MODULATION, DETECTION AND CODING docx

MODULATION, DETECTION
AND
CODING
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MODULATION,
DETECTION
AND
CODING
Tommy
Oberg
Signals
and
Systems Group,
Uppsala
University
Uppsala,
Sweden
JOHN WILEY
&
SONS,
LTD
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• New
York
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©
2001
by
John Wiley
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Ltd
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Congress Catatoging-in-Publication Data
A
Library
of
Congress
catalogue
record
has
been applied
for
British
Library Cataloguing
in
Publication Data

A
catalogue record
for
this
book
is
available
from
the
British Library
ISBN
0-471-49766-5
Typeset
in
Times
by
Deerpark Publishing Services Ltd, Shannon.
Printed
and
bound
in
Great Britain
by
Antony Rowe Ltd, Chippenham.
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book
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paper
responsibly manufactured
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sustainable forestry
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one
used
for
paper production.
CONTENTS
Preface
xi
1
TELECOMMUNICATIONS
1
1.1
Usage today
1
1.2
History
1

1.3
Basic elements
5
1.3.1
Transmitter side
6
1.3.2
The
channel
6
1.3.3 Receiver side
6
1.3.4
Another system
for
communication
7
1.3.5
The
scope
of the
book
7
1.4
Multiple user systems
8
1.4.1 Methods
for
multiple
access

8
1.4.2 Continued analysis
15
1.5
Appendix:
the
division
and
usage
of the
electomagnetic
spectrum
15
2
LINK BUDGET
19
2.1
Signal
to
noise ratio
19
2.1.1
Calculation
of the
signal power
20
2.1.2
Calculation
of
noise

24
2.1.3
SNR in
digital transmission
30
3
INFORMATION THEORY
AND
SOURCE CODING
37
3.1
The
concept
of
information
38
3.1.1
Discrete source
40
3.1.2
Continuous
source
41
3.2
Channel
43
3.2.1 Mutual information
44
3.2.2 Channel models
46

3.2.3 Calculation
of
channel capacity
48
3.3
Source coding
55
3.3.1 Data compression
56
3.3.2 Speech coding
70
3.4
Appendix
76
3.4.1
Example
of
image coding, MPEG
76
Vi
CONTENTS
4
CHANNEL CODING
81
4.1
Error detection
and
error correction
81
4.1.1 Fundamental concepts

in
block coding
83
4.1.2 Performance
of
block
codes
86
4.2
Automatic repeat request
95
4.2.1 Function
of ARQ
systems
95
4.2.2 Performance
of ARQ
systems
97
4.3
Block codes
100
4.3.1 Galois fields
100
4.3.2 Linear block
codes
102
4.3.3 Cyclic codes
111
4.3.4 Non-binary block codes

123
4.3.5
Modifying
block codes
126
4.4
Convolutional codes
129
4.4.1 Description
of
convolutional
codes
129
4.4.2 Performance
of
convolutional
codes
135
4.4.3 Decoding
of
convolutional codes
141
4.5
Interleaving
155
4.6
Turbo coding
157
4.6.1 Coding
158

4.6.2 Decoding
159
4.7
Cryptography
170
4.7.1
The RSA
algorithm
174
4.8
Appendix
177
4.8.1 Examples
on
application
of
error correcting coding
181
5
MODULATION
185
5.1
Baseband modulation
186
5.1.1
Preceding
187
5.1.2 Pulse shapes
for
lowpass channels

188
5.2
Calculation methods
for
bandpass systems
and
signals
192
5.3
Analogue carrier modulation
202
5.3.1 Analogue amplitude modulation
203
5.3.2 Analogue phase
and
frequency
modulation
215
5.4
Digital carrier modulation
222
5.4.1 Digital amplitude modulation
223
5.4.2 Digital phase
and
frequency modulation
225
5.4.3 Non-linear methods
with
memory

227
5.4.4 Spectrum
in
digital modulation
237
5.4.5 Combined modulation
and
error correction coding
251
5.4.6 Transmission
using
multiple
carriers
258
5.5
Appendix
260
CONTENTS
VI1
5.5.1 Various
frequency
pulses
260
5.5.2 Computing spectra
for
signals with large state diagrams
261
6
DETECTION
IN

