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NEAR EAST UNIVERSITY
FACULTY OF ENGINEERING
DEPARTMENT OF ELECTRICAL & ELECTRONIC
ENGINEERING
EE 346
COMMUNICATION SYSTEMS
LECTURE NOTES
Prepared by
Dr. Tayseer Alshanableh
Nicosia-2007
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CHAPTER I
INTODUCTION TO COMMUNICATION SYSTEMS
The Structure of a Communication System
An electrical communication system is designed to send messages or information from a
source that generates the messages to one or more destinations. In general, a communication
system can be represented by the functional block diagram shown in Figure 1.1.
The information generated by the source may be of the form of voice (speech source), a
picture (image source), or plain text in some particular language, such as English, Japanese,
German, French, etc. an essential feature of any source that generates information is that its
output is described in probabilistic terms; that is, the output of a source is not deterministic.Otherwise, there would be no need to transmit the message.
Output
signal
Figure 1.1. Functional block diagram of a communication system.
A transducer is usually required to convert the output of a source into an electrical signal that
is suitable for transmission. For example, a microphone serves as the transducer that converts
an acoustic speech signal into an electrical signal, and a video camera converts an image into
an electrical signal. At the destination, a similar transducer is required to convert the electrical
signals that are received into a form that is suitable for the user; for example, acoustic signals,
images, etc.
The heart of the communication system consists of three basic parts, namely, the transmitter,
the channel, and the receiver. The functions performed by these three elements are described
below.
Information
source and
input transducer
Transmitter
Channel
Receiver
Output
transducer
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Transmitter
A transmitter converts the electrical signal into a form that is suitable for transmission through
the physical channel or transmission medium. For example, in radio and TV broadcast, the
Federal Communications Commission (FCC) specifies the frequency range for each
transmitting station. Hence, the transmitter must translate the information signal to be
transmitted into the appropriate frequency range that matches the frequency allocation
assigned to the transmitter. Thus, signals transmitted by multiple radio stations do not
interfere with one another. Similar functions are performed in telephone communication sys-
tems, where the electrical speech signals from many users are transmitted over the same wire.
In general, the transmitter performs the matching of the message signal to the channel by a
process called modulation. Usually, modulation involves the use of the information signal to
systematically vary the amplitude, frequency, or phase of a sinusoidal carrier.In general, carrier modulation such as AM, FM, and PM is performed at the transmitter, as
indicated above, to convert the information signal to a form that matches the characteristic of
the channel. Thus, through the process of modulation, the information signal is translated in
frequency to match the allocation of the channel. The choice of the type of modulation is
based on several factors, such as
- the amount of bandwidth allocated,- the types of noise and interference that the signal encounters in transmission over the
channel, and
- the electronic devices that are available for signal amplification prior to transmission.In any case, the modulation process makes it possible to accommodate the transmission of
multiple messages from many users over the same physical channel.
In addition to modulation, other functions that are usually performed at the transmitter are
filtering of the information-bearing signal, amplification of the modulated signal, and in the
case of wireless transmission, radiation of the signal by means of a transmitting antenna.
Channel
The communications channel is the physical medium that is used to send the signal from the
transmitter to the receiver. In wireless transmission, the channel is usually the atmosphere
(free space). On the other hand, telephone channels usually employ a variety of physical
media, including wire lines, optical fibre cables, and wireless (microwave radio). Whatever
the physical medium for signal transmission, the essential feature is that the transmitted signal
is corrupted in a random manner by a variety of possible mechanisms. The most common
form of signal degradation comes in the form of additive noise, which is generated at the front
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end of the receiver, where signal amplification is performed. This noise is often called
thermal noise. In wireless transmission, additional additive disturbances are man-made noise
and atmospheric noise picked up by a receiving antenna.
Signal distortions are usually characterised as random phenomena and described in statistical
terms. The effect of these signal distortions must be taken into account in the design of the
communication system.
In the design of a communication system, the system designer works with mathematical
models that statistically characterise the signal distortion encountered on physical channels.
Often, the statistical description that is used in a mathematical model is a result of actual
empirical measurements obtained from experiments involving signal transmission over such
channels. In such case, there is a physical justification for the mathematical model used in the
design of communication systems. On the other hand, in some communication system
designs, the statistical characteristics of the channel may vary significantly with time. In such
cases, the system designer may design a communication system that is robust to the variety of
signal distortions. This can be accomplished by having the system adapt some of its
parameters to the channel distortion encountered.
Receiver
The function of the receiver is to recover the message signal contained in the received signal.
If the message signal is transmitted by carrier modulation, the receiver performs carrier
demodulation to extract the message from the sinusoidal carrier. Since the signal
demodulation is performed in the presence of additive noise and possibly other signal
distortions, the demodulated message signal is generally degraded to some extent by the
presence of these distortions in the received signal. The fidelity of the received message
signal is a function of the type of modulation, the strength of the additive noise, the type and
strength of any other additive interference, and the type of any non-additive interference.
Besides performing the primary function of signal demodulation, the receiver also performs a
number of peripheral functions, including signal filtering and noise suppression.
Digital Communication System
In a digital communication system, the functional operations performed at the transmitter and
receiver must be expanded to include message signal discrimination at the transmitter and
message signal synthesis or interpolation at the receiver. Additional functions include
redundancy removal, and channel coding and decoding.
Figure 1.2 illustrates the functional diagram and the basic elements of a digital
communication system. The source output may be either an analog signal, such as audio or
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video signal, or a digital signal, such as the output of a Teletype machine, which is discrete
in time and has a finite number of output characters. In a digital communication system, the
messages produced by the source are usually converted into a sequence of binary digits.
Figure 1.2. Basic elements of a digital communication system
Ideally, we would like to represent the source output (message) by as few binary digits as
possible. In other words, we seek an efficient representation of the source output that results
in little or no redundancy. The process of efficiently converting the output of either an analog
or a digital source into a sequence of binary digits is called source encoder or data
compression.
The sequence of binary digits from the source encoder, which we call the information
sequence, is passed to the channel encoder. The purpose of the channel encoder is to introduce
in a controlled manner some redundancy in the binary information sequence, which can be
used at the receiver to overcome the effects of noise and interference encountered in the
transmission of the signal through the channel. Thus, the added redundancy serves to increase
the reliability of the received data and improves the fidelity of the received signal. In effect,
redundancy in the information sequence aids the receiver in decoding the desired information
sequence. For example, a (trivial) form of encoding of the binary information sequence is
simply to repeat each binary digit m times, where m is some positive integer.
The binary sequence at the output of the channel encoder is passed to the digital modulator,
which serves as the interface to the communications channel. Since nearly all of the
communication channels encountered in practice are capable of transmitting electrical signals
(waveforms), the primary purpose of the digital modulator is to map the binary information
sequence into signal waveforms.
At the receiving end of a digital communications system, the digital demodulator processesthe channel-corrupted transmitted waveform and reduces each waveform to a single number
that represents an estimate of the transmitted data symbol. A measure of how well the
Information
source andinput transducer
Source
encoder
Channel
encoder
Digital
modulation
Channel
Digital
demodulator
Channel
decoder
Source
decoder
Output
transducer
Output
signal
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demodulator and encoder perform is the frequency with which errors occur in the decoded
sequence. More precisely, the average probability of a bit-error at the output of the decoder is
a measure of the performance of the demodulator-decoder combination. In general, the
probability of error is a function of the code characteristics, the types of waveforms used to
transmit the information over the channel, the transmitter power, the characteristics of the
channel (i.e., the amount of noise), the nature of the interference, etc., and the method of
demodulation and decoding. These items and their effect on performance will be discussed in
detail in subsequent chapters.
As a final step, when an analog output is desired, the source decoder accepts the output
sequence from the channel decoder, and from knowledge of the source encoding method
used, attempts to reconstruct the original signal from the source. Due to channel decoding
errors and possible distortion introduced by the source encoder and, perhaps, the source
decoder, the signal at the output of the source decoder is an approximation to the original
source output. The difference or some function of the difference between the original signal
and the reconstructed signal is a measure of the distortion introduced by the digital
communications system.
Early Work in Digital Communications
Although Morse is responsible for the development of the first electrical digital
communication system (telegraphy), the beginnings of what we now regard as modem digital
communications stem from the work of Nyquist (1924), who investigated the problem of
determining the maximum signalling rate that can be used over a telegraph channel of a given
bandwidth without intersymbol interference. He formulated a model of a telegraph system in
which a transmitted signal has the general form
n
nnTtgatS )()(
Where g(t) represents a basic pulse shape and {an} is the binary data sequence of {1}
transmitted at a rate of 1/Tbits per second.
