5 Theory
Lecture number 1 2
log 64 = 6
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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 & ECE 463 Spring 2007 Lecture number 1 61
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)
TCOM 551 & ECE 463 Spring 2007 Lecture number 1 62
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
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Logarithms - 17
Example
2+3=5 100 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 & ECE 463 Spring 2007 Lecture number 1 64
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 & ECE 463 Spring 2007 Lecture number 1 65
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 & ECE 463 Spring 2007 Lecture number 1 66
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
Lecture number 1 TCOM 551 & ECE 463 Spring 2007 67
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) 1 463 Spring 2007 TCOM 551 & ECEmW (unit would benumber 1 Lecture dBm)
Some examples
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Decibel (dB) Notation - 3
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 & ECE 463 Spring 2007 Lecture number 1 69
Decibel (dB) Notation - 4
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
Lecture number 1 70
TCOM 551 & ECE 463 Spring 2007
Core Concepts of Digital Communications - 1
Frequency Amplification and transmission RF to IF Modulation Channel coding Multiplexing Source encoding Source; Transmission medium Frequency Reception and amplification RF to IF Demodulation Channel decoding Demultiplexing Sink; Information user
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Distance
TCOM 551 & ECE 463 Spring 2007 Lecture number 1
Core Concepts of Digital Communications - 2
Frequency Amplification and transmission RF to IF Modulation Channel coding Multiplexing Source encoding Source; Transmission medium Lectures 2, 6, 7, 11, 12, &14 Lectures 3, 4, & 8 Lectures 9 & 10 Lecture 13 Lecture 4 Lectures 3 & 5 Distance
TCOM 551 & ECE 463 Spring 2007 Lecture number 1 72
Frequency Reception and amplification RF to IF Demodulation Channel decoding Demultiplexing Sink; Information user
Key Design Issues - 1
S/N
Signal-to-Noise Ratio (Analog)
Need to be above user's threshold for Required QoS
C/N
Carrier-to-Noise Ratio (Analog and Digital)
Need to be above demodulation threshold for useful transfer of information
BER
Need to satisfy the Performance and Availability Specifications
TCOM 551 & ECE 463 Spring 2007 Lecture number 1
We will look at each of these
Bit Error Rate (Sometimes Bit Error Ratio) S/N
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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 range of frequencies close to zero
TCOM 551 & ECE 463 Spring 2007
Information is what is sent to the user and the channel over which it is sent is the Information Channel
Lecture number 1 74
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 & ECE 463 Spring 2007 Lecture number 1 75
Signal-to-Noise Ratio - 3
S/N
Level B
Analog Reception
A Good Marginal Bad
100
80 60 40 20 Percentage Time above Threshold
Lecture number 1
0
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TCOM 551 & ECE 463 Spring 2007
Signal-to-Noise Ratio - 4
The S/N is what the user perceives, but it is usually measured at the demodulator output
Received signal
Demodulator
Output S/N
User's Application Device
The C/N at the demodulator input will determine the output S/N
TCOM 551 & ECE 463 Spring 2007 Lecture number 1 77
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 & ECE 463 Spring 2007 Lecture number 1 78
Carrier-to-Noise Ratio - 2
= Wideband (passband) signal with modulation = Baseband signal with raw information Transmitter RF Mixer Information to be sent IF Modulator Receiver RF Mixer IF Demodulator
Lecture number 1
The C/N at the input to the demodulator is the key design point in any communications system
Information received
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TCOM 551 & ECE 463 Spring 2007
Carrier-to-Noise Ratio - 3
Input C/ N
C/N 12 10 8 6 4 2 0
Demodulator
Useful output?
Conservative design Level (10 dB) with no coding
Can use these C/N levels with Coding, etc.
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Carrier-to-Noise Ratio - 4
Useful design reference for uncoded QPSK
BER = 10-6 at 10.6 dB input C/N to Demodulator
BER 10-3 10-4 10-5 10-6 10-7 10-8 0 10.6 dB BER Voice Maximum BER Data Maximum Goal is 10-10
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BER?
10
20
Lecture number 1
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C/N
TCOM 551 & ECE 463 Spring 2007
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 & ECE 463 Spring 2007 Lecture number 1 82
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 & ECE 463 Spring 2007 Lecture number 1 83
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 & ECE 463 Spring 2007 Lecture number 1 84
Fig. 8.4 in Pratt et al., Satellite Communications
BER - 4
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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 Attenuation of signal We will look at this one
Changes in N (i.e. noise power level)
Interference Enhanced noise input
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BER - 6
Attenuation, dB 20 16 12 8 4 0 100 10 1 0.1 0.01 Percentage of the Time
Lecture number 1
99.999% = 0.001% outage is a typical single-hop specification 99.99% = 0.01% outage is a typical high availability spec. 99.7% = 0.03% outage is a typical VSAT spec.
19 dB
6 dB 3 dB 0.001
87
TCOM 551 & ECE 463 Spring 2007
BER 7 Performance & Availability
BER 10-10 10-8 10
-6
Exceeds Performance Spec. Exceeds Availability Spec. Does not meet Performance or Availability Specs.
10 1 0.1 0.01 Percentage of the Time
Lecture number 1
10-4 10-2 100
0.001
88
TCOM 551 & ECE 463 Spring 2007
BER 8 Performance & Availability
BER 10-10 With Coding 10-8 10-6 10
-4
Without Coding
10-2 100 10 1 0.1 0.01 Percentage of the Time
Lecture number 1
0.001
89
TCOM 551 & ECE 463 Spring 2007