NOISE
265
6.1
Fundamentals
of
narrowband noise
266
6.2
Analogue systems
269
6.2.1 Influence
of
noise
at
amplitude modulation
269
6.2.2
Noise
in
angle modulation
274
6.3
Digital systems
280
6.3.1 Optimal receiver
281
6.3.2 Signal space
289
6.3.3 Calculation
of bit

error rate
297
6.3.4 Calculation
of
error rate
for a
complicated decision space
313
6.3.5 Non-coherent receivers
316
6.3.6 Comparison
of
some types
of
modulation
326
6.4
Diversity
337
6.4.1
Methods
of
combination
338
6.4.2
Bit
error rate
339
6.5 The
radio receiver

340
6.6
Appendix
343
6.6.1
Error probabilities
for
some cases
of
modulation
343
6.6.2
The
Q-function
343
6.6.3
Some
important density
functions
in
communication
345
6.6.4 Norm
345
7
ADAPTIVE CHANNEL EQUALISERS
351
7.1
Channel equaliser
352

7.1.1
Zero
forcing equaliser
353
7.1.2
Equalisers based
on
minimum
mean square error
354
7.2
Algorithms
for
adaptation
358
7.2.1
The LMS
algorithm
361
7.2.2
The
recursive least squares algorithm
370
7.3
Appendix
374
7.3.1
Systolic array
374
8.

ADAPTIVE ANTENNAS
377
8.1
Array antennas
377
8.1.1
Antennas with steerable main beam
378
8.1.2
Vector description
of the
output signal
of
array antennas
382
8.1.3
Multilobe antennas
384
8.2
Signal processing
with
array antennas
388
8.2.1
The
reference signal method
388
Vlll
CONTENTS
8.2.2

The
linear constraint minimum variance method
389
8.2.3 Music
392
8.3
Spatio-temporal equalisers
396
8.3.1
The
transmission channel
396
8.3.2 ST-MLSE
399
8.3.3 ST-MMSE
402
8.3.4 Estimation
of
channel parameters
404
9
CDMA: CODES
AND
DETECTORS
407
9.1
Spreading
codes
408
9.1.1 Walsh

codes
409
9.1.2 m-Sequences
411
9.1.3
Gold sequences
415
9.1.4
Kasami sequences
416
9.2
Detectors
for
CDMA
416
9.2.1 Linear detectors
418
9.2.2 Interference cancellation
422
9.3
Appendix: generator polynomials
for
m-sequences
424
10.
SYNCHRONISATION
425
10.1
Introduction
425

10.2 Fundamentals
of
phase
locked
loops
426
10.2.1
Analysis
of an
analogue phase-locked loop
426
10.2.2 Digital phase locked loop
432
10.3 Carrier synchronisation
434
10.3.1
Squaring loop
435
10.3.2 Costas loop
436
10.4 Clock synchronisation
437
10.5 Frame synchronisation
438
10.5.1 Synchronisation probability
438
10.5.2
Synchronisation
codes
440

10.5.3
Locking strategies
441
APPENDIX
A 443
A.
1
Review
of
mobile telephone systems
443
A.
1.1
Second generation systems
444
A.
1.2
Third generation systems
445
A.
1.3
Roaming
445
A.2
Review
of
sysems
for
cordless
telephones

447
A.3
Review
of
television systems
448
A.4
Digital Television
449
CONTENTS
IX
A.4.1
Source coding
449
A.4.2 Modulation
450
A.4.3
Channel coding
451
A.5
FM
broadcasting
and RDS 453
A.6
Digital audio broadcasting
455
A.6.1
Source coding
455
A.6.2

