Wireless Communications
Maja Bystrom
I.
Introduction
A. History
The field of wireless communications has been in existence since the first humans
learned to communicate. In early days of civilization humans would transmit notices of
important events, such as enemy invasions or royal births, through the sounding of horns
or the lighting of fires. While simple messages could be effectively transmitted in this
manner, in order to communicate over long distances the manpower expense was great,
since watchtowers had to be built within sight of each other and continually manned, and
the number of messages was small. It was not until the 1800’s that wireless
communications became what we know it as today. Now we are able to use radio
frequencies to communicate information over long distances (think of the Cassini mission
to Saturn), we can send voice or video at rates of more than hundreds of megabits per
second, and the associated technology has become so inexpensive that many people are
able to afford a mobile phone in order to be in constant contact with others.
We often attribute the beginnings of wireless communication to Guglielmo Marconi
(1874-1937); however, to paraphrase Isaac Newton, “he stood on the shoulders of
giants”. In Marconi’s case these giants were scientists such as James Clerk Maxwell who
proved that radio waves existed, although he could not produce them, and Heinrich Hertz
whose name is now used as a unit of frequency, who transmitted the first man-made radio
waves. Besides being the first to use the antenna, Marconi did not in fact invent anything
new. Instead, he was a remarkable engineer who combined the work of many others to
produce something that was known theoretically to be feasible. It took him through his
adolescence and into his early twenties to develop a wireless system which would even
transmit as far as several miles, but after that point the scaling up of radio systems to
longer transmission ranges was rapid. By 1897 Marconi and his associates had
established a 14.5-mile fixed wireless link over water and the Italian navy had begun to
use his invention for ship-to-shore communication. These first communications were
digital, using Morse code, which was already widely established for wireline telegraphy.
However, the communication rate was slow on the order of 12 words per minute (wpm).
The early transmission systems operated at wavelengths of few thousands of meters up to
10,000 meters; this corresponds to 3-30 kHz. At this time many of the great
communications companies, which still exist today in various forms, were founded:
American Telephone and Telegraph, Marconi Company, Westinghouse, the Radio
Corporation of America.
At the same time as Marconi was laboring on his systems, others were racing to build
improved ones. Development came quickly despite the setbacks of fierce storms that
repeatedly destroyed many of the transatlantic antennas. On Christmas Eve 1906
Reginald Fessenden transmitted the first voice and music that was heard by many
wireless operators in the northeast. He was then granted a US patent for voice
transmission. At the same time Lee DeForest developed his Audion tube, which could
amplify signals. Edwin Armstrong, a Columbia University graduate student, made use of
this vacuum tube to develop a system that made long-distance voice transmission
possible. During the early 1900’s voice transmission across oceans and continents was
proven; however, many were in doubt of the usefulness of the “radio telephone”; since
there was no way of ensuring privacy, anyone with a wireless receiver could listen in.
This remains one of the concerns with many of the wireless systems in use today.
Many of the developments of radio came during the two world wars. Spurred by the
necessity of creating effective military communications, the U.S. government forced the
communications companies and scientists to work together. At the same time many
scientists in other countries were working to develop systems for their militaries. WW I
saw the first air-to-ground communication. Marconi was the first to recognize the
usefulness of short waves, these 1-100 meter waves would use less power and travel less
far and thus could hide information from a distant enemy as well as reduce interference
with neighboring transmitters. Actually, short waves ended up being much more efficient
than longer waves, used less power, and were not reflected off of the ionosphere (which
prohibits daytime transmission) but were reflected off of a higher layer. More
importantly, short waves could transmit information faster than 100 wpm. Several
researchers also noted that ultrashort radio waves could be reflected from objects in their
path, thus laying the basis for radar, a technology perfected during WWII.
While there were sporadic radio broadcasts of music and news to the public in both the
US and Europe prior to WW I, these broadcasts, and indeed all amateur radio operation
was shut down in the US during WW I for reasons of national security. Broadcasts were
resumed in the fall of 1919 and the first radio station KDKA in Pittsburgh opened on
Nov. 2, 1920 to begin daily broadcasts. The total number of amateur radio operators in
the US at that time was perhaps 30,000, so to ensure a listening audience the
Westinghouse company manufactured cheap radio sets and when news of the broadcast
spread the general public hastily bought parts to build their own sets. After the rapid
success of broadcast radio, manufactures quickly improved their receivers, but yet, these
sets cost on the order of $25-$400, a month’s wages, and needed frequent replacement of
vacuum tubes. Compare this to the price and quality of a Walkman today! Introduction
of the analog color and digital television sets saw the same problems. In 1954 the US saw
its first color TV sets for sale for $1300, which was near the price of a car at that time.
Currently, you can purchase an HDTV set for $5000-$7000, still a significant amount of
money.
The number of telecommunications innovations grew rapidly during the last half of the
20th century. Currently there is widespread and growing use of cellular phones, cordless
phones, digital satellite systems, and personal mobile radio networks. Wireless
communications occurs at many different frequencies, from underwater communication
at extremely low frequencies on the order of tens or hundreds of Hertz, to infrared at 1014
Hertz. See Fig. 1 for a partial diagram of the radio frequency (RF) spectrum. In the
United States the spectrum is allocated by the Federal Communications Commission
(FCC).
Fig. 1 A section of the RF spectrum showing some of the frequency assignments in
MHz.
A significant development in telecommunications in the United States was the 1996
Telecommunications Act. This act was written in part to promote competition
(telecommunications had hitherto been controlled mainly by a group of monopolies),
promote integration of advanced services to all Americans and development of the
underlying infrastructure. Furthermore, it created measures, such as a rating code, to deal
with violence and obscenities, and laid out punishments for misuse, such as harassing
phone calls, of the telecommunications systems.