In light of Nyquist's work Hartley (1928) considered the issue of the amount of data that can
be transmitted reliably over a bandlimited channel when multiple amplitude levels are used.
Due to the presence of noise and other interference, Hartley postulated that the receiver could
reliably estimate the received signal amplitude to some accuracy, say A. This investigation
led Hartley to conclude that there is maximum data rate that can be communicated reliably
over a bandlimited channel when the maximum signal amplitude is limited to Amax (fixed
power constraint) and the amplitude resolution isA.
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Another significant advance in the development of communications was the work of Wiener
(1942) who considered the problem of estimating a desired signal waveform s(t) in the
presence of additive noise n(t), based on observation of the received signal r(t) = s(t) + n(t).
This problem arises in signal demodulation. Wiener determined the linear filter whose output
is the best mean-square approximation tothe desired signal s(t). The resulting filter is called
the optimum linear (Wiener) filter. Hartleys and Nyquist results on the maximum
transmission rate of digital information were precursors to the work of Shannon (1948 a, b)
who established the mathematical foundations for information theory and derived the
fundamental limits for digital communication systems. In his pioneering work, Shannon
formulated the basic problem of reliable transmission of information in statistical terms, using
probabilistic models for information sources and communication channels. Based on such a
statistical formulation, he adopted a logarithmic measure for the information content of a
source. He also demonstrated that the effect of a transmitter power constraint, a bandwidth
constraint, and additive noise can be associated with the channel and incorporated into a
single parameter, called the channel capacity For example, in the case of an additive white
(spectrally flat) Gaussian noise interference, an ideal bandlimited channel of bandwidth W has
a capacity Cgiven by
P
C= W log2(1 +) bits/sWN0
where P is the average transmitted power andN0 is the power spectral density of the additive
noise. The significance of the channel capacity is as follows: If the information rate R from
the source is less than C (R < C), then it is theoretically possible to achieve reliable (error-
free) transmission through the channel by appropriate coding. On the other hand, ifR > C,
reliable transmission is not possible regardless of the amount of signal processing performed
at the transmitter and receiver. Thus, Shannon established basic limits on communication of
information and gave birth to a new field that is now called information theory.
Initially the fundamental work of Shannon had a relatively small impact on the design and
development of new digital communications systems. In part, this was due to the small
demand for digital information transmission during the 1950's. Another reason was the
relatively large complexity and, hence, the high cost of digital hardware required to achieve
the high efficiency and high reliability predicted by Shannon's theory.
Another important contribution to the field of digital communications is the work of
Kotelnikov (1947), which provided a coherent analysis of the various digital communication
systems based on a geometrical approach. Kotelnikov approach was later expanded byWozencraft and Jacobs (1965).
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The increase in the demand for data transmission during the last three decades, coupled with
the development of more sophisticated integrated circuits, has led to the development of very
efficient and more reliable digital communications systems. In the course of these
developments, Shannon's original results and the generalization of his results on maximum
transmission limits over a channel and on bounds on the performance achieved have served as
benchmarks for any given communications system design. The theoretical limits derived by
Shannon and other researchers that contributed to the development of information theory
serve as an ultimate goal in the continuing efforts to design and develop more efficient digital
communications systems.
The classic work of Hamming (1950) on error detecting and error-correcting codes to combat
the detrimental effects of channel noise came after Shannon's publications. Hamming's work
stimulated many researchers in the years that followed, and a variety of new and powerful
codes were discovered, many of which are used today in the implementation of modem
communication systems.
Communication Channels and Their Characteristics
The physical channel may be a pair of wires that carry the electrical signal, or an optical fibre
that carries the information on a modulated light beam, or an underwater ocean channel in
which the information is transmitted acoustically, or free space over which the information-
bearing signal is radiated by use of an antenna. Other media that can be characterized as
communication channels are data storage media, such as magnetic tape, magnetic disks, and
optical disks.
One common problem in signal transmission through any channel is additive noise. In
general, additive noise is generated internally by components such as resistors and solid-state
devices used to implement the communication system. This is sometimes called thermal
noise. Other sources of noise and interference may arise externally to the system, such as
interference from other users of the channel. When such noise and interference occupy the
same frequency band as the desired signal, its effect can be minimized by proper design of the
transmitted signal and its demodulator at the receiver. Other types of signal degradations that
may be encountered in transmission over the channel are signal attenuation, amplitude and
phase distortion, and multipath distortion.
Increasing the power in the transmitted signal may minimize the effects of noise. However,
equipment and other practical constraints limit the power level in the transmitted signal.
Another basic limitation is the available channel bandwidth. A bandwidth constraint is usuallydue to the physical limitations of the medium and the electronic components used to
implement the transmitter and the receiver. These two limitations result in constraining the
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amount of data that can be transmitted reliably over any communications channel.
Shannon's basic results relate the channel capacity to the available transmitted power and
channel bandwidth.
Wireline Channels
The telephone network makes extensive use of wirelines for voice signal transmission, as well
as data and video transmission. Twisted pair wirelines and coaxial cable are basically guided
electromagnetic channels, which provide relatively modest bandwidths. Telephone wire
generally used to connect a customer to a central office has a bandwidth of several hundred
kilo-hertz (kHz). On the other hand, coaxial cable has a usable bandwidth of several
megahertz (MHz). Figure 1.3 illustrates the frequency range of guided electromagnetic
channels, which includes waveguides and optical fibres.
Signals transmitted through such channels are distorted in both amplitude and phase and
further corrupted by additive noise. Twisted-pair wireline channels are also prone to crosstalk
interference from physically adjacent channels. Because wireline channels carry a large
percentage of our daily communications around the country and the world, much research has
been performed on the characterization of their transmission properties and on methods for
mitigating the amplitude and phase distortion encountered in signal transmission.
Fibre Optic Channels
Optical fibres offer the communications system designer a channel bandwidth that is several
orders of magnitude larger than coaxial cable channels. During the past decade, optical fibre
cables have been developed that have relatively low signal attenuation, and highly reliable
photonic devices have been developed for signal generation and signal detection. These
technological advances have resulted in a rapid deployment of optical fibre channels, both in
domestic telecommunication systems as well as for transatlantic and trans-pacific
communications. With the large bandwidth available on fibre optic channels it is possible fortelephone companies to offer subscribers a wide array of telecommunication services,
including voice, data, facsimile, and video.
The transmitter or modulator in a fibre optic communication system is a light source, either a
light-emitting diode (LED) or a laser. Information is transmitted by varying (modulating) the
intensity of the light source with the message signal. The light propagates through the fibre as
a light wave and is amplified periodically (in the case of digital transmission, it is detected
and regenerated by repeaters) along the transmission path to compensate for signalattenuation. At the receiver, the light intensity is detected by a photodiode, whose output is an
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electrical signal that varies in direct proportion to the power of the light impinging on the
photodiode.
Waveguide
Coaxial cable
channels
Wirelines
Channels
Figure 1.3. Frequency range for guided wire channel.
Wireless Electromagnetic Channels
In wireless communication systems, electromagnetic energy is coupled to the propagation
medium by an antenna, which serves as the radiator. The physical size and the configuration
of the antenna depend primarily on the frequency of operation. To obtain efficient radiation of
electromagnetic energy the antenna must be longer than 1/10 of the wavelength.
Consequently, a radio transmitting in the AM frequency band, say at 1 MHz (corresponding
to a wavelength of = c/fc = 300m), requires an antenna of at least 30 meters.
Figure 1.4 illustrates the various frequency bands of the electromagnetic spectrum. The mode
of propagation of electromagnetic waves in the atmosphere and in free space may be
subdivided into three categories, namely, ground-wave propagation, sky-wave propagation,
and line-of-sight (LOS) propagation.
Ultraviolet
Visible light
Infrared
1015Hz
100 mm
100 GHz
10 GHz
1 GHz
100 MHz
10 MHz
1 MHz
10Hz
100 kHz
1 kHz
Frequency
10-6
m
100m
10 cm
1m
100 km
10 m
1 km
10 k
m
1 cm
Wavelen
th
1014
Hz
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In the VLF and ELF frequency bands, where the wavelengths exceed 10 km, the earth and
the ionosphere act as a waveguide for electromagnetic wave propagation. In these frequency
ranges, communication signals practically propagate around the globe. For this reason, these
frequency bands are primarily used to provide navigational aids from shore to ships around
the world. The channel bandwidth available in these frequency bands are relatively small
(usually from 1% to 10% of the center frequency), and hence, the information that is
transmitted through these channels is relatively slow speed and, generally, confined to digital
transmission.