Channel coding
456
A.6.3
Modulation
456
Answers
to
exercises
457
Index
463
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PREFACE
This book
is
intended
for
courses
at
least
at
Masters level
to
provide
an
introduc-
tion
to the field of
signal processing
in

telecommunications.
The
text therefore
deals mainly with source coding, channel coding, modulation
and
demodulation.
Adaptive channel equalisation,
the
signal processing
aspects
of
adaptive antennas
as
well
as
multi-user detectors
for
CDMA
are
also included. Shorter sections
on
link budget, synchronising
and
cryptography
are
also included. Network aspects
are not
discussed
and
very little

is
given about wave propagation.
The
book aims
to
give
the
reader
an
understanding
of the
fundamental signal processing func-
tions
and of the
methods
used
when analysing
the
capacity
of a
complete commu-
nication
system.
The field of
telecommunications
is
developing rapidly.
Therefore,
a
thorough understanding

of
analysis methods, rather than just
the
results
of the
analysis,
is
important knowledge which will remain
up to
date
for a
longer period
and
make
it
possible
for the
reader
to
follow
the
progress within this
field. The
presentation
in the
book
is at the
block diagram level. Hardware
and
software

solutions
are
only treated sporadically,
and it is
therefore recommended
that
the
student
has
completed basic courses
in
electronics
and
digital systems
in
order
to be
able
to
make
the
connection between real systems
and the
block
diagrams
and
methods treated here.
The
material
has a

theoretical base which
makes
it
possible
for the
student
to
continue with both deeper studies
and
design
work
with
new
systems
not
treated
in
this text. Completed courses
in
basic signal
processing
and
probability theory
are
necessary
for the
understanding
of the
material
presented here.

The
book includes: text where theory
and
methods
are
presented, completely solved examples, exercises with answers, where
the
reader
can
test
his/hers
understanding
of the
content,
and
short
presentations
of
some
communication
systems.
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ACKNOWLEDGEMENTS
The
author wishes
to
thank
all his
colleagues,
friends

and
students
who
inspired
him,
read manuscripts
and in
several positive ways contributed
to
this book.
This page intentionally left blank
1
TELECOMMUNICATIONS
1.1
Usage
today
Today telecommunications
is a
technology deeply rooted
in
human society
and
has
its
foundation
in our
need
to
communicate with each other.
It may be two

people talking
on the
telephone,
a
so-called point
to
point connection.
The end
points
of
connection
can be in the
same building
or on
opposite sides
of the
earth,
and may be
stationary
or
mobile.
An
example
of
mobile connection
is air
commu-
nication, e.g. where
the
information

is
transferred between control tower
and
aircraft.
Another example
is
coastal radio, where
the
information
is
transferred
between ships
at sea and
stationary coastal
radio
stations. Mobile telecommuni-
cations
is a
rapidly growing application. Future telephone systems
will
be
based
on
the
idea
of a
personal telephone.
A
telephone number will
not

then lead
to a
particular
communication terminal, such
as a
telephone,
but to a
certain person,
irrespective
of
which terminal he/she happens
to be at. Not
only voices
are
transferred. Picture
and
data transfer represents
a
growing fraction
of the
infor-
mation
flow.
Bank transfers ranging
from
cash points
to
transfers between large
monetary
institutions

are
examples
of
data communications which
set
high
demands
on
reliability
and
security. Radio broadcasting
is a
kind
of
communica-
tion
which,
in
contrast
to the
point
to
point connection,
usually
has one
transmitter
and
many receivers. Apart
from
radio

and TV
entertainment, weather maps
are
transferred
via
radio
broadcasting
from
a
satellite
to
several receivers
on
Earth.
Future communication systems will continue
to
enlarge their capacity
for
transmitting
information
and
provide greater mobility
for
users.
Different
types
of
information will
be
handled

the
same
way in the
telecommunication networks.
Other aspects will make
the
difference
in
handling, such
as
requirements
on
maximum
delay, maximum number
of
errors
in the
data
and how
much
the
users
are
willing
to pay for the
transmission.
1.2
History
Communication based
on

electrical methods
(bonfires,
mechanical semaphores,
etc.
are not
included) began
in
1833 when
two
German Professors, Gauss
and
Weber, established
a
telegraph connection using
a
needle telegraph. Samuel
TELECOMMUNICATIONS
Morse was, however,
the man who
further
refined
the
methods, made them usable
and
developed
the
Morse
Code
of the
alphabet. This

is the first
application
of
coding theory
within
telecommunications, where combinations
of
dots
and
dashes were used
for
letters; short combinations were used
for the
common
letters.
In
1837 Morse demonstrated
his
telegraph
in
Washington,
and it
spread
quickly
to
become
a
commonly used means
of
communication