The area of wireless communications will continue to grow for many reasons. People are
becoming accustomed to immediate access to information wherever their locations, and
technological improvements have made providing universal telecommunications access
feasible. There currently is an expansion in the number of personal mobile radio networks
that are the systems used by law enforcement groups, ambulance services, and on the
floor of factories. The signals are meant to be relatively short-range and communication
takes place on designated frequency ranges where they will not interfere with other
applications such as wireless or mobile phones. In the near future there will be
significant growth in wireless for the office, such as wireless local area networks and
wireless private branch exchanges. New developments in personal communications
systems (PCS) include integrated phone/paging/email/data transmission. Currently
handheld units are offered by the major wireless industries with many of these features.
These units range from cell phones with email capability, wireless pen tablets (low-end
laptops without keyboards – interaction is via a pen), PDAs, and personal organizers, At
the moment these have low-rate internet service on the order of 10 kbps, however speed
and interconnectivity will be increased.
Television and radio broadcasts, while still in analog, are rapidly changing to digital. One
example of this is the direct broadcast satellite (DBS) systems that send a digital TV
signal from a satellite to an antenna at each subscriber’s home. The digital signal is a
composite of many television channels. The home antenna is connected to a set-top box
that extracts the desired channel and converts it to an analog signal for display on the
television set. Now the terrestrial broadcast of digital TV is mandated with switch to all
digital required in 2006. These signals are typically called digital television (DTV) or
high-definition television (HDTV). Similarly, digital radio is an area of recent significant
research and development. It is currently deployed and growing in popularity in Europe
and will likely become a standard in the U.S. The motivation behind digital transmission
is that the quality is better and there is no slow degradation as the receiver is moved
farther from the transmitter. The aspect ratio, ratio of width to height, is different than in
analog television, so that movies can be shown without truncation of the sides or being
displayed in “letterbox” format. Also, DTV allows for easier video manipulation such as
split screens or display of video in video. The drawbacks of digital systems are an
increase in required bandwidth and the “cliff effect” in which either reception is good or
no reception is possible.
B. Communications Systems Overview
All of the systems mentioned previously, regardless of frequency or purpose, are
communications systems. A communications system necessarily consists of three parts: a
transmitter, a receiver, and a channel. The transmitter takes a signal, whether analog or
digital, and formats it for transmission over the channel. A wireless channel can be water,
air, or vacuum, and may contain obstructions such as buildings, terrestrial features, or
planets, depending on the medium. The receiver captures the transmitted signal and
performs signal processing, changing it from a form that can be transmitted over the
channel into a form that can be viewed, heard, or stored. All of these system components
introduce degradation to the transmitted signals; furthermore each system has a limit on
the number of signals that can be transmitted. By carefully studying and compensating
for the degradation caused by the system components, and by carefully designing the
signal processing within a communications system, the number of signals that can be
transmitted at one time can be maximized while the signals’ degradation can be
minimized. In the following sections the signals and system design tradeoffs are briefly
considered.
II.
Introduction to Signals
When we listen to radio or the telephone, or watch television, we are observing analog
signals, that is, signals that are continuous in amplitude and time. Fig. 2 illustrates a
segment of speech. From this figure we can see how the signal is able to take on any
amplitude value within the range [-1,1].
Fig.2 A sample of speech with a section extracted.
As was mentioned in the previous section, one of the fundamental constraints to our
transmission systems is the available bandwidth. The FCC only allocates a limited
amount of bandwidth for each application, and no one is allowed to exceed his or her
limitation. Therefore, we need a method of determining the bandwidth or frequency
content of a signal; this bandwidth is measured in cycles per second, commonly called
Hertz.
One of the greatest mathematical discoveries of the 19th century was made by Jean
Baptiste Joseph Fourier, who determined that most aperiodic signals could be represented
by summing their frequency components. That is, for most signals we are interested in
the equation

V( f ) 
 v(t )e
 j 2 ft
dt

holds. This means that a time-domain signal, v (t ) , such as our speech of Fig 2., can be
represented by the different frequencies in it. In the frequency domain our signal is
represented by V ( f ) . This is perhaps best illustrated by an example. Fig. 3 shows the
Fourier transform of extracted segment of speech from Fig. 2. This figure demonstrates
that the speech sample is composed of frequencies between 0 Hz and 16 kHz. This
implies that if the channel or, correspondingly, the bandwidth allowance is greater than
16 kHz, then the signal can be transmitted over the channel and not interfere with any
other transmitters. Thus, the Fourier transform is a very powerful tool in communications
system design. Note that this is not a typical speech sample, since it has high-frequency
noise; speech is typically bandlimited to 300-4000 Hz.
Fig 3. The discrete Fourier transform of the speech sample.
Rather than transmitting an analog signal, we may instead wish to transmit a digital
signal. Digital signals are signals that are discrete in both time and frequency and may
arise in many ways. For instance, to transmit information stored in the memory of
computer such as an email, a stream of bits (1’s and 0’s), called a bitstream, is formed.
We can also change our analog signals into digital signals through sampling and
quantization. Fig. 4 illustrates the process of converting the voice signal of Fig. 2 to a
digital signal. First, the signal is sampled periodically, that is every TS seconds we
1
record the amplitude of the signal. Nyquist proved that the sampling frequency, f S  ,
TS
must be at least twice the maximum frequency in the signal. Typically, voice signals are
sampled at a rate of 8400 samples/second. For compact-disk quality music, which is
typically limited to the range 0 to 15 kHz, the sampling rate is 44,100 samples/second.
(a) Sampling and quantization
of an analog signal.
(b) Reconstruction from sampled
values.
Fig. 4 Sampling, quantization and reconstruction of a signal.