A dominant type of noise at these frequencies is generated from thunderstorm activity around
the globe, especially in tropical regions. Interference results from the many users of these
frequency bands.
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Ultraviolet
ExperimentalVisible light
Infrared
Millimetre wave Experimental
Navigation
Satellite to Satellite
Microwave relay
Earth-satellite
Rader
Super high
Frequency
(SHF)
Ultra High
Frequency
(UHF)UHF TV
Very High
Frequency
(VHF)
Mobile, aeronautical
VHF TV and FM
broadcast
Mobile radio
High Frequency
(HF)
Business
Amateur radio
International radio
Citizens bandMedium Frequency
(MF)AM broadcast
Aeronautical
Navigation
Radio teletypeLow Frequency
(LF)
Very Low Frequency
(VLF)
Audio
band
Figure 1.4. Frequency range wireless electro magnetic channel.
Ground-wave propagation, as illustrated in Figure 1.5, is the dominant mode of propagation
for frequencies in the MF band (0.3 to 3 MHz). This is the frequency band used for AM
broadcasting and maritime radio broadcasting. In AM broadcasting, the range with ground-
wave propagation of even the more powerful radio stations is limited to about 100 miles.
1015
Hz
1014
Hz
100 GHz
10 GHz
1 GHz
100 MHz
10 MHz
1 MHz
100 kHz
10 kHz
1 kHz
10-6
m
1cm
10
cm
1m
10m
100
m
1 km
10km
Frequency Use
Microwave
radio
Shortwave
radio
Longwave
radio
Frequency
Wav
elenth
1mm
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Atmospheric noise, man-made noise, and thermal noise from electronic components at the
receiver are dominant disturbances for signal transmission of MF.
Figure 1.5. Illustration ofground-wave propagation.
Sky-wave propagation, as illustrated in Figure 1.6, results from transmitted signals being
reflected (bent or refracted) from the ionosphere, which consists of several layers of charged
particles ranging in altitude from 30 to 250 miles above the surface of the earth. During the
daytime hours, the heating of the lower atmosphere by the sun causes the formation of the
lower layers at altitudes below 75 miles. These lower layers, especially the D-layer serves to
absorb frequencies below 2 MHz, thus severely limiting sky-wave propagation of AM radio
broadcast. However, during the night-time hours, the electron density in the lower layers of
the ionosphere drops sharply and the frequency absorption that occurs during the daytime is
significantly reduced. As a consequence, powerful AM radio broadcast stations can propagate
over large distances via sky wave over the F-layer of the ionosphere, which ranges from 90
miles to 250 miles above the surface of the earth.
A frequently occurring problem with electromagnetic wave propagation via sky wave in the
HF frequency range is signal multipath. Signal multipath occurs when the signal multipath
generally results in intersymbol interference in a digital communication system.
Moreover, the signal components arriving via different propagation paths may add
destructively, resulting in a phenomenon called signal fading, which most people have
experienced when listening to a distant radio station at night when sky wave is the dominant
propagation Mode. Additive noise at HF is a combination of atmospheric noise and thermal
voice.
Sky-wave ionospheric propagation ceases to exist at frequencies above approximately 30
MHz, which is the end of the HF band. However, it is possible to have ionospheric scatter
propagation at frequencies in the range of 30 MHz to 60MHz, resulting from signal scattering
from the lower ionosphere. It is also possible to communicate over distances of several
hundred miles by use of troposphere scattering at frequencies in the range of 40 MHz to 300
MHz. Troposcatter results from signal scattering due to particles in the atmosphere at altitudes
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of 10 miles or less. Generally, ionospheric scatter and tropospheric scatter involve large
signal propagation losses and require a large amount of transmitter power and relatively large
antennas.
Figure 1.6. Illustration of sky-wave propagation.
Frequencies above 30 MHz propagate through the ionosphere with relatively little loss and
make satellite and extraterrestrial communications possible. Hence, at frequencies in the VHF
band and higher, the dominant mode of electromagnetic propagation is line-of-sight (LOS)
propagation. For terrestrial communication systems, this means that the transmitter and
receiver antennas must be in direct LOS with relatively little or no obstruction. For this
reason, television stations transmitting in the VHF and UHF frequency bands mount their
antennas on high towers to achieve a broad coverage area.
In general, the coverage area for LOS propagation is limited by the curvature of the earth. Ifthe transmitting antenna is mounted at a height h feet above the surface of the earth, the
distance to the radio horizon, assuming no physical obstructions such as mountains, is
approximately=2h miles. For example, a TV antenna mounted on a tower of 1000 ft. in
height provides coverage of approximately 50 miles. As another example, microwave radio
relay systems used extensively for telephone and video transmission at frequencies above 1
GHz have antennas mounted on tall towers or on the top of tall buildings.
The dominant noise limiting the performance of communication systems in the VHF and
UHF frequency ranges is thermal noise generated in the receiver front end and cosmic noise
picked up by the antenna. At frequencies in the SHF band above 10 MHz, atmospheric
conditions play a major role in signal propagation. Figure1.7 illustrates the signal attenuation
in dB/mile due to precipitation for frequencies in there range of 10 to 100GHz. We observe
that heavy rain introduces extremely high propagation losses that can result in service outages
(total breakdown in the communication system).
At frequencies above the EHF band, we have the infrared and visible light regions of the
electromagnetic spectrum, which can be used to provide LOS optical communication in free
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10 30 100
Frequency, GHz
space. To date, these frequency bands have been used in experimental communication
systems, such as satellite-to-satellite links.
.
Figure 1.7. Signal attenuation due to precipitation.
Underwater Acoustic Channels
Over the past few decades, ocean exploration activity has been steadily increasing. Coupled
with this increase is the need to transmit data collected by sensors placed under water to the
surface of the ocean. From there it is possible to relay the data via a satellite to a data
collection center.Electromagnetic waves do not propagate over long distances under water except at extremely
low frequencies. However, the transmission of signals at such low frequencies is prohibitively
expensive because of the large and powerful transmitters required. The attenuation of
electromagnetic waves in water can be expressed in terms of the skin depth, which is the
distance a signal is attenuated by1/e. For sea water, the skin depth
f250
wherefis expressed in Hz and is in meters. For example, at 10 kHz, the skin depth is 2.5
meters. In contrast, acoustic signals propagate over distances of tens and even hundreds of
kilometres.
An underwater acoustic channel is characterized as a multipath channel due to signal
reflections from the surface and the bottom of the sea. Because of wave motion, the signal
multipath components undergo time-varying propagation delays, which result in signal
fading. In addition, there is frequency-dependent attenuation, which is approximately
proportional to the square of the signal frequency.
Fog (0.01 in/h)
Light rain (0.05 in/h)
Medium rain (0.1 in/h)
Heavy rain (1 in/h)
10.0
1.0
0.1
0.01
0.001
Attenuation,dB/mi
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Ambient ocean acoustic noise is caused by shrimp, fish, and various mammals. Near
harbours, there is also man-made acoustic noise in addition to the ambient noise. In spite of
this hostile environment, it is possible to design and implement efficient and highly reliable
underwater acoustic communication systems for transmitting digital signals over large
distances.
Storage Channels
Information storage and retrieval systems constitute a very significant part of data-handling
activities on a daily basis. Magnetic tape, including digital audio tape and video tape,
magnetic disks used for storing large amounts of computer data, optical disks used for
computer data storage and compact disks are examples of data storage systems that can be
characterized as communication channels. The process of storing data on a magnetic tape or a
magnetic or optical disk is equivalent to transmitting a signal over a telephone or a radiochannel. The feedback process and the signal processing involved in storage systems to
recover the stored information is equivalent to the functions performed by a receiver in a
telephone or radio communication system to recover the transmitted information.
Additive noise generated by the electronic components and interference from adjacent tracks
is generally present in the read back signal of a storage system, just as is the case in a
telephone or a radio communication system.
The amount of data that can be stored is generally limited by the size of the disk or tape and
the density (number of bits stored per square inch) that can be achieved by the write/read
electronic systems and heads. For example, a packing density of 109
bits per square inch has
been recently demonstrated in an experimental magnetic disk storage system. (Current
commercial magnetic storage products achieve a much lower density.) The speed at which
data can be written on a disk or tape and the speed at which it can be read back is also limited
by the associated mechanical and electrical subsystems that constitute an information storage
system.
