Transcript Chapter1_Lect2.ppt

Chapter 1
INTRODUCTION
 Propagation of Electromagnetic Waves
 Information Measure
 Channel Capacity and Ideal Communication
Systems
Huseyin Bilgekul
Eeng360 Communication Systems I
Department of Electrical and Electronic Engineering
Eastern Mediterranean University
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Frequency Bands
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Regulations specify, modulation type, bandwidth, power,
type of information and etc. that a user can transmit
over designed frequency bands.
Frequency assignments and technical standards are set
internationally by International Telecommunication
Union (ITU).
Each nation of ITU retains sovregnity over spectral
usage and standards adopted in its territory.
Each nation is expected to abide by the overall
frequency plan adopted by ITU.
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Propagation of Electromagnetic Waves
The propagation characteristics of electromagnetic waves
used in wireless channels are highly dependent on the
frequency.
 Based on carrier frequency EM wave propagations can be
classified as:
• GROUND-WAVE PROPAGATION
• SKY-WAVE PROPAGATION
• Line of Sight (LOS) PROPAGATION
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Ionized Regions Above Earth.
• Ionization of air is caused
by UV rays from the sun.
• Ionized air shows different
properties at different
levels (Density and pressure).
• Speed of the wave differs
with the changing properties.
• Dominant regions are
named as D, E, F1 and F2 .
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GROUND-WAVE PROPAGATION
 Dominant mode of propagation for frequencies below 2 MHz.
 Diffraction of the wave causes the wave to propagate along the surface
of the earth.
 This propagation mode is used in AM Radio Broadcasting.
 Diffraction of waves in “D” layer helps propagation along the surface of
earth.
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SKY-WAVE PROPAGATION
 Dominant mode of propagation for EM waves in the
frequency range of 2 MHz to 30 MHz.
 Long coverage is obtained by reflection of wave at the
ionosphere and at the Earth’s boundary.
 This mode is used in HF band International Broadcasting
(Shortwave Radio).
 Sky-wave propagation is caused primarily by reflection
from the F layer (90 to 250 miles in altitude).
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SKY-WAVE PROPAGATION
 The refraction index of the ionosphere can be approximated as
Where,
n -- Refractive index,
N -- Free electron density (number of electrons/m3) ( ~ 1010/m3)
f -- Frequency of the wave (Hz).
 Refractive index will change gradually with the altitude.
 Traveling waves will gradually bend according to Snell’s law.
nr Sin φr = ni Sin φi
 Waves will be bent back to earth. Ionosphere acts as a reflector.
Transmitting station will have coverage areas along the surface of earth.
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LINE-OF SIGHT (LOS) PROPAGATION
 Dominant mode of propagation for EM waves above 30 MHz.
 Since the frequency is high,
f2 >> 81 N so that n ≈ 1 ( Free Space)
 This mode can be used in Satellite Communications.
 The disadvantage of LOS is that the signal path has to be above the horizon and
the receiver antennas need to be placed on tall towers so that they can see
each other.
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LOS Calculations
 Let’s assume
d = Distance to the horizon;
h = Antenna height...
r = Effective radius of earth Where h << r
d 2  r 2  ( r  h) 2
or d 2  2rh  h 2
d  2rh
 Effective radius of earth = 4/3 * real radius
Effective radius of earth
r = 4/3 * 3960 = 5280 miles
Converting feet to mile
Example: For a television station with an h=1000 ft
tower,
d = √(2000) = 44.7 miles.
The transmitter will cover an area of 44.7 miles
around.
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Measuring Information
 Definition: Information Measure (Ij)
The information sent from a digital source (Ij) when the jth
massage is transmitted is given by:
where Pj is the probability of transmitting the jth message.
• Messages that are less likely to occur (smaller value for Pj) provide
more information (large value of Ij).
• The information measure depends on only the likelihood of sending
the message and does not depend on possible interpretation of the
content.
• For units of bits, the base 2 logarithm is used;
• if natural logarithm is used, the units are “nats”;
• if the base 10 logarithm is used, the units are “hartley”.
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Measuring Information
 Definition: Average Information (H)
The average information measure of a digital source is,
– where m is the number of possible different source messages.
– The average information is also called Entropy.
• Definition: Source Rate (R)
The source rate is defined as,
– where H is the average information
– T is the time required to send a message.
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Measuring Information-Example1.1
 Find the information content of message that consists of a digital word 12
digits long in which each digit may take on one of four possible levels. The
probability of sending any of the four levels is assumed to be equal, and
the level in any digit does not depend on the values taken on by pervious
digits.
Answer:
Possible combinations of 12 digits ( # of possible messages) = 412
Because each level is equally likely,
all different words are equally likely.
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Channel Capacity & Ideal Comm. Systems
 For digital communication systems, the “Optimum System” may defined as
the system that minimize the probability of bit error at the system output subject
to constraints on the energy and channel bandwidth.
 Is it possible to invent a system with no error at the output
even when we have noise introduced into the channel?
Yes under certain assumptions !.
 According Shannon the probability of error would approach zero, if R< C
Where
• R - Rate of information (bits/s)
• C - Channel capacity (bits/s)
Capacity is the maximum amount of information that
a particular channel can transmit. It is a theoretical
upper limit. The limit can be approached by using
Error Correction
 B - Channel bandwidth in Hz and
 S/N - the signal-to-noise power ratio
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Channel Capacity & Ideal Comm. Systems
ANALOG COMMUNICATION SYSTEMS
In analog systems, the OPTIMUM SYSTEM might be defined as the one that
achieves the Largest signal-to-noise ratio at the receiver output, subject to
design constraints such as channel bandwidth and transmitted power.
Question:
Is it possible to design a system with infinite signal-to-noise ratio at the output
when noise is introduced by the channel?
Answer: No!
DIMENSIONALITY THEOREM for Digital Signalling:
Nyquist showed that if a pulse represents one bit of data,
noninterfering pulses can be sent over a channel no faster than 2B
pulses/s, where B is the channel bandwidth.
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Problems
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Problems
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