Note that the resulting signal is discrete in the time domain, but each sample can take on
a continuous value. For instance, if we look at the first sample taken at time t  1 the
sample value v (1) could be a number such as 0.01045972… with an infinite number of
digits after the decimal point. To represent even this one sample as a series of bits would
obviously require an infinite-length bitstream, this would involve much more computer
memory or transmission bandwidth than we would be prepared to spend. Therefore we
need a way to decrease the size of our numbers and we turn to quantization to represent
each sample by a fixed (and usually small) number of bits. In Fig. 4(a) the vertical axis is
divided up into 8 “bins”. Each quantized value is assigned the midpoint of the bin. For
example, any sample value falling in the range [0.0 ,0.019) would be assigned the value
0.0095. Then to represent the sample efficiently, the bins are labeled with binary
sequences, and the sample falling in each bin is given the appropriate binary sequence. In
this case, 3-bit sequences are employed, since it takes 3 bits to represent 8 numbers. Thus
we see that the first sample v (1) is assigned the value 0.0095 corresponding to bits 100
while the second sample is assigned the value –0.0395 corresponding to bits 001.
Therefore, quantization of the first two samples results in the bitstream 100001.
Since the samples are assigned to bins, obviously the bin size, or number of bins will
affect the quality of the quantized signal. Fig. 4(b) shows how a signal is reconstructed
from quantized values. When the bits 100 are received after transmission, in order to be
fair, since it is impossible to know where in the range [0.0,0.019) the original sample fell,
the value 0.0095 is assigned to this sample. Therefore, the reconstructed signal, which is
drawn in blue, becomes 0.0095 for the length of the sample interval TS . It can be seen
that with this bin size the reconstructed signal is an approximation to the original signal.
To improve the quality of the reconstructed signal we could increase the number of bins,
and hence increase the number of bits required to represent a sample. However, this
increase in the number of bits/sample, although it results in a better reconstructed signal,
requires more storage or more transmission bandwidth. A typical number of bits per
sample for voice signals is 8, however, for compact-disk quality music 65,536
quantization levels are employed.
To further reduce the number of bits required to represent a signal, a compression scheme
can be utilized. Common image and video compression standards are JPEG and MPEG;
these are based on further quantization of signal components, and are used in digital
television. Speech and other signals rely on schemes such as linear prediction, which
relies on estimation of signals and transmission of the difference between the true signals
and their estimates. These types of compression are lossy; they discard information, and
thus reduce the quality of the signal. However, when carefully employed, the degradation
may be kept to a minimum, or even be made not perceptually apparent, and the bitstream
size significantly reduced.
III.
Signal Propagation and Channel Effects
Besides the lack of readily available bandwidth and the number of users who desire
access to wireless systems, the largest obstacle to building systems is that of noise and
fading. This was seen in the early transmission experiments, the Morse code dots and
dashes were hidden in noise, making long-distance transmission a challenge. Noise in
car radios is a familiar phenomenon, as you drive away from a transmitter, the station
becomes noisier until it finally drops out and all you can hear is static. This effect derives
from the decreasing power in a received signal as the transmitter-receiver separation
increases. The power at the receiver is governed by the following equation
A A c2
(1)
PR  PT T R 2 ,
 4 fd 
where PR and PT are the received and transmitter power, respectively, AR and AT
represent the amplification of the receiver and transmitter antennas, c is the speed of light
 3 108 m / s  , f is the signal frequency, and d is the distance between the transmitter
and receiver. We can see from this equation that the received power decreases with the
square of the distance from the radio to the transmitting antenna.
The electrical components of every communications system generate something called
thermal noise. Noise typically appears like a random (unpredictable) signal added to our
desired signal, and the noise increases with system temperature. A picture of a clean
signal, that is, our transmitted signal, and the signal with noise, n(t ) , added to it is shown
in Fig. 5. According to equation (1) as the receiver and transmitter separation grows the
received signal power decreases. After a time the received power is so low that the noise
becomes audible, and, if the separation is wide enough, the noise dominates, so that all
you can hear is static. This static is an example of the noise in the system, it is entirely
random so you cannot hear anything recognizable in it. Because it is unpredictable, it
cannot easily be removed from the desired signal without degrading the desired signal.
Fig. 5 A signal with noise.
In addition to noise, signals are often subject to fading. Signals can be reflected off of the
ground, buildings, walls, trees or almost any object in their paths. One result of this is
that, on average, the signal strength may decrease by a factor greater than the square of
the distance. Furthermore, receivers at the same distance from the transmitter, but in
different directions, may have greatly differing signal strengths. This phenomenon is
accounted for by a path loss exponent, n, which is a number computed by many
measurements in many areas and is the power to which the distance, d, in (1) is raised. It
is further accounted for by a random number for each location at radius d from the
transmitter. Thus, the power loss equation of (1) can be rewritten as
AT AR c 2
(2)
PR  PT
N.
2
 4 f  d n
In this equation, N is a noise factor, which is determined for different terrains and can
capture some of the differences in signal strengths. The parameter n can take on values of
2 for free space loss (as in equation (1)), 4 for some urban cellular systems, and can range
as high as 6 for intrabuilding communication. Naturally, this parameter will vary
depending on whether the signals can penetrate walls and how many buildings or other
obstacles there are in the neighborhood.
Fig. 6 Multipath fading.
Another problem called multipath adds challenge to the signal transmission. Multipath is
illustrated in Fig. 6 where four signals are received at the transmitter. Each of the four has
traveled a different path and is received at a different strength. Thus, the total received
signal is the sum of these four signals
4
r (t )   ai v(t   i )e ji .
i 1
Each signal on each path is delayed by time  i , and has amplitude and phase shifts ai and
i , respectively. One can imagine the difficulty in extracting an unknown signal
embedded in many others.
Finally, movement of the mobile will affect the received signal by producing a change in
frequency. This, as with noise is a familiar phenomenon; think of the wail of an
ambulance approaching and then leaving, the frequency increases and then decreases. If a
sinusoid is transmitted, the received frequency is the sum of the transmitted frequency
and the Doppler shift
f R  fC  f D ,
where f C is the transmitted sinusoid. Assuming the receiver is co-linear with the mobile
vf
the Doppler shift is given by f D  C where v is the velocity of the mobile. As the
c
velocity increases (the mobile moves toward the transmitter) the apparent frequency
increases, as it moves away the frequency decreases. Since mobile velocities are rarely
constant, this frequency can change quite a bit, making reception a difficult prospect.