Channel coding and modulation are essential components of a well-designed digital magnetic
or optical storage system. In the read back process, the signal is demodulated and the added
redundancy introduced by the channel encoder is used to correct errors in the read back
signal.
Mathematical Models for Communication Channels
In the design of communication systems for transmitting information through physical
channels, we find it convenient to construct mathematical models that reflect the most
important characteristics of the transmission medium. Then, the mathematical model for the
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channel is used in the design of the channel encoder and modulator at the transmitter and
the demodulator and channel decoder at the receiver. Below, we provide a brief description of
the channel models that are frequently used to characterize many of the physical channels that
we encounter in practice.
The Additive Noise Channel
The simplest mathematical model for a communication channel is the additive noise channel,
illustrated in Figure 2.3. In this model, the transmitted signal s(t) is corrupted by an additive
random noise process n(t). Physically, the additive noise process may arise from electronic
components and amplifiers at the receiver of the communication system, or from interference
encountered in transmission as in the case of radio signal transmission.
If the noise is introduced primarily by electronic components and amplifiers at the receiver, it
may be characterised as thermal noise. This type of noise is characterised statistically as a
Gaussian noise process. Hence, the resulting mathematical model applies to a broad class of
physical communication channels, and because of its mathematical tractability this is the
predominant channel model used in the channel is usually called the additive Gaussian noise
channel.
Figure 1.8. The additive noise channel.
The Linear Filter Channel
In some physical channels such as wireline telephone channels, filters are used to ensure that
the transmitted signals do not exceed specified bandwidth limitations and thus do not interfere
with one another. Such channels are generally characterized mathematically as linear filter
Channels with additive noise, Figure 2.4. Hence, if the channel input is the signal s(t) the
channel output is the signal
r(t) = s(t) * h(t) + n(t)
)()()( tndtsh
where h() is the impulse response of the linear filter and denotes convolution.
Channel
n(t)
r(t) = s(t) + n(t)s(t)
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r(t) = s(t) * h(t) + n(t)
Channel
n(t)
s(t)
Channel
n(t)
s(t) r(t) = s(t) * h(; t) + n(t)
Figure 1.9. The linear filter channel with additive noise.
When the signal undergoes attenuation in transmission through the channel, the received
signal is
r(t) = s(t) + n(t)
where represents the attenuation factor.
The Linear Time-Variant Filter Channel
Physical channels such as underwater acoustic channels and ionospheric radio channels which
result in time-variant multipath propagation of the transmitted signal may be characterized
mathematically as time-variant linear filters. Such linear filters are characterized by a time-
variant channel impulse response h(; t), where h(; t) is the response of the channel at time t
due to an impulse applied at time t - . Thus, represents the delay (elapsed-time)
variable. The linear time-variant filter channel with additive noise is illustrated Figure 2.5. For
an input signal s(t), the channel output signal is
)()();( tndtsth (1)
Figure 1.10. Linear time-variant filter channel with adaptive noise.
Linear
filter h(t)
Linear
Time-variant
filter h(;t)
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-3400 3400-300 300 f
Sx(f)
A good model for multipath signal propagation through physical channels, such as
the ionosphere (at frequencies below 30 MHz) and mobile cellular radio channels, is a
special case of Eq. (1) in which the time-variant impulse response has the form
L
k
kk ttath1
)()();( (2)
where the {ak(t)} represents the possibly time-variant attenuation factors for the L
multipath propagation paths. If Eq. (2) is substituted into Eq. (1), the received signal has
the form
L
k
kk tnttath1
)()()();( (3)
Hence, the received signal consists ofL multipath components, where each component
is attenuated by {ak(t)} and delayed by {k}.
The three mathematical models described above adequately characterize a large
majority of physical channels encountered in practice. These three channel models are
used in this text for the analysis and design of communication systems.
Modelling of Information Sources
The information source produces outputs that are of interest to the receiver of
information, who does not know these outputs in advance. The role of a communication
system designer is to make sure that this information is transmitted correctly.
Since the output of the information source is time-varying unpredictable function, it can
be modelled as a random process.
In communication channels the existence of noise causes stochastic dependence
between the input and output of the channel. Therefore, a communication system
designer designs a system that transmits the output of a random process (information
source), to a destination via a random medium (channel) and ensures low distortion.
The properties of the random process depend on the nature of the source. For example,
when modelling speech signals, the resulting random process has all its power in a
frequency band of approximately 300-4000 Hz.
Therefore, the power-spectral density of the
speech signal also occupies this band of frequencies.
Video signals are restored from a still or a moving image and, therefore, the bandwidth
depends on the required resolution. For TV transmission, depending on the system
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... x-2, x-1, x0, x1, x2, ...
p
1-p
0 1 x
The PMF for the Bernolli
random variable.
Mathematical model for a
discrete information source.
0.3
0 2
x
The PMF for binomial
random variable.
0.25
0.2
0.15
0.1
0.050
4
6
8
10
12
employed (NTSC, PAL or SECAM), this band is typically between 0-4.5 MHz and
0-6.5 MHz. For telemetry data the bandwidth depends on the rate of change of data.
These processes are band limited processes and, therefore, can be sampled at the
Nyquist rate or larger and reconstructed from the sampled values. The information
source can be modelled by a discrete-time random process
iiX .
The alphabet over which the random variables Xi are defined can be either discrete (in
transmission of binary data) or continuous (e.g. sampled speech).
The simplest model for information source is the discrete memoryless source (DMS). A
DMS is a discrete-time, discrete-amplitude random process in which all Xis are
generated independently and with the same distribution.
Let set A={a1, a2, , aN} denote the set in which the random variableXtakes its values,
and let the probability mass function for the discrete random variable Xbe denoted byPi=p(X=ai) for all i=1, 2, , N. A full description of the DMS is given by the set A,
called the alphabet, and the probabilities Nii
P1 .
Important Random Variables
The most commonly used random variables in communications are:
- Bernolli Random VariableThis is a discrete random variable taking two values one and
zero with probabilitiesp and 1-p. A Bernolli random variable
is a good model for a binary data generator. We can model an
error by modulu-2 addition of a 1 to the input bit, thus
changing a 0 into a 1 and a 1 into a 0. Therefore, Bernolli
random variable can be employed to model channel errors.
- Binomial Random VariableThis is a discrete random variable giving the number of 1s in a sequence ofn independent
Bernolli trials. The PMF is given by
Information source
otherwise
nkppk
n
kXp
knk
,0
0,)1()(
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change the information delivered by that output by a large amount. In other words, the
information measure should be a decreasing and continuous function of the probability of that
source.
Now let us assume that the information about output aj can be broken into two independent
parts say aj1 and aj2;
i.e.,Xj=(X(j1)
+X(j2)
), aj={aj1
,aj2
}, andp(X=aj)=p(Xj1
=aj1
)p(X(j2)
=aj2
).
If the components are independent, revealing information about one component does not
provide any information about the other component, and therefore, the amount of information
provided revealing aj is the sum of information obtained by revealing aj1
and aj2
.
Consequently, the amount of information revealed about an output aj with probabilitypj must
satisfy the following conditions:
1. The information content of output aj depends only on the probability ofaj and not onthe value ofaj. We denote this function byI(pj) and call it self-information.
2. Self-information is a continuous function ofpj; i.e.,I(.) is a continuous function.3. Self-information is a decreasing function of its arguments, i.e., the least probable
outputs convey most information.
4. Ifpj=p(j1)p(j2), thenI(pj)= I(p(j1))+ I(p(j2)).
The only function that satisfies all the above properties is the logarithmic function; i.e.,
I(x)=-log(x). The base of the logarithm determines the units used for information measure.
Thus, for units of bits the base 2 is used. If the natural logarithm is used, the units are
nats, and for base 10 logarithms, the unit is Hartley. (From now on we will assume alllogarithms are in base 2 and all information is given in bits).
Each source output ai is defined as the self-information of that output, given bylog (pi). (We
can define the information content of the source as the weighted average of the self-
information of all source outputs. This is justified by the fact that various source outputs
appear with their corresponding probabilities). Therefore, the information revealed by
unidentified source output is the weighted average of the self-information of the varioussource outputs; i.e.,
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N
i
N
i
iiii pppIp1 1
log)(
The information content of the information source is known as the entropy of the source and
is denoted byH(x).