all
over
the
world.
In
February 1877, Alexander Graham Bell presented
a new
invention,
the
tele-
phone.
In a
crowded lecture hall
in
Salem,
MA,
USA,
the
amazed audience heard
the
voice
of
Bell's assistant
30 km
away.
After
the first
Atlantic cable
for
tele-

graphy
had
been completed
in
1864 considerable development
had
taken place.
The first
telephone
cables
could transfer
one
telephone call
at a
time.
The
intro-
duction
of
coaxial cables
in the
1950s
made
it
possible
to
transfer
36-4000
calls
per

cable, using analogue carrier wave techniques. From 1965 satellites have
had
a
considerable impact
on the
development
of
telecommunications
across
the
world.
The
earliest communication satellites were Telstar
and
Relay
which
began operation
in
1962.
In
1963
the first
geo-stationary satellite, Syncom,
was
launched.
Its
altitude must
be
35,800
km to

give
it an
orbit time
of 24 h,
Figure
1.1 A
selection
of
optical transmission links
across
the
North Atlantic.
©
1993 IEEE
J.
Thiennot;
F.
Pirio;
J. B.
Thomine, Optical Undersea Cable Systems
Trends.
Proceedings
of
the
IEEE, November 1993.
HISTORY
3
making
it
possible

to use day and
night between
the
same continents.
After
1985
optical
fibres
have offered
the
possibility
of
point
to
point connections with very
high transfer capacity (cf. Figure 1.1).
An
optical
fibre of
good
quality
can
transfer
information
at a
rate
of 400
Gbit/s, which means that
one
single

fibre can
carry more
than
4,000,000
telephone calls simultaneously. With proper additional equipment
an
information transfer
per fibre of
5-10 Tbits/s
is
expected
in the
future.
Wireless communication began
in
1895.
A 21
year
old
student, Guglielmo
Marconi
from
Bologna, Italy, then managed
to
transfer Morse codes without
using
wires between
two
stations. What made this possible
was a

theory
presented
by the
English mathematician Maxwell
in
1867 (well known
to
today's
physics
students).
He
never managed
to
experimentally
verify
his
theory,
however.
This
was
achieved
by the
German physicist Hertz
in
1886. Hertz
was, however, sceptical about
the
feasibility
of
electromagnetic waves

for
tele-
graphic transfer.
On
12th December 1901 Marconi managed
to
transfer
a
simple
message across
the
Atlantic. Marconi, together with
the
German Ferdinand
Braun,
received
the
1909 Nobel Prize
in
Physics
as
recognition
of
their work
for
the
development
of
wireless telegraphy
(in

Russia Alexander Popov simulta-
neously
did
successful experiments with radio transmission. However,
he
never
obtained
the
industrial
importance
that Marconi did).
Radio
offered
the first
real example
of
mass communication.
The first
radio
broadcasting probably took place
from
a
garage
in
Pittsburgh
on the 2nd
Novem-
ber
1920.
The

idea
of
radio broadcasting
was
launched
by a
Russian-American
named David
Sarnoff,
who
started
as a
messenger
boy at
Marconi's company
in
New
York. Edwin Howard Armstrong,
the
great engineer, inventor
and
researcher,
further
developed radio technology
at
this time.
He
invented
the
regenerative

receiver,
the
superheterodyne
receiver
and the FM
modulation tech-
nique.
He
invented
the
latter when, because
of his
perfectionist nature,
he was
dissatisfied
with
the
sound quality that
the AM
modulation technique could
offer.
The
television
was not far
behind.
In
1926,
the
Scotsman John Baird succeeded
in

transferring
a
moving image
from
one
room
to
another
by
electric means.
The
technology
was
built
on the use of
rotating disks with holes
to
successively
acquire
the
entire image line
after
line.
It was a
Russian, Vladimir Zworykin,
who
fully
developed
electronic
television.