Therefore, it is obvious that there are many challenges in system design. Transmitters
must be closely spaced closely or use large enough powers so that receivers can
overcome the inherent system noise. If there is multipath, fading and Doppler shift, these
must be compensated for either with careful signal design or intelligent receivers. One
method of protecting against poor channels is channel coding. Bits are added to the
bitstream in a controlled manner, so that if noise or fading degrades some bits, these lost
bits can be recovered from others. Because the size of the bitstream is increased, the
bandwidth must be increased proportionally in order to maintain the transmission rate.
Thus, there is another tradeoff between protection against channel errors and bandwidth
required.
IV.
Modulation for Analog and Digital Transmission
In order to transmit a baseband signal, which is an analog signal composed of frequencies
near 0 Hz, at radio frequencies we need to change or modulate a high-frequency carrier
with our signal. There are two primary methods of analog modulation, amplitude
modulation (AM) and frequency modulation (FM); this is where our radio transmission
schemes take their names.
In AM we change the amplitude of a carrier by our message. For AM radio the carrier or
sinusoidal wave has frequencies in the range of 540-1700 kHz. The equation for AM is
given by
vc (t )  AC [1  v(t )]cos(2 f ct )
where vc (t ) is the modulated signal to be transmitted, Ac cos(2 f ct ) is a carrier of
amplitude Ac and frequency f c , and the baseband analog signal, v (t ) , is scaled by a
modulation index  . The construction of the AM signal is shown in Fig. 7. Fig. 7(a)
shows the original signal, while Fig. 7(b) shows the signal scaled by the modulation
index and shifted by 1. Fig. 7(c) shows the original carrier, which has a frequency much
greater, typically by several orders of magnitude, than that of the baseband signal.
Finally, Fig. 7 (d) shows the modulated signal. Observe how the message, the original
baseband signal v (t ) , is contained in the amplitude or envelope of the modulated signal
vc (t ) .
(a) Original signal.
(c) Carrier
(b) Scaled and raised signal.
(d) AM signal with information
embedded in the
shape of the high-frequency carrier.
Fig. 7 Generation of an AM signal.
Frequency modulation is similar to amplitude modulation, except with FM the amplitude
of the carrier remains constant, but the frequency changes with the message. The FM
equation is
t
vc (t )  AC cos(2 f ct    v( )d  )

.
Now the integral of the message, scaled by a modulation index  , changes the phase or,
correspondingly, the frequency of the carrier Ac cos(2 f ct ) . Fig. 8 shows the message
and the results of modulating the carrier. Observe how as the amplitude of the message
increases the frequency of the carrier increases.
(a) Original Signal.
(b) FM signal.
Fig. 8 Generation of an FM signal.
B. Digital Modulation
Since bitstreams are not continuous signals, the AM or FM modulation schemes
described above cannot be directly employed, and different ways to modulate a highfrequency carrier must be found. One method is binary phase shift keying (BPSK). While
the name is complicated, building the modulated waveform is actually a very simple
process.
To transmit a 1 the signal v1 (t )  cos  2 fC t  is transmitted for time Tb , while to send a 0
the signal v2 (t )  cos  2 fC t    would be transmitted. Note that these two signals are
180 out of phase with each other. In Fig. 9 the BPSK signal corresponding to the
bitstream 10110 is shown. Observe that there is a phase change at every bit change, these
changes occur at times t  1000, 2000, and 4000 seconds.
Fig. 9 A BPSK waveform.
In order to determine which bit was transmitted in time interval nTb  t  (n  1)Tb all we
have to do is to detect the phase of the received signal in that time interval. A more
common method of transmitting bits is to take two bits at a time from the bitstream and
use four-level phase shift keying. Variations on this method are used in many of today’s
digital systems today. Since four signals are required to represent all of the possible
combinations of two bits, we then assign each combination the associated signal
i 

vi (t )  cos  2 f C t   ; i  1 4 .
4

Again, we detect which of the four signals was sent by determining the phase of the
received signal.
Naturally, there are other methods of transmitting bits, we could instead choose between
two signals of different frequencies or amplitudes to represent our two bits. Another
method is to use a combination of phase-shift keying and amplitude modulation; the
information is then contained in both the amplitude and phase of the signal.
The different modulation schemes are selected on the basis of their robustness in the face
of noise and fading, the power required to transmit each and the complexity of the
hardware required for transmission.
V.
Multiple Access
Until this point we have discussed how to create a signal for one user, but the available
bandwidth must be shared between many users. There are many methods of doing so;
two of these methods, frequency division multiple access (FDMA) and time division
multiple access (TDMA), are what is termed controlled multiple access, other methods
such as code division multiple access (CDMA) and carrier-sense multiple access
(CSMA) effectively permit users to access the channel whenever desired, under certain
constraints.
(a) FDMA frequency division.
(b) TDMA time division.
Fig. 10 Division of frequency or time in two multiple-access schemes.
Frequency division multiple access implies splitting the available spectrum between the
users. This the method broadcast radio and television stations employ, each station is
assigned a band (a certain range of frequencies in which they can transmit) and there is a
short band in between the limits of each station called a guard band. The guard band is
used to protect against flaws in the system such as carrier drift. A diagram of this is
shown in Fig. 10(a). In the U.S. analog cellular phone standard (AMPS) the channels are
30 kHz wide and there are a total of 832 channels in the system, each having a forward
and a reverse link.
For the TDMA system each user has control of the total channel bandwidth for a short
amount of time, then the channel is handed off to the next user. Each waiting user has a
turn and then control is returned back to the first user. A diagram of a TDMA system is
shown in Fig. 10(b). TDMA is used in the European cellular phone standard Global
System for Mobile (GSM). Each channel supports 8 users; each user is allowed to
transmit for 577 microseconds before it is the next user’s turn.