Definition 1
The entropy of a discrete random variable X is a function of the PMF and is defined by
N
i
N
i i
iiip
pppxH1 1
)1
log(log)(
Sampling Theorem
Nyquist Rate: Nyquist set out to determine the optimum pulse shape that was bandlimited to
WHz and maximized the bit rate 1/T under the constraint that the pulse caused no inter
symbol interference at the sampling times k/T, k=0, 12,.
The maximum pulse rate 1/Tis 2Wpulse/sec. This rate is called the Nyquist rate.
Nyquist rate (sampling rate)=2W
This pulse rate can be achieved by using the pulses
g(t)=(sin2Wt)/ 2Wt
where g(t) represents a basic pulse shape.
The sampling theorem states that a signal of bandwidth Wcan be reconstructed from samples
taken at the Nyquist rate of 2W samples per second using the interpolation formula (any
physical waveform may be represented over the interval -
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Quantisation
Quantizing is the process of rounding-off the flat-top samples to certain predetermined levels.
The PCM signal is generated by carrying out three basic operations: sapling, quantizing and
encoding. The sampling operation generates a flat-top PAM signal.
The quantizing operation is illustrated in the following figure, for the case of M=8 levels. This
quantiser is said to be uniform because all of the steps are of equal size. Error is introduced
into the recovered output analog signal because of the quantizing effect. If we sample at the
Nyquist rate (2W) or faster and there is negligible channel noise, there will still be noise,
called quantizing noise, on the recovered analog waveform due to this error. The quantiser
output is a quantised PAM signal.
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CHAPTER II
Modulation
(Analogue Signal Transmission)
A large number of information sources are analogue sources. An analogue source can be
modulated and transmitted directly or can be converted to digital data and transmitted using
digital modulation techniques.
Speech, image, and video are examples of analogue sources of information. Each of these
sources is characterised by its bandwidth, dynamic range, and the nature of the signal. (For
instance, in case of audio and black & white video, the signal has just one component
measuring the intensity, but in case of colour video, the signal has four components
measuring red, blue, green colour components, and the intensity).
The analogue signal to be transmitted is denoted by m (t), which is assumed to be a lowpass
signal of bandwidth W, i.e.,M(f) 0, for f W. we also assume that the signal is a power-
type signal whose power is denoted by Pm, where
dttmT
imP
T
TT
m 2
2
2)(1
Modulation is a process by which some parameter of a carrier signal is varied in accordance
with a message signal. The analogue signal is transmitted by impressing it on the amplitude,
the phase or the frequency of a sinusoidal carrier. The message signal is called a modulating
signal. Modulation converts the message signal m(t) from lowpass to bandpass, in the
neighborhood of the carrier (centre) frequencyfc.
Modulation of the carrier c(t) by the message signal m(t) is performed in order to achieve one
or more of the following objectives:
1- The lowpass signal is translated in frequency to the passband of the channel so that thespectrum of the transmitted bandpass signal will match the passband characteristics of
the channel.
2- To accommodate for simultaneous transmission of signals from several messagesources, by means of FDM; and
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3- To expand the bandwidth of the transmitted signal in order to increase its noiseimmunity in transmission over noisy channels.
Definitions
A bandpass signal is represented by
ccAtc cos)( ..(2.1)
where Ac is the carrier amplitude (envelope) and ccccc tft 2 , c is called the
instantaneous phase deviation of c(t) and fc is the carrier frequency. For amplitude
modulation, we can write
ccc tfAtc 2cos)( (2.2)
Ac is linearly related to the modulating signal m(t) and is called the instantaneous amplitude
of c(t). Amplitude modulation is also referred to as linear modulation. Depending on the
relationship between m(t) and Ac, we have the following types of amplitude modulation
schemes: normal (conventional) amplitude modulation (AM), double-sideband suppressed
carrieramplitude modulation (DSB-SC), single-sidebandamplitude modulation (SSB), and
vestigial-sidebandamplitude modulation (VSB).
Normal (Conventional) Amplitude Modulation (AM)
A normal amplitude-modulated signal is given by
tftmAts cc 2cos)()( (2.3)
tftmtfAts ccc 2cos)(2cos)( (2.4)
carrier sidebands
m(t) is the modulating (message) signal. It is also very common to define a normal amplitude-
modulated signal as
tftmAts cc 2cos)(1)( (2.5)
The modulation index m is defined as
cA
tmm
)(min .(2.6)
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m(t)
c(t)
s(t)
t
t
t
Amin
Amax Ac
s(t) )(1 tmAc
Figure 2.1 shows normal AM signal. Clearly, the envelope of the modulated signals has the
same shape as m(t).
Modulating signal (audio)
Carrier frequency
AM signal
Figure 2.1. Amplitude modulation
As long as 1)( tm , the amplitude )(1 tmAc is always positive. This is a desired condition
for normal AM that make it easy to demodulate. On the other hand, when m > 1, the carrier
signal is said to be overmodulatedand the envelope is distorted, also its demodulation become
more complex.
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t
m(t)
max m(t)
min m(t)
t
s t
A
-A
Envelope
0
m1
m t
-m t
(Overmodulated signal)
Figure 2.2. Normal Am signal for various values of modulation index
Definition
The percentage of positive modulation on a normal AM signal is
100)(max100max
oo tm
AAAulationmodpositive
c
c ..........(2.7)
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.... (2.11)
and the percentage of negative modulation is
100)(min100minoo
tmA
AAulationmodnegative
c
c ..........(2.8)
the overall modulation percentage is
1002
)(min)(max100minmaxoo
tmtm
A
AAulationmod
c
.........(2.9)
In practice , m(t) is scaled so that its magnitude is always less than unity. Sometimes it is
convenient to express m(t) as
)()( tmtm n
where mn(t) is normalised such that its min. value is -1. This can be done for example, by
defining
)(max
)()( tm
tmtmn
The scale factor is called the modulation index. Then the modulated signal can be
expressed as
tftmAtuts cnc 2cos)(1)()( (2.10)
In normal AM signaling, only the sideband components convey information, so that the
modulation efficiency is
100)(1
)(
2
2
tm
tmE %
The highest efficiency that can be attained for a 100% AM signal would be 50%, (for the case
where square-wave modulation is used).
Also, efficiency, denoted as , of a normal AM signal is defined as
%100t
s
P
P
where Ps is the power carried by the sidebands and Pt is the total power of the normal AM
signal.
m
cc
t PAA
P22
22
Pm is the power of the message signal.
The normalised peak envelope power (PEP) of the AM signal is
22
)(max12
tmA
PEP c ..(2.12)
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0 v
v-i characteristic
of P-N diode
Spectrum of Normal AM Signal
For normal amplitude modulation,
tftmAts cc 2cos)()(
tftmtfAts ccc 2cos)(2cos)(
The Fourier transform ofs(t) is
)()(2
1)()(
2
1)( ccccc ffMffMffffAfS ..(2.13)
Figure 2.2 shows the spectrum of a normal AM signal. Normal amplitude modulation simply
shifts the spectrum of m(t) to the carrier frequency fc. Obviously, the spectrum of a normal
AM signal occupies a bandwidth of the message signal, therefore, the bandwidth of the
modulated signal is 2fmHz, wherefmis the bandwidth of the modulating signal m(t).
Figure 2.3. Spectrum of normal AM signal
Generation of Normal AM Signals
Since the process of modulation involves the generation of new frequency components,
modulators are generally characterised as nonlinear or time-variant systems.
Power-Law Modulation
Consider the use of a nonlinear device such as a P-N diode which has a voltage-current
characteristic as shown in the following figure. i
Suppose that the voltage input to such a device is the sum of
the message signal m(t) and the carrier c(t). The nonlinearity
will generate a product of the message signal with the carrier,
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tfA cc 2cos
plus additional terms. The desired modulated signal can be filtered out by passing the
output of the nonlinear device through a bandpass filter.