In
1931
he had
designed
the first
electronic picture tube
and the first
feasible camera tube.
The BBC
(British
Broadcasting Cooperation) started
TV
transmissions
in
London
in
1932.
One of the
main applications
of
radio communication
is
within
the
transport
sector. Today's
air
traffic
would
be

unthinkable without radio, radar
and
radio-
based navigation
and
landing aids. Shipping
was
very early
in
utilising
radio
to
improve
safety.
For the first
time
it was
possible
to
call
for
help when
in
distress,
no
matter what
the
weather
and
sight conditions.

In
1899
the
American passenger
ship
St
Paul
was
equipped with
a
Marconi transmitter
of the
spark type
as a
test.
The first
kind
of
radio communication
was
Morse telegraphy. Today
this
techni-
TELECOMMUNICATIONS
que
is no
longer used
and
communication
is

achieved
by
direct
speech
or
data,
usually
via the
satellite-based INMARSAT
(international
MARitime SATellite
organisation) system.
One of the first
great achievements that made this technique
known
was the
sending
of
distress signals
from
the
Titanic when
she
sank
in
1912.
Mobile telephone systems
offer
the
possibility

of
having
access
to the
same
services with mobile terminals
as
with stationary networks.
In
1946,
the
American
company
AT&T
(American Telephone
and
Telegraph
Company)
started
a
mobile
telephone network
in St
Louis, USA.
The
system
was
successful
and
within

one
year mobile networks were established
in
another
25
cities. Each network
had a
base
station (main station) which
was
designed
to
have
as
large
a
range
as
possible.
The
problem with such
a
system
is
that
the
mobile station must have
a
high output
power

to
match
the
range
of the
base station, i.e. small battery-operated mobile
telephones
are not
possible, and, furthermore,
the
available radio spectrum
is not
efficiently
utilised.
As
early
as in
1947 solutions were
based
on the
principle
of
dividing
the
geographical
area,
covered
by a
mobile network, into
a

number
of
smaller cells arranged
in a
honeycomb structure.
A
base station having
a
relatively
short range
of
operation
was
placed inside each cell,
a
so-called cellular system.
A
closer
reuse
of
carrier frequencies
is
therefore possible
and
user capacity
is
increased.
A
problem which then occurred
was

that
it was
necessary
to
have
some kind
of
automatic handover, i.e. when
a
mobile terminal passes
the
border
between
two
base stations,
the
connection
must
be
transferred
to the
other base
station without interruption.
As it
turned
out it
took
a
long time before this problem
was

solved.
The first
cellular mobile telephone network
was not in
operation
until
the
autumn
of
1981.
The
system
was
called Nordic Mobile Telephone (NMT)
and
it
had
been jointly developed
by the
Nordic telephone authorities (Sweden,
Finland, Norway, Denmark
and
Iceland).
The first
generation
of
mobile phone
systems, such
as
NMT, were analogue. Today

the
mobile phone systems
are
based
on
digital signal processing.
The
third generation mobile phones
are
also based
on
Code
Division Multiple Access (CDMA).
A
communication system based
on
CDMA
was
presented
as
early
as
1950
by De
Rosa-Rogoff.
The first
applications
of the
technique were
in

military systems
and
navigation systems.
The first
mobile
telephony standard based
on the
CDMA technique
was the
North American IS-95
which
was
established
in
July
1993. Mobile phone systems have also taken
the
leap into
space
through systems
like
Iridium
and
Globalstar
which
make world
wide coverage possible
for
hand held terminals.
The

latest step
in the
progress
of
telecommunications
was
taken when
different
computer networks were connected together into
an
internet.
The
origin
of
what
today
is
called
the
Internet
is
ARPANET (Advanced Research Project Agency)
which
was the
result
of a
research project.
The aim was to
create
a

computer
network which
was
able
to
function
even
if
parts
of the
network were struck out,
in
for
example
a
war.
The
year 1969
was a
milestone when
four
computers
in
different
universities
in the US
were connected.
In
another part
of the

world,
at
BASIC
ELEMENTS
the
European nuclear research laboratory, CERN, they were
in
need
of a
system
for
document handling. Development
and
standardisation
of
protocol
and
text
formats
was
started, which resulted
in the
World Wide
Web
(WWW), which
is an
efficient
way to use the
Internet.
In