Code division multiple access is a hybrid system, which allows all users to occupy the
same bandwidth and time simultaneously. Essentially, everyone transmits at the same
time; signals are differentiated at the receiver because they are orthogonal to each other.
The orthogonality and knowledge of characteristics of the orthogonal signal make it
possible to extract one user’s signal from the entire transmission. The CDMA detection
process can be envisioned as a noisy room. Without concentrating it seems as if what you
hear is simply an unintelligible combination of sounds. However, if you can focus on a
familiar voice, the words from this voice start to become distinguishable, and you can
block out the background noise in the room.
CSMA is a method used in many wireline communications that can also be used for
digital wireless communications. Each user’s voice or data is broken into packets. The
user then listens in on the channel in order to determine if anyone is transmitting. If the
channel is unoccupied, then the user transmits. However, a collision occurs if two more
users attempt to transmit at the same time. The receivers detect the collision and the users
must retransmit their information at a later time. This system is only efficient if there is
not a strict time constraint on the data, or if there are few users who wish to
simultaneously transmit.
VI.
Cellular Systems, Frequency Reuse and Wireless Networks
Even with the multiple access schemes mentioned previously, only a small number of
users could be handled at the same time. Certainly, one system would not be able to
handle an entire city, perhaps not even an entire building. Therefore, in order to
accommodate more than a small number of users, space is divided into cells as illustrated
in Fig. 11. Each cell contains a basestation that handles all mobiles within the boundaries
of the cell. Cells do not necessarily have to be of the same size. In rural areas cells are
large, with radii of kilometers. On the other hand, consider a building such as the
Philadelphia Convention Center. During conventions there are expected to be thousands
of people in the building; they may all access their mobile phones at the same time, for
instance, after the conclusion of a seminar. Thus, there may be tens or hundreds of
microcells, on the order of a few square meters within a building such as this. Each cell
is assigned its own frequency range, and neighboring cells will not be assigned the same
range. Thus, the spectrum is shared in a cellular system much as it is in the radio and
television system today. Cities which are widely enough separated, for instance,
Philadelphia and New York, have radio and television stations at the same frequencies,
the frequency spectrum is re-used in space. In a cellular system if cells which are
assigned the same frequency range are widely separated, then there will be little inter-cell
interference. However, if there is to be wide cell separation, there must be a large number
of frequency ranges to assign, and thus each range is small. This limits the number of
calls that can be handled in a cell, consider FDMA as an example.
Fig. 11 illustrates the interconnections of basestations, the transmitters/receivers of the
cells. Three cells of an n-cell system are shown. The basestations are connected via a
landline or microwave link to the mobile telephone switching office (MTSO), which
controls all of the calls in this n-cell region. The MTSO also routes calls to the public
telephone system, the traditional wireline system.
Fig. 11 An example of cell and basestation layout.
There are many important considerations in the design of cellular systems, ranging from
cell placement, to switching users between basestations as they move from cell to cell, to
providing service to users when they are roaming outside their provider’s network. Each
of these is discussed briefly below.
Cell layout and system development is a difficult proposition. To determine the size of
cells required in a particular area, precise traffic models, models of the number of users at
a given time, must be developed. A provider would like to be able to provide service to
all users within an area, but the cost of erecting basestations and expanding an existing
network is large. The space for a basestation must be bought or leased and it must be
connected, either through a wireline connection or a high-speed microwave or optical
link, to the network. Furthermore, space is not always available for basestations. In the
U.S. there are many service providers, in each area each provider establishes its own
networks. There is continual competition for the best basestation locations, typically on
high buildings or hills. Often there is resistance from communities to new basestations in
their neighborhoods, either from dislike of the aesthetics of the towers or from concerns
about the effect of radio waves on human health.
In a mobile system, since the users can travel between cells, the number of users within a
cell at a given time can never be known exactly. However, given the number of slots
available in a cell, C, and the average usage within a cell of a selected size, T, the grade
of service providable can be calculated from
T C / C!
.
Pr{blocking}  C
k
T / k !
k 1
This is the probability that a call will be blocked, that the entire channel will be entirely
occupied by other users when the call is placed. If this number is greater than users will
tolerate, the parameters such as the cell size must be adjusted to compensate, balancing
the cost of cell placement with the desired grade of service.
The switching of a call from one basestation to another as a user travels through cells is
termed a handoff. Often, just turning a corner and moving out of sight of the basestation
can decrease the mobile received power enough to require a handoff to a stronger, yet
more distant basestation. There are four types of handoffs varying on whether the handoff
is controlled by the mobile or the basestation or network. There are advantages to these,
first, if the mobile makes the decisions, it can react quickly. However, if the network or
basestation makes the decisions the delay can be long, since the basestation must judge
the received signal, therefore, there are advantages and disadvantages to all types of
handoffs. The main requirement of handoffs is that they should be seamless, that is, the
user should have no awareness of the switch between basestations.
Roaming is placing a call from outside a home area, typically the roaming should be
seamless, and invisible to the user, that is, the user should have no idea that the call is
being placed through a system other than the home system, with the possible exception of
a roaming light or indicator. Therefore, systems must have roaming agreements in place
and be compatible; it must be possible to identify a user’s home system as the call is
being placed and the two systems must be able to exchange information for billing
purposes.
There are many competing wireless systems and services in the U.S., some are all analog,
some are all digital, while others are hybrid systems which operate at times on either
digital or analog. There are also competing standards, which use different multiple-access
and modulation schemes. Therefore, if a user would like to change service providers he
or she must purchase a new phone along with the service. Furthermore, many of the
European and Asian standards are different from the U.S. standards, thus phones for U.S.
systems may not work abroad. There is some movement in the U.S. to adopt the
European mobile phone standard; this will lay the basis for extension of global service.
Another increasingly employed solution to worldwide coverage is to manufacture a
multi-mode phone, which is able to detect the type of system of the local provider and
adjust transmission accordingly.