A process of generating a normal AM signal is shown in Figure 2.3. This type of modulation
can be achieved by using a non-linear device, such as a diode, that is shown in Figure 2.4.
m(t) s(t)
Figure 2.4. Block diagram of power-law AM modulator
Figure 2.5. Amplitude modulator using a diode
Suppose that the nonlinear device has an input-output (square-law) characteristic of the form:
)()()( 2 tbvtavtv iio (2.14)
where parameters a, b are constants and
)(2cos)( tmtfAtv cci ..(2.15)
Substituting equation (2.15) into (2.14), we have
tftmbAtfaA
tbmtfbAtam
tmtfAbtmtfAatv
cccc
cc
cccco
2cos)(22cos
)(2cos)(
)(2cos)(2cos)(
222
2
(2.16)
The output signal vo(t) of a bandpass filter with bandwidth 2Wand centred at fc is
or
tftma
baAtvts
tftbmaAtv
cc
cco
2cos)(2
1)()(
2cos)(2)(
'
0
'
(2.17)
whereAc=a /2b , 2b|m(t)|/a
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tfA cc 2cos
)(tvi
vo
0 vi
Input-output
characteristic
s(t)
)(tm
LR
Switching Modulator
A normal amplitude-modulated signal can also be obtained by multiplying m(t) by a periodic
digital signal s(t). The modulator is called a switching modulator. Figure 2.6 shows the
periodic rectangular waveform and its line spectrum.
+
- ...
-Tp 0 Tp
(a) (b) (c)
Figure 2.6. Switching modulator & periodic switching signal
Such a modulator can be implemented by the system illustrated in Figure 2.6 (a). The sum of
the message signal and the carrier; i.e., vi(t) given in equation (2.15) above, are applied to a
diode that has input-output characteristic, shown in Figure 2.6(b), where Ac>> m(i). The
output across the load resistor is simply
0)(,0
0)(),(
)( tc
tctv
tv
i
o .(2.18)
This switching operation may be viewed mathematically as a multiplication of the input vi(t)
with the switching function s(t);
)(2cos)()( tstfAtmtv cco ..(2.19)
where s(t) is shown in Figure 2.6(c).
Since s(t) is a periodic function, it is the represented in the Fourier series as
1
1
)12(2cos12
)1(2
2
1
)(n
c
n
ntfnts ..(2.20)
Hence,
termsothertftmA
A
tstfAtmtv
c
c
c
cco
2cos)(4
12
)(2cos)()(
The desired AM modulated signal is obtained by passing vo(t) through a BPF with centre
frequencyf=fc and bandwidth 2W. At its output, we have the desired normal (conventional)
DSB AM signal;
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Amplitude
0 t
Envelope
tftmA
Ats c
c
c
2cos)(4
12
)(
..(2.21)
Demodulation of Normal AM SignalsThe process of recovering the message signal from the modulated signal is called
demodulation or detection.
Envelope Detection
Normal (conventional) DSB AM signals are easily demodulated by means of an envelope
detector. An envelope detector consists of a diode and an RC circuit which basically a
lowpass filter. This is shown in Figure 2.7.
Figure 2.6. Envelope detector
During the positive half-cycle of the input (modulated) signal, the diode is forward biased and
the capacitor charges up to the peak value of the modulated signal. When the modulated
signal falls below its maximum voltage on the capacitor, the diode becomes reverse-biased
and the input is disconnected from the output. During this period, the capacitor discharges
slowly through the load resistorR. On the next cycle of the carrier, the carrier conducts again
when the modulated signal exceeds the voltage across the capacitor. The capacitor charges up
again to the peak value of the modulated signal and the process is repeated again.
To follow the variations in the envelope of the carrier signal, the discharge time constant RC
must be selected properly.
WRC
fc
11
In such a case, the capacitor discharges lowly through the resistor, and thus, the output of the
envelope closely follows the message signal.
m (t)
s(t)
m (t)r(t) C R
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Double-Sideband Suppressed Carrier
A Double-Sideband Suppressed Carrier (DSB-SC) AM signal is obtained by multiplying the
message signal m(t) with the carrier signal c(t). Thus, we have the amplitude modulated signal
tftmA
tctmtuts
cc 2cos)(
)()()()(
(2.22)
The Fourier transform ofs(t) is
)()(2
)()( ccc ffMffM
AfUfS ..(2.23)
Figure 2.7 shows the waveforms and spectra associated with a DSB signal. Clearly, the
envelope of the modulated signal does not have the same shape as m(t). As with AM, DSB-
SC modulation shifts the spectrum of m(t) to the carrier frequency fc. The bandwidth of the
modulated signal is 2W(2fm) Hz, where W(fm) is the bandwidth of the modulating signal
m(t). Therefore, the channel bandwidth required to transmit the modulated signal s(t) is
Bc=2W.
The frequency content of the modulated signal s(t) in the frequency band | f |>fc is called the
upper sideband ofS(f), and the frequency content of the modulated signal s(t) in the frequency
band |f|
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tfA cc 2cos
m(t) s(t)
DSB
tfA cc 2cos
m(t)
-m(t)
+ tftmAts cc 2cos)(2)(
tftmA cc 2cos)(1
tftmA cc 2cos)(1
Figure 2.8. Generation of DSB signal
Balanced Modulator
A relatively simple method to generate DSB-SC AM signals is to use two normal AM
modulators arranged as in the configuration shown in Figure 2.9, called a single balanced
modulator(or simply a balanced modulator). (For example, we may use two square-law AM
modulators as described before).
-
Figure 2.9. A balanced modulator
Let the input-output characteristic of a diode be approximated by a power series
)()()( 2 tbvtavtv iio (2.24)
where parameters a, b are constants. The input voltage to the diode D1 is
)(2cos)(1, tmtfAtv cci ..(2.25)
and let the output voltage of the diode be vo,1(t) = vo(t). Substituting equation (2.25) into
(2.24), we have
tftmbAtfaA
tbmtfbAtamtmtfAbtmtfAatv
cccc
cc
cccco
2cos)(22cos
)(2cos)()(2cos)(2cos)(
222
2
1,
(2.26)
Nonlinear
device
AM
modulator
AM
modulator
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m(t) vo(t)
Square-wave carrier
atf=fc
Now, consider diode D2, the input voltage to the diode D2 is
)(2cos)(2, tmtfAtv cci ..(2.27)
and let the output voltage of the diode be vo,2(t) = vo(t). Substituting equation (2.27) into
(2.24), we have
tftmbAtfaA
tbmtfbAtam
tmtfAbtmtfAatv
cccc
cc
cccco
2cos)(22cos
)(2cos)(
)(2cos)(2cos)(222
2
1,
(2.28)
Subtracting equation (2.28) from (7.26), we get
tftmbAtmaAtvtvtv cccooo 2cos)(4)(2)()()( 2,1, ..(2.29)
The output signal vo(t) of a bandpass filter with bandwidth 2Wand centred at fc is
tftmbAtstv cco 2cos)(4)()(' (2.30)
That is, we generate a DSB-SC AM signal.
Ring Modulator
It is possible to design a balanced modulator such that the input to the bandpass filter does not
contain the message signal m(t) or the carrier signal c(t). A circuit balanced with respect to
both input signals is called a double-balanced modulator, known as a ring modulator. Figure
2.10 shows a ring modulator. The switching of the diodes is controlled by a square wave of
frequencyfc, denoted as c(t), which is applied to the centre taps of the two transformers.
Figure 2.10. Ring modulator generating DSB-SC AM signal
When c(t)>>0, the top and bottom diodes conduct, while the two diodes in the cross arms are
off. In this case, the message signal m(t) is multiplied by +1. When c(t)
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r(t) m(t)
1
1
)12(2cos12
)1(4)(
n
c
n
ntfn
tc
(2.31)
Hence, the desired DSB-SC AM signal s(t) is obtained by passing vo(t) through a BPF with
centre frequencyfc and bandwidth 2W.
The balanced modulator and the ring modulator systems multiply the message signal m(t)
with the carrier to produce a DSB-SC AM signal. The multiplication ofm(t) with tfA cc 2cos
is called a mixing operation. Hence, a mixer is basically a balanced modulator.
Demodulation of DSB-SC Signals
Since the envelope of the modulated signal does not have the same shape as m(t), an envelope
detector cannot be used to recover the message signal. Therefore, demodulation of a DSB-SC
AM signal requires a synchronous detector (demodulator). That is, the demodulator must use
a coherent phase reference, see Figure 2.11, which is usually generated by means of a phase-
locked loop (PLL) to demodulate the received signal.
Figure 2.11. Demodulation of DSB-SC AM signal
A PLL is used to generate a phase-coherent carrier signal that is mixed with the received
signal in a balanced modulator. The output of the balanced modulator is passed through a LPF
of bandwidth W that passes the desired signal and rejects all signal and noise components
above WHz.