1993
a
further
milestone
was
reached when
the
computer program Mosaic
was
presented.
The
program gave
a
simple inter-
face
to the WWW and
made
the
resources
of the
network accessible
for
others
than
computer specialists. Simultaneously
the
Internet
was
given attention
from

high
political level. Thereby
an
increase
in the use of
telecommunications began.
No
retrospective survey
can
avoid mentioning
the
pioneering theorist Claude
E.
Shannon
(1916-2001),
Bell Laboratories. During
a
time when major progress
was
being made
in
analogue
communications
he
laid
the
foundation
of
today's
digital

communications
by
formulating much
of the
theoretical basis
for
secure commu-
nication.
One of his
best known works
is the
formulation
of the
channel transmis-
sion
capacity,
A
Mathematical
Theory
of
Communication, published
in
July
and
October 1948.
A
great deal
of the
content
in

this book
has its
basis
in his
works.
For
telecommunication systems
to be
really powerful
a
large operational range
is
required
so
that many customers
can be
reached.
It is
then necessary that
different
systems
can
communicate with each other, which requires
a
standard
format
for
communication.
One of the
international organisations dealing

with
the
standardisation
of
telecommunications
is
ITU,
the
International Tele
Union.
1.3
Basic elements
A
telecommunication system
can be
divided
up in
several
different
ways.
One is
founded
on the OSI
model
with
its
seven layers. This model formalises
a
hier-
archy

and is not
suitable
for
describing
a
telecommunication system
from
the
signal
processing
point
of
view, which mainly
deals
with layer one,
the
physical
layer,
and
layer two,
the
link layer.
A
model more suitable
for
this purpose
is
described
in
Figure 1.2; this model

is
suitable
for
physical connections
for
speci-
Figure
1.2
Fundamental
blocks
of a
telecommunication system.
6
TELECOMMUNICATIONS
fic
applications, so-called circuit switched connections (e.g. telephony),
and for
radio,
TV,
etc. When
it
comes
to
packet
switched networks, e.g.
the
Internet,
you
cannot identify
a

single path between
the
source
and the
user
of the
information.
The
data
find its way
through where there
is
free capacity
and
different
parts
of
the
information
can
take
different
routes.
In
these
cases,
you
must,
from
the

point
of
view
of
signal processing, study single physical links
in the net or use
channel
models which describe
the
connection
on a
word
or
packet level.
1.3.1
TRANSMITTER
SIDE
Information
is
generated
by
some
kind
of
source
which could
be the
human
speech organ,
a

data point,
a
picture,
a
computer, etc.
In
most
cases
this informa-
tion
has to be
somehow transformed
in a way
suitable
for the
electric commu-
nication system.
The
transformation must
be
carried
out in an
efficient
way
using
a
minimum
of
expensive resources such
as

communication capacity. This
is
done
in
the
source coder.
In
some
cases
the
information
is to be
ciphered, which
can be
done
after
source coding. This
is
only
briefly
treated
in
this book,
why a
cipher
block
is not
included. However,
the
fact that

all
information
is in
digital form
makes
it
easy
to
implement communication which
can
prevent eavesdropping
by
an
unauthorised user.
The
coded
information
may
then require further
processing
to
eliminate shortcomings
in the
channel transferring
or
storing
the
information.
This
is

carried
out by
using
different
methods
in the
channel encoder.
The
modu-
lator
is a
system component which transforms
the
message
to a
type
of
signal
suitable
for the
channel.
1.3.2
THE
CHANNEL
The
channel
is the
medium over which
the
information

is
transferred
or
stored.
Examples are:
the
cable
between
two end
points
in a
wire bound
connection,
the
environment
between
the
transmitter
and
receiver
of a
wireless connection,
or the
magnetic medium
on
which
the
information
is
stored.