Up until this point we have considered mainly the mobile telephone networks; however,
paging, PCS and other mobile networks operate on the same principles. Furthermore,
although mobile wireless networks dominate the industry, there is a growing market for
fixed wireless networks. This class of networks may have the same cellular layout as a
network for mobile communications, but has both fixed basestations and users. A simple
example is an infrared wireless link from computers to printers in an office, while a much
more complex system could involve providing wireless internet access to a community.
The reason for the growth of interest in fixed wireless systems is the cost of installing
cable or fiber in established areas, and the ease of relocation possible with wireless.
Additionally, a fixed wireless network does not have the problems of time-varying fading
or Doppler shift and does not require the extensive processing for handoffs and roaming
as would a mobile network, and thus is easier to implement.
In the future there will most likely be an increased number of wireless systems, but also a
move to standardize more so that these systems can intercommunicate. With an everincreasing number of services and a desire for seamless handoffs between providers,
developing the next generation of wireless networks will present significant challenges. A
lesson can be learned from one of the more spectacular failures in the
telecommunications industry, the Iridium project. Iridium was proposed as a worldwidecoverage cellular phone system for the business traveler and to provide telephone service
to areas such as Russia and India where there is currently a small market penetration. In
many ways it was an excellent engineering feat, the final design consisted of 66 low earth
orbiting satellites built at a cost of about $30 million dollars each. With this many
satellites almost total coverage is possible and each satellite could handle 48*230 calls.
The goal of Iridium was to provide seamless service in much of the world, since, for
reasons mentioned previously, equipment from one cellular provider in one geographical
area will not operate on the networks of competing providers in other geographical areas.
Unfortunately, the system has declared bankruptcy due to undersubscription and the
satellites will likely be discarded unless a purchaser is found. The service was not popular
for many reasons: the phones were large, much larger than the phones people are
accustomed to; the price per phone was on the order of $3000; the phones did not
function well indoors; and, the cost per phone call was very high as compared with
terrestrial systems. Therefore, Iridium was obsolete almost before it was built. However,
this should not prohibit development of large or even worldwide systems, but instead
should serve as a caution of the care required in system development and marketing.
Others are currently meeting the challenge of providing worldwide coverage with a single
system; one example is the Globalstar system which employs the European GSM
standard and both terrestrial and satellite coverage.
VII.
Conclusions
It is apparent that the design of communications systems is a complex process with a
large number of tradeoffs to deal with the limitations of channels and equipment. This
chapter began by examining signals and how to determine the bandwidth of signals, in
order to ensure that the transmitted signals had a small enough bandwidth to fit within
spectrum allocations. It was shown how analog signals can be sampled and quantized,
and that there are size versus quality tradeoffs in this process. Next, channel effects are
studied. It was seen that there is inherent noise in systems, but that this noise can be
overcome by increasing the power at the transmitter. On the other hand, large transmitter
power requires larger batteries, a stringent constraint in applications such as mobile
telephony. In wireless channels there can be multipath or time-varying fading and
Doppler shift to complicate reception.
Having discussed single signals, we then considered how to share channels and examined
four primary methods. Next, the further sharing of the spectrum was considered with an
examination of cellular systems and frequency re-use. Several of the inherent challenges
were discussed, it was seen that systems must be carefully developed and synchronized in
order to provide for all users and to provide the services desired. Finally, as a case study,
the Iridium system was discussed.
Even with the enormous growth in wireless communications systems within the past few
decades, there are constantly new advancements in research and development. Currently,
there are many concerns about the security and reliability of wireless systems, challenges
which are important but which are not addressed here.
There is certainly much more to be done, frequencies to be explored and systems to be
developed, that a quotation by Marconi appropriately summarizes the current state of
wireless communications
It is dangerous to put limits on wireless.
Further Reading
“Marconi Father of Radio”, D. Gunston, Crowell-Collier Press: NewYork. 1965.
“Digital and Analog Communication Systems”, L.W. Couch II, Fifth Edition, Prentice
Hall: NJ, 1997.
“Wireless Communications: Principles & Practice”, T.S. Rappaport, Prentice Hall: Upper
Saddle River, NJ. 1996.
“CDMA IS-95 for Cellular and PCS”, L. Harte, M. Hoenig, D. McLaughlin, and R.
Kikta, McGraw-Hill: New York, 1999.
“Direct Broadcast Satellite Communications”, D.C. Mead, Addison-Wesley: Upper
Saddle River, NJ, 2000.
“DTV Survival Guide”, J. Boston, McGraw-Hill: New York, 2000.
“Wireless Personal Communications The Future of Talk”, R. Schneiderman, IEEE Press:
New York, 1994.
“Advances in Wireless Terminals”, P. Lettieri and M.B. Srivastava, IEEE Personal
Communications, vol 6, no. 1, pp 6-19 Feb 1999.
Telecommunications Act of 1996, Pub. LA. No. 104-104, 100 Stat.56 (1996).
http://www.fcc.gov/telecom.html
“Are mobile phones safe?”, K.R. Foster and J.E. Moulder, IEEE Spectrum, August 2000.
Exercises
1. Consider the bitstream 101101… . Draw a BPSK waveform that could be used to
transmit the bits. Draw an FSK waveform for this bitstream. Compare the
bandwidth of these two modulation schemes.
2. Assume in a cellular system that there are 10 channels (or slots) available and that
the average use of these slots is 50%. What is the blocking probability of this
system? Discuss whether this is a reasonable number.
3. Suppose you have been allocated 79 MHz of bandwidth by the FCC for a wireless
system using FDMA with 25 KHz channels not including guard band. For a
telephone call with full-duplexing, both an uplink and downlink channel is
required. This means that at least 50 KHz would be required per call. If your
carrier can drift by 80 Hz, which means that a guard band is required between
each channel, how many users can the system support at any one time. Explain
your reasoning.