Single-Sideband and Vestigial-Sideband Modulations
We have seen that both normal AM and DSB signals require a transmission bandwidth equal
to twice the bandwidth of the message signal m(t). Since either the upper sideband (USB) or
the lower sideband (LSB) contains the complete information of the message signal, we can
conserve bandwidth by transmitting only one sideband. The modulation is called single-
sideband (SSB) modulation. It is widely used by the military and by radio amateurs in high-
frequency (HF) communication systems. It is popular because the bandwidth is the same asthat of the modulating signal m(t) (half of the BW of AM or DSB-SC signal)
Balanced
modulator LPF
PLL
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Single-Sideband Signals
An upper single sideband (USSB) signal has a zero-valued spectrum at |f | > fc and a lower
single sideband (LSSB) signal has a zero-valued spectrum at |f |
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tfA cc 2cos
m(t)
)( tm
)(ts
tfA cc 2sin
SSB
S(f)
- fc fc
M(f)
S(f)
- fc fc
Figures 2.13 and 2.14 show the generation of a SSB and the spectra associated with it.
Figure 2.13. Generation of a SSB-AM signal using phasing method
-USSB AM signal is: ttmttmAts cccu sin)(cos)()( (2.33)
-LSSB AM signal is: ttmttmAts cccl sin)(cos)()( (2.34)
The spectra of the USSB and LSSB are given as follows:
cc
c
c
c
cc
cffffM
ffA
ff
ffffMAfS
),(
,0
,0
),()( .(2.35)
cc
c
c
c
cc
cffffM
ffA
ff
ffffMAfS
),(
,0
,0
),()( ....(2.35a)
0
M(f+fc) M(f-fc)
0
(a)
M(f+fc) M(f-fc)
0
(b)
Figure 2.14. Spectra for (a) USSB and (b) LSSB
Hilbert
transform
90o
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m(t) LSSBm(t) s(t)
tfA cc 2cos
LPF
HPF
)(2cos mcc ffA
)(2cos mcc ffA
USSB
c(t)
Advantages:
Does not employ bandpass filter.
Suitable for message signals with frequency content down to dc.
Disadvantage:
Practical realization of a wideband 90o
phase shift circuit is difficult.
Filter Method
In this method, a balanced modulator is used to generate a DSB signal, and the desired
sideband signal is then selected by a bandpass filter, which selects either upper sideband or
lower sideband of the SSB AM signal. Figures 2.15 and 2.16 show the generation of a SSB
signal using the filter method, and the spectra associated with it.
Figure 2.15. Generation of SSB signal using filter method
Figure 2.16. Spectra associated with SSB AM signal using filter method
The technique is suitable for message signals with very little frequency content down to dc
and hence does not require sharp filter cut-off characteristics.
BPF
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r(t) m(t)
VSB AM signal
m(t) s(t)
tfA cc 2cos
DSB
Demodulation of SSB Signals
Demodulation of SSB signals also requires the use of a phase coherent reference. In the case
of signals such as speech, that is relatively little or no power content at dc, it is straight
forward to generate the SSB signal, as in the case of filtering method, and then to insert a
small carrier component that is transmitted along with the message signal. In such a case a
balanced modulator is used for the purpose of frequency conversion of the bandpass signal to
lowpass or baseband. This is shown in Figure 2.17.
Figure 2.17. Demodulation of SSB AM signal with a carrier component
Vestigial Sideband (VSB) Modulation
Vestigial sideband modulation is a compromise between DSB and SSB modulations. It is
often chosen when DSB takes too much bandwidth and SSB is too complicated for particular
application. Typically, the bandwidth of a VSB modulated signal is about 1.25 times that of
the corresponding SSB modulated signal. It is commonly used for transmission of video
signals in commercial television broadcasting. To generate a VSB one of the sidebands of the
DSB is partially suppressed. In other words, the DSB-SC AM signal is passed through a
sideband filter with frequency response h(t).h(t) is the transfer function of the BPF.
Figures 2.18 and 2.19 show the generation of a VSB signal, and the spectra associated with it.
h(f)
Figure 2.18. Generation of VSB signal
Balanced
modulator LPF
Estimatecarrier
component
Sideband
filter
h(f)
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m(t) Acm(t)
tfA cc 2cos
Figure 2.19. Spectra associated with VSB signal.
In the time domain the VSB signal may be expressed as
)(2cos)()()()( thtftmAthtsts ccVSB .(2.36)
where s(t) is a DSB signal and h(t) is the impulse response of the VSB filter.
To recover an undistorted message signal m(t) the SVB filter characteristic must satisfy the
condition
WfffHffH cc ||,constant)()(
|f|W
Figure 2.20. Demodulation of VSB signal
In the frequency domain, the corresponding expression is
)()()(2
)( fHffMffMA
fS ccc (2.36)
To determine the frequency-response characteristics of the filter, consider the demodulation
of the VSB signal s(t). We multiply s(t) by the carrier component tfc2cos and pass the result
through an ideal LPF.
Ideal
LPF
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H(f)
H(f-fc)+ H(f+fc)
H(f-fc)H(f+fc)
- fc fc
H(f)
- fc fc
Thus, the product signal is
tftstv c2cos)()(
or equivalently,
)()()(2
1)( fHffSffSfV cc
)()2()(4
)()()2(4
)(
ccc
ccc
ffHffMfMA
ffHfMffMA
fV
The LPF rejects the double frequency term and passes only the components in the frequency
range |f|W. Hence, the signal spectrum at the output of the ideal LPF is
)()()(4
)( ccc
l ffHffHfMA
fV .(2.37)
-f-W -fc-fa -fc+fa 0 fc-fa fc+fa fc+W f
-2fc -W - fa 0 fa W 2fc f
-f-fa -fc+W 0 fc-W fc+fa f
H(f) selects the upper sideband as a vestige of the lower sideband. It has odd symmetry about
the carrier frequency fc, in the frequency range aacac fffff where, is a conveniently
selected frequency that is small fraction of W; i.e., fa
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Demodulation of VSB Signals
In VSB a carrier component is generally transmitted along with the message sidebands. The
existence of the carrier component makes it possible to extract a phase-coherent reference for
demodulation in a balanced modulator, as shown in Figure 2.20.
In some applications such as TV broadcast, a large carrier component is transmitted along
with the message in the VSB signal. In such a case, it is possible to recover the message by
passing the received VSB signal through an envelope detector.
Signal Multiplexing
Frequency Division Multiplexing (FDM)
The process of combining a number of separate message signals into a composite signal for
transmission over a common channel is called multiplexing. One of the basic problems in
communication engineering is the design of a system which allows many individual signals
from users to be transmitted simultaneously over a single communication channel. The most
commonly used methods are: time-division multiplexing (TDM), and frequency-division
multiplexing (FDM). TDM is usually used in the transmission of digital information. FDM
however, may be used with either analogue or digital signal transmission.
FDM, involves dividing the multiplexed channel into a number of unique frequencies, each
one assigned to a pair of communicating entities. FDM can be achieved only if the available
bandwidth on the multiplexed channel exceeds the bandwidth needs of all the communicating
entities.
Whenever a multiplexer receives data for transmission, the data is transmitted by it on the
frequency allocated to the transmitting entity. The receiving multiplexer forwards the
information received on a specific frequency to the destination associated with that frequency.
The following example illustrates how a frequency division multiplexer connects DTEs 1, 2,
and 3 with ports E, L, and S, respectively, on a central host. The frequency allocation is given in
the following Table.
The 1000-Hz separation between the channels is known as the guard band and is used to
ensure that one set of signals does not interfere with another. Diagrammatically, theconnections and their frequencies are shown in Figure 2.22.
DTE-Port Pair Frequency (Hz)
1 and E 10,000-14,000
2 and L 5,000-9,000
3 and S 0-4,000
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m1(t)
m2(t)
mk(t)
m1(t)
f1
m2(t)
mk(t)
f2
fk
s1(t)
s2(t)
sk(t)
s1(t)
s2(t)
sk(t)
Figure 2.22. Frequency-division multiplexing of k number of signals
The advantage of FDM is that each DTE is assigned a unique frequency that can be treated as
an unshared channel. An everyday example of FDM is cable television, in which many signals
are "stacked up" and transmitted simultaneously over the cable. The user selects a viewing
channel by tuning to that channel's frequency.