The
channel model
is a
mathematical
model
of the
channel characteristics.
1.3.3
RECEIVER
SIDE
After
the
signal
has
passed
the
channel
it is
distorted.
In the
demodulator
the
information
is
retrieved
as
accurately
as
possible.
A

unit
which
can be
said
to be
included
in the
demodulator
is the
equaliser.
To
minimise
the
bit-error rate
the
equaliser should adjust
the
demodulation process
to the
changes
in the
signal,
which
can
take place
in the
channel. Even
if the
demodulator
is

functioning
as
well
as
possible there
may
still
be
errors
left
in the
information. Channel coding
BASIC ELEMENTS
provides
the
possibility
of
correcting these errors within certain limits.
The
error
correction
or
error
detection
is
made
in the
channel
decoding
block.

Since
the
information
is
coded
at the
source
it has to be
transformed
in
such
a way
that
it
can
be
understood
by the
receiver,
for
example
so
that
a
human voice
is
restored
or
a
picture restored. This

is
done
in the
source
decoder.
For the
system
to
function
properly certain time parameters must
be
common
for the
transmitter
and
receiver.
The
receiver,
for
instance, must know
at
what rate
and at
what
instance
the
transmitter changes
the
information symbol. These parameters
are

measured
by the
receiver
in the
synchronising block.
1.3.4 ANOTHER
SYSTEM
FOR
COMMUNICATION
The
same communication model
can be
used
for the
situation
in
which
you
presently are.
The
writer wants
to
transfer information
to the
receiver, which
is
you.
The
writer codes
the

information
with
the aid of
language. Hopefully
in an
efficient
way
without unnecessary chat. Error correction
is
built into
the
system
since
you
understand even
if one or
another letter should
be
erroneous.
The
book
which
you
have
in
front
of you is the
channel. Disturbances come into
the
trans-

mission,
for
instance
in the
form
of
different
factors distracting
the
reader.
You
decode
the
message
and
obtain understanding
for the
subjects treated
in the
book.
1.3.5
THE
SCOPE
OF THE
BOOK
This book describes
the
signal processing carried
out in the
blocks above (cf.

Figure 1.3),
the
models that
are
being used
and the
capacity which
can be
obtained
in the
systems.
The
methods described give
the
basic ideas
for the
TELECOMMUNICATIONS
respective block
and
provide continuity throughout
the
book.
The
limiting factor
in
telecommunication systems
is
usually
the
capacity

of the
channel, which
is
limited
either
by
noise
or by the
available bandwidth. Methods
for the
calculation
of
channel capacity
are
therefore given.
The
channel capacity
has to be put in
relation
to the
amount
of
information which needs
to be
transferred
from
the
source. Methods
for the
calculation

of the
amount
of
information
or the
entropy
of
the
source
are
therefore treated. Perhaps demands
go
beyond
the
capacity
of
the
channel.
The
book describes
fundamental
methods
of
doing
the
source coding
and
how the
efficiency
of the

coding
is
calculated. Furthermore,
it
describes
how
error-correcting
and
error-detecting coding
can be
done
and the
capacity,
in
terms
of
bit-error rate, which
can be
obtained.
Different
methods
for
modulation
are
described.
An
important property
of the
modulated signal
is its

spectrum which
must
be put in
relation
to the
bandwidth that
the
channel
can
provide.
The
book
describes
how the
demodulator must
be
designed
to
retrieve
the
information
as
accurately
as
possible. Ways
of
calculating
the
probability
of the

demodulator
misinterpreting
the
signal, i.e.
the bit
error rate, when certain properties
of the
channel
are
given beforehand,
are
also discussed. Fundamental methods
for
adaptive
equalisers
are
also
treated.
Synchronisation
is
treated, where
the
phase-locked loop
is an
important
component
and is
therefore treated
in a
special section.

The
adaptive antenna
is
a
system component
which
is finding an
increasing number
of
applications,
even
outside military systems,
and its
fundamental
aspects
are
also treated
in
this
book.
1.4
Multiple
user
systems
1.4.1
METHODS
FOR
MULTIPLE
ACCESS
When

several users
are
using
the
same physical transfer channel
(fibre,
coaxial
cable, space, etc.)
for
communication, ways
of
separating
the
messages
are
required. This
is
achieved
by
some method
for
multiple
access.
Three fundamen-
tal
methods exist.
In the first
each user
is
given

his own
relatively narrow
frequency
band
for
communication. This method
is
called FDMA
or
frequency-division
multiple
access.
The
basic concept
is
simple
but
requires
efficient
filters for the
separation
of the
messages.
The
next method
is
TDMA,
"time-division multiple
access".
In