4. Consider the bitstream 101001… . This bitstream can be converted into a
waveform by holding the voltage at +1 for T seconds when a 1 appears in the
bitstream and then holding the voltage at –1 when a 0 appears. Draw the resulting
waveform. Now suppose amplitude modulation is to be used to transmit the
bitstream. Draw the modulated signal by using the waveform from the first part in
Eq. (6). Show all steps.
5. Assume unit gain transmit and receive antennas, a transmission frequency of 900
MHz, and a transmission power of 1mW. Find the received power in Eq. (2) at a
transmitter-receiver separation of 10m, 100m and 1km. Now, assume that the path
loss exponent is 4 (you may assume the noise figure is 1). Find the received
power in Eq. (3) at a transmitter-receiver separation of 10m, 100m and 1km.
Compare the six results.
6. Discuss the advantages and disadvantages of different cell layouts and degrees of
frequency use. Consider the performance, the cost, and the societal impact.
MATLAB Exercises
Project 1 - AM, PM and Signal Bandwidth
The goal of this project is to discover the effect of amplitude modulation and phase
modulation on the time- and frequency-domain representations of the modulated carrier.
Steps:
1. Save the code given below for the first part of the project in a MATLAB directory
as proj1a.m, save the second part of the project as proj1b.m
2. Run the first part by typing proj1a
3. Print the resulting plots.
4. Discuss the shape of the time-domain AM and PM signals. Consider where the
message is contained, and how it might be extracted from the modulated carrier.
5. Discuss the differences and similarities in the frequency-domain signal, the
magnitude spectrum of the modulated carrier.
6. Change the frequency of the message slightly by changing the parameter f0
7. Repeat steps 3-5 comparing the results of the new signal with the previous results.
8. Save the PM signal by typing save PM xpm
9. Run the second project by typing proj1b
10. Print the resulting plot
11. Discuss the resulting bandwidth occupied by the signal.
12. Comment out the lines generating the cosine and uncomment the lines for
loading a signal.
13. Replace <filename> with PM or the name of another signal file
14. Run the program and print the resulting plot.
15. Discuss the resulting bandwidth occupied by the signal. Compare this to the
results from step 11.
16. Submit all plots and written discussions.
%
%
%
%
%
%
%
Project 1
Part I - AM and PM Signal Generation
Wireless Communications
clear
% Generate a message which is a sinusoid
% First initialize variables
%
N = number of samples
%
f0 = cyclical frequency of message signal
%
T0 = period of the message signal
N = 1000;
f0 = 10;
w0 = 2*pi*f0;
T0 = 1/f0;
% Generate the message
n = 0:1:N-1;
t = n*T0/N;
x = 0.75*cos(w0*t);
figure
subplot(711);
%
% AM SIGNAL GENERATION
%
% Plot message signal
plot(t, x);
title('Message signal v(t)');
xlabel('t');
ylabel('v(t)');
% Generate carrier signal
fc = 100;
wc = 2*pi*fc;
Tc = 1/fc;
xc = cos(wc*t); % Ac=1
subplot(713);
plot(t, xc);
title('Carrier signal');
xlabel('t');
ylabel('c(t)');
% Generate AM signal
mu = 0.5;
xam = (1+mu*x) .* xc;
% Plot AM signal
subplot(715);
plot(t, xam);
title('AM signal')
xlabel('t');
ylabel('vc(t)');
% Find the spectrum of the AM signal
XAM = fft(xam);
XAMshift = 1/N*fftshift(XAM);
n1 = -500:499;
freq_n1 = n1/T0;
% Plot the magnitude spectrum of the AM signal at frequencies of
interest
subplot(717);
plot(freq_n1, abs(XAMshift), 'o');
axis([-200 200 0 1]);
title('Magnitude spectrum of the AM signal');
xlabel('f');
ylabel('Vc(f)');
%
% PM SIGNAL GENERATION
%
% Plot message signal this is the signal generated above
figure
subplot(511);
plot(t, x);
title('Message signal v(t)');
xlabel('t');
ylabel('v(t)');
% Generate PM signal
k_p = 3*pi/4;
xpm = cos(wc*t + k_p*x);
% Plot PM signal
subplot(513);
plot(t, xpm);
title('PM signal')
xlabel('t');
ylabel('vc(t)');
% Find spectrum of the PM signal
XPM = fft(xpm);
XPMshift = 1/N*fftshift(XPM);
n2 = -500:499;
freq_n2 = n2/T0;
% Plot spectrum of the PM signal
subplot(515);
plot(freq_n2, abs(XPMshift), 'o');
axis([-200 200 0 1]);
title('Magnitude spectrum of the PM signal');
xlabel('f');
ylabel('Vc(f)');
%
%
%
%
%
%
%
Project 1
Part II - Signal Bandwidth
Wireless Communications
%
%
Either load in a previously stored signal or create a new
uncomment the appropriate following section.
%
LOAD a signal - uncomment five command lines
%
replace <filename> the name of the stored file
%
it must be in filename.mat (Matlab) form
%
%load <filename>;
%w = <filename>;
%N = length(w);
%n=0:1:N-1;
%To=0.01;
%
CREATE a new signal - uncomment seven command lines
%
the signal will be a cosine with variables
%
N = number of samples
%
fo = cyclical frequency of sinusoid
%
wo = angular frequency of sinusoid
%
To = period of sinusoid
N = 50;
fo = 10000;
wo = 2*pi*fo;
To = 1/fo;
n = 0:1:N-1;
t = n*To/N;
w = 4*cos(wo*t);
% Find Fast Fourier Transform of the signal
W = fft(w);
% Convert samples 0,1,...,N-1 into positive and negative
Wshift = 1/N*fftshift(W);
% Plot signal vs. sample
subplot(3,1,1);
plot(n,w,'o');
xlabel('Sample Number');
ylabel('Sample Amplitude');
% Plot FFT vs sample
subplot(3,1,2);
plot(n,abs(Wshift),'o');
xlabel('Sample Number');
ylabel('Magnitude Spectrum');
% Shift the samples so that they are centered at 0
% Scale the axis
n1 = -1*round(N/2):1:round(N/2-1);
freq_n1= n1/To;
if length(freq_n1) > length(Wshift)
freq_n1=freq_n1(1:length(Wshift));
end
%
Plot the transform vs. cyclical frequency
subplot(3,1,3);
plot(freq_n1,abs(Wshift),'o');
xlabel('Cyclical Frequency (Hz)');
ylabel('Magnitude Spectrum');
Project 2 - Noise in Baseband Signals
The goal of this project is to investigate the effect of varying degrees of noise on digital
baseband signals.