Transmitter Receiver
Figure 2.23. Frequency-division multiplexing of k number of signals
In FDM, the message signals are separated in frequency as described above. A typical
configuration of an FDM system is shown in Figure 2.23. This figure illustrates the
frequency-division multiplexing of k message signals at the transmitter and their
demodulation at the receiver. The LPFs at the transmitter are used to ensure that the
bandwidth of the message signals is limited to W Hz. Each signal modulates a separatecarrier; hence, kmodulators are required. Then, the signals from kmodulators are summed
DTE 1
MUX
DEMUX
DTE 3
0-4,000 Hz5,000-9,000 Hz
10,000-14,000 HzDTE 2 Port E
Port L
Port S
ModulatorLPF
ModulatorLPF
ModulatorLPF
Frequency
synthesizer
Demodulator LPF
Frequency
synthesizer
BPF
Demodulator LPFBPF
Demodulator LPFBPF
channel
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and transmitted over the channel. For SSB and VSB modulation, the modulator outputs are
filtered prior to summing the modulated signals.
At the receiver of an FDM system signals are usually separated by passing through a parallel
band and BPFs, where each filter is tuned to one of the carrier frequencies and has a
bandwidth that is sufficiently wide to pass the desired signal. The output of each BPF is
demodulated and each demodulated signal is fed to a LPF that passes the baseband message
signal and eliminates the double frequency components.
FDM is widely used in radio and telephone communications. For example, in telephone
communications, each voice-message signal occupies a nominal bandwidth of 3 kHz. The
message signal is SSB modulated for bandwidth efficient transmission. In the first level of
multiplexing, 12 signals are stacked in frequency, with a frequency separation of 4 kHz
between adjacent carriers. Thus, a composite 48-kHz channel, called a group channel, is used
to transmit 12 voice-band signals simultaneously. In the next level of FDM, a number of
group channels (typically five or six) are stacked together in frequency to form a super-group
channel, and the composite signal is transmitted over the channel. Higher-order multiplexing
is obtained by combining several super-group channels. Thus, an FDM hierarchy is employed
in telephone communication systems.
Quadrature-Carrier Multiplexing
A totally different type of multiplexing allows us to transmit two message signals (for
example m1(t) and m2(t)) on the same carrier frequency, using two quadrature carriers
tfA cc 2cos and tfA cc 2sin . The signal m1(t) amplitude modulates the carrier tfA cc 2cos
and m2(t) amplitude modulates the carrier tfA cc 2sin . The two signals are added and
transmitted over the channel. Hence, the transmitted signal is
tftmAtftmAts cccc 2sin)(2cos)()( 21 ..(2.38)
Therefore, each message signal is transmitted by DSB-SC AM. This type of signal
multiplexing is called quadrature-carrier multiplexing. Figure 2.24 illustrates the modulation
and demodulation of the quadrature-carrier multiplexed signals. As shown, a synchronous
demodulator is required at the receiver to separate and recover the quadrature-carrier
modulated signal.
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tfA cc 2cos
m1(t)
tfA cc 2sin
channel
m2(t)
m1(t)
m2(t)
PLL
Transmitter Receiver
Figure 2.24. Quadrature-carrier multiplexing
Quadrature-carrier multiplexing results in a bandwidth-efficient communication system that is
comparable in bandwidth efficiency to SSB AM.
Angle Modulation
Amplitude modulation methods are also called linear-modulation methods. Frequency and
phase modulation are jointly referred to as angle-modulation methods, and they are non-
linear.
Frequency and phase modulation systems generally expand bandwidth such that the effective
bandwidth of the modulated signal is usually many times the bandwidth of the message
signal. Although angle modulation is more complex to implement and occupy more
bandwidth, the major benefit of these systems is their high degree of noise immunity. That is
the reason that FM systems are widely used in high-fidelity music broadcasting and point-to-
point communication systems where the transmitter power is quite limited.
FM and PM Signals
An angle-modulated signal can be written in general as
))(cos()( tAts c
)(t is the phase of the signal, and its instantaneous frequencyfi(t) is given by
)(2
1)( t
dt
dtf
i
Balancedmodulator
-90o phase
shift
Balancedmodulator
Balancedmodulator
-90o phase
shift
Balancedmodulator
LPF
LPF
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FM modulator
m(t) FM
modulator
m(t) PM
modulatorIntegrator
PM modulatorm(t) PM
modulator
m(t) FM
modulatorDifferentiator
Since s(t) is a bandpass signal, it can be represented as
)(2
1)(
))(2cos()(
tdt
dftf
ttfAts
ci
cc
Ifm(t) is the message signal, then in a PM system we have
)()( tmkt p (2.39)
and in an FM system we have
)(2
1)()( t
dt
dtmkftf fci
..............(2.40)
where kp and kfare phase and frequency deviation constants.
t
f
p
FMdmk
PMtmk
t,)(2
),(
)(
.(2.41)
Equation 2.41 shows the close relation between FM and PM systems. This relationship makes
it possible to analyse these systems in parallel.
- If we phase modulate the carrier with the integral of the message, it is equivalent toFM of the carrier with the message.
- If we frequency modulate the carrier with derivative of a message, the result isequivalent to PM of the carrier with the message.
FMtmk
PMtmdtdk
tdt
d
f
p
),(2
),()(
..(2.42)
Figure 2.25. A comparison of FM and PM modulators
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1
0
-1
1
0
-1
1
0
-1
1
0
-1
2 4
FM
signal
PM
signal
Equivalent
1
0
-1
0
Figure 2.26. FM & PM square and sawtooth waves
The demodulation of an FM signal involves finding the instantaneous frequency of the
modulated signal and then subtracting the carrier frequency from it. In PM, the demodulation
process is done by finding the phase of the signal and then recovering m(t). the maximum
phase deviation in a PM system is given by
)(maxmax tmkp
and the maximum frequency-deviation in an FM system is given by
)(maxmax tmkf f
Narrowband Angle Modulation
If max| t |
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vs(t)
cos
-sin
Ac Acm(t)
vs(t)
cos
-sin
Ac
Ac(t)
AM phasor
(a)
FM phasor
(b)
tfA cc 2cos
m(t)
tfA cc 2sin
NBFM
Signal out
Figure 2.27. Vector representation of (a) AM and (b) FM phasor
As shown in Figure 2.28, the narrowband signal can be generated by using a balanced
modulator (multiplier).
Figure 2.28. Generating of NBFM using a balanced modulator
Angle Modulation by a Sinusoidal Signal
))2sin(2cos()( tftfAts mcc ..(2.45)
whereis the modulation index that can be eitherp orf.
The modulated signal can be written as
)()(2sin2 tfjtfj
cmc eeARts e
.(2.46)
Since tfm2sin is periodic with periodm
mf
T1
, the same is true for the complex exponential
signaltfj me
2sin
Therefore, it can be expanded in a Fourier series representation. The Fourier series
coefficients are obtained from the following integral
2
0
)sin(
2
1
0
2sin
2
1due
dteefC
nuuj
tfjnf tfj
mnmm m
This integral is known as the Bessel function of the first kind of order n and is denoted by
Jn(). Therefore, the Fourier series for the complex exponential is
Oscillator
f=fc-90o
Phase shift
Integrator
gain=Df
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n
tfj
n
tfj mm eJe
22sin
)(
))(2cos()(
)()()(22
tnffJA
eeJARts
mcnc
tfj
n
tfj
ncecm
The angle modulated signal contains all frequencies of the form ,...2,1,0for nnff mc .
Therefore, the bandwidth of the modulated signal is infinite. Thus, we can define a finite
effective bandwidth for the modulated signal. A series expansion for the Bessel function is
given by
0
2
)!(!
1)(
2
k
kn
k
nnkk
J
(2.47)
For small, we can use the approximation
!2)(
nJ
n
n
n
(2.48)
Thus, for small modulation index , only the first sideband corresponding to n =1 is of
importance.
The symmetry properties of the Bessel function is
oddnJ
evennJJ
n
n
n),(
),()(
Some useful properties of theJn()
- Jn() =J-n() for n even.- Jn() = -J-n() for n odd.- 1)0(1for
2
1)( 0
2
JJn
.
- 0if,0)0(1for0when2!
1)(
2
nJnn
J nn
.
Ex.
Let the carrier be given by )2cos(10)( tftc c and let the message signal be )2cos()( tftm c .
Assume that the message is used to frequency modulate the carrier with kf = 50. Find the
expression for the modulated signal and determine how many harmonics should be selected to
contain 99 % of the modulated signal power.
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Solution
The power content of the carrier signal is given by
502
100
2
2
ccA
P
The modulated signal is represented by
)20sin(52cos(10
)20sin(10
502cos(10
))20cos(22cos(10)(
ttf
ttf
dktfts
c
c
t
fc
The modulation index is given by
5
)(max
m
ff
tmk
))10(2cos()5(10
))(2cos()()(
tnfJ