this case each user
has
access
to a
limited
but
repeated time span
for the
communication. This concept requires great care
for
time
synchronisation
but
does
not
require
as
efficient
filters as the
FDMA
method. These methods
are
depicted
in
Figure 1.4, where time
is
along
the x-
axis
and

frequency along
the
v-axis.
A
FDMA system
has a
relatively narrow
bandwidth
along
the
frequency axis
but
extends along
the
whole
.v-axis.
A
TDMA
MULTIPLE USER SYSTEMS
Figure
1.4
FDMA
and TDM A
systems.
system
needs
a
broader bandwidth
to
transfer

the
same amount
of
information,
but
only takes
up
sections
of the
time axis.
The
third method
is
CDMA, code-division multiple access. Each user includes
a
special code
in his
message, which
is
orthogonal
to the
other users' codes. This
means that
the
other users will only
be
regarded
as
random noise sources
in

relation
to the
actual message. CDMA provides
a
flexible
system
but it can be
complicated
if the
number
of
users
and
their distribution
in
space vary.
To
include
CDMA
in a
diagram
a
third axis representing
the
coding dimension
has
to be
added,
as
shown

in
Figure 1.5.
An
acronym which ought
to be
explained
in
this context
is
SDMA, spatial-
division
multiple access. This means that
the
antenna
is
pointing
the
signal power
in
the
desired direction.
The
same
frequency,
time
frame
or
code
can
then

be
used
by
another user
in
another direction.
All
real systems
are
hybrids
of two or
more
of the
above-mentioned
multiple
Figure
1.5
Diagram depicting FDMA, TDMA
and
CDMA
in the
multiple access
space.
10
TELECOMMUNICATIONS
access methods. Thus,
a
TDMA system
is, for
instance, also

an
FDMA system
as
the
TDMA frames have
a
limited bandwidth
and
other systems operate outside
this
frequency band.
The
choice
of
multiple-access method depends
on
several
factors, such
as the
properties
of the
physical channel, implementation
aspects
and
coexistence with other systems.
To
give
the
reader some insight
into

these
issues,
the
multiple-access methods
are
described
in
more detail below.
The
word multiplexing
is
used when
access
by the
different
users
to the
channel
is
controlled
by a
master control, i.e.
as in
wire-bound telephony.
TDM and FDM are
often
used, corresponding
to
TDMA
and

FDMA.
FDMA
Each user,
or
message,
has its own
frequency band.
At the
transmitting
end the
messages
are
transferred
to the
respective frequency bands through modulation
of
different
carrier waves. Figure
1.6
shows
an
example
with
seven
different
messages, each with
a
bandwidth
of 2 W
(Hz). Each carrier wave

is a
sinusoidal
signal
having,
for
example,
the
frequency
f
2
(Hz)
for
message
2.
The
signals
are
transferred
on a
common channel which
can be a
coaxial
cable
or the
space between
the
transmitter
and
receiver.
At the

receiving
end the
different
signals
are
separated
by
bandpass
filters,
which
can
distinguish
the
relevant frequency band
for
each
message.
The
signals
are
then transformed
back
to the
original frequency band using demodulators.
When
analysing FDMA systems
the
influence
of the
channel

on
each message
is
usually evaluated individually.
In a
real system
it is
difficult
to
completely
eliminate
the
influence
of the
other messages
and
these
will
enter
the
analysis
as
an
increased noise level.
For a
digital communication system, speech
and
channel
coding
of

each message
are
separately added
at the
transmitting
end
(cf. Figure
1.3).
At the
receiving
end
corresponding decoding
is
obviously added.
For
optical
fibre
communication,
different
messages
can be
transferred
in the
same
fibre
using
different
wavelengths.
The
method

is
basically
identical
to
FDMA,
but in
this
case
it is
called WDM, wavelength
division
multiplex.
Figure
1.6 The
positions
of the
different
messages
along
the
frequency axis. Each signal
has a
bandwidth
of 2 W and
must therefore take
up at
least
the
corresponding bandwidth
on

the
frequency axis.