Steps:
1. Save the code given below for the first part of the project in a MATLAB directory
as proj2a.m
2. Run the first part by typing proj2a
3. Print the resulting plot.
4. Record the noise standard deviation and the bit error count.
5. Discuss the appearance of the signal with noise as compared to the noise-free
signal.
6. Change the noise standard deviation to a value within the permitted range given in
the code and re-run the program
7. Record the noise standard deviation and the bit error count.
8. Repeat steps 6 and 7 for at least 10 values of the standard deviation.
9. As the noise standard deviation increases and decreases note the appearance of the
noisy signal. Discuss the changes in the signal.
10. Follow the directions in the code for the second part of the project.
11. Print the resulting plot.
12. Discuss the changes in the bit error rate as a function of the noise.
13. Submit all plots and discussions.
%
%
%
%
%
%
%
Project 2
Part I - Noise in Baseband Signals
Wireless Communications
% Change this following line to change the standard deviation of the
noise,
% which will change the noise power. The valid range is [0.01,1]. A
large number
% indicates more noise
stdev=1;
%
% Create an arbitrary bitstream
%
bitstream = [1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 1 1
1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 1 0 0 0
1 1 0 1 1 0 1 01 0 0 1 1 1 1 1 0 0 1 0 1 0 1 0 1 0 0 1 1 1 1 0 0 1 0
1];
%
% Generate the baseband signal,v[n], from the above bitstream with
pulses
% of width 5 and height 1/sqrt(5).
%
for i=0:99
if bitstream(i+1) == 1
v(i*5+1) = 1;
v(i*5+2) = 1;
v(i*5+3) = 1;
v(i*5+4) = 1;
v(i*5+5) = 1;
else
v(i*5+1) = 0;
v(i*5+2) = 0;
v(i*5+3) = 0;
v(i*5+4) = 0;
v(i*5+5) = 0;
end
end
%
% plot the NRZ baseband waveform
%
subplot(3,1,1), plot(v,'o');
axis([0 40 0 1.0]);
%
% add zero-mean Gaussian noise to the waveform
%
for i=1:500
y(i) = v(i) + stdev*randn;
end;
%
% plot the noisy waveform
%
subplot(3,1,2), plot(y,'o');
axis([0 40 -4 4]);
%
% create an integrate and dump filter with output z(i)
%
for i=0:99
temp = y(i*5+1) + y(i*5+2)+ y(i*5+3) + y(i*5+4) + y(i*5+5);
z(i*5+1) = temp;
z(i*5+2) = temp;
z(i*5+3) = temp;
z(i*5+4) = temp;
z(i*5+5) = temp;
end
%
% plot the matched filter output
%
subplot(3,1,3), plot(z,'o');
axis([0 40 -10 10]);
%
% sample and determine the number of bit errors
%
bit_error_count = 0;
for i=0:99
if z(i*5+3) > 0.5
temp = 1;
else
temp = 0;
end
if bitstream(i+1) ~= temp bit_error_count = bit_error_count +1;
end
end
bit_error_count
% Run this program for many choices of the standard deviation and
record
% the standard deviation and the number of bit errors for each trial
%
%
%
%
%
%
%
Project 2
Part II - Bit Error Rate Curves
Wireless Communications
% For each standard deviation compute the signal-to-noise ratio
% using the following. Replace stdev with your value and record
% the result
SNR = 10*log10(1/(stdev^2));
% Now plot the first point with the following three commands
% Replace SNR and bit_error_count with the appropriate values
semilogy(SNR,bit_error_count,'o');
axis([0 40 0.000001 0.1]);
hold;
% Now add the other points by repeating the following command
% Replace SNR and bit_error_count with the appropriate values
semilogy(SNR,bit_error_count,'o');
Project 3 - Number of Users and Blocking Probability
The goal of this project is to determine the average amount of traffic, effectively the
number of users, which can be served in a cell given a desired grade of service and a
number of available channels.
Steps:
1. Save the code given below for the auxiliary function in a MATLAB directory as
ErlangB.m, save the code for the project as proj3.m
2. Run the program by typing proj3
3. Record the capacity
4. Change the number of channels, the parameter channels, to a number between 2
and 100.
5. Repeat steps 2 through 4 for 10 channel values.
6. Change the desired grade of service, the parameter desired_GOS, to a value
between 0.1 and 0.0001
7. Repeat steps 2 through 6 four times.
8. Discuss the results. Consider the tradeoffs in desired grade of service and the
number of users in the system.
9. Submit the discussion.
%
%
%
%
%
%
%
Project 3 - Auxiliary function
Number of Users and Blocking Probability
Wireless Communications
function [diff] = ErlangB(A,C,GOS)
sumA = 0;
for i=0:C
sumA=sumA+(A^i/factorial(i));
end
GOS1 = (A^C/factorial(C))/sumA;
diff=GOS-GOS1;
%
%
%
%
%
%
%
Project 3 Main Routine
Number of Users and Blocking Probability
Wireless Communications
% Change the following two parameters and plot the number of
% users, the capacity, as a function of desired_GOS for a
% selected number of channels
channels = 10;
desired_GOS = 0.01;
init_capacity=channels*4/5;
options=optimset;
capacity=fsolve('ErlangB',init_capacity,options,channels,desired_GOS)