hello welcome to another module in this massive
open online course on the principles of c
d m a mimo o f d m wireless communication
systems so in the previous module we have
seen various aspects of mimo communication
system properties the behavior and the various
transmissions schemes and the analysis will
related to mimo communication systems let
us now in this module start with the new technology
that is o f d m so what we are going to look
at in this module is that is starting with
this module is introduction to a new technology
and in fact a very prominent and a very key
technology that is o f d m which stands for
orthogonal frequency orthogonal frequency
division multiplexing
so we are going to start with o f d m which
stands for orthogonal frequency division multiplexing
and this is a key standard because o f d m
is employed in four g wireless system so this
is a key technology which is employed in four
g wireless that is the fourth generation wireless
systems such as if we look at for instance
l t e l t e this is a four g cellular standard
this is a fourth generation cellular standard
and this stands for long term long term evolution
correct we already seen this another four
g or three point seven five g standard is
wimax as we have seen this stands for worldwide
interoperability 
for microwave access that is worldwide interoperability
for microwave access so we have l t e which
is long term evolution which is a four g cellular
standard and another competing standard which
is wimax world wide interoperability for microwave
access both of these are based on these are
dominant standards and both of these are based
on o f d m so if you look at the cellular
world both of these are based on o f d m similarly
l t e advance that is denoted by l t e a so
if we look at l t e a that is l t e advanced
which stands for l t e advanced this is also
based on o f d m which is orthogonal frequency
division multiplex so o f d m what is the
important aspect of o f d m of d m is a key
broadband wireless technology so this is a
key wireless and we can emphasis broadband
key wireless broadband technology and by broadband
we mean a system basically a wireless system
which has a large bandwidth so this wireless
systems supports a large
so what are been looking at we are looking
at o f d m which is orthogonal frequency division
multiplexing which is a key wireless technology
and not just that it is a broadband technology
so it operates on a huge bandwidth it operates
on a large or a very wide band for instance
if we look at a g s m system a g s m system
has a bandwidth of about two hundred kilohertz
but an o f d m system can have a bandwidth
up to twenty megahertz right so this is several
times that of for instance is about hundred
times that of it g s m system so it operates
over a large bandwidth it is a broadband system
since it has a large bandwidth therefore naturally
the data rate is higher and these high data
rates are used in three g and four g in fact
four g wireless systems to enable data rates
up to hundreds or even more than hundred megabit
per second about five hundred megabit per
second or even up to one gigabit per second
so l t e and l t e advanced which are based
o f d m and operate thereby are broadband
wireless cellular system can support can ah
can enable a very high data rate of the order
of hundreds of megabits per second this is
possible because of o f d m which stands for
orthogonal frequency division multiplexing
and not simply cellular standard but if we
look at wifi or wireless lan standards so
several wifi 
wifi or wireless lan that is wireless local
area network standards so these are wireless
so wifi or wireless local area w lan wireless
local area network standards so these w lan
standards what are the various w lan standards
for instance eight o two dot eleven a eight
o two dot eleven g eight o two dot eleven
n and the more resent eight o two dot eleven
a c if you look at all of these these are
the various i triple e w lan standards so
these are i i triple e w lan standards and
these are based on these enable high data
rates because these are based on o f d m or
orthogonal frequency division multiplexing
so several wireless lan standards such as
eight o two dot eleven g eight o two eleven
a eight o two dot eleven n eight o two dot
eleven a c which are the wifi standards equivocally
these are these are known as wifi standards
where technically these are wireless lan wireless
local area network standard these are also
based on o f d m so o f d m is a key wireless
technology which is used in several cellular
four g cellular and several wireless lan standard
because it is a broadband wireless technology
which enables high data rates at the same
time it has it is practically it has a low
complexity of a implementation it implements
it enables easy implementation of these broadband
wireless communication systems so let us look
at the basic principles of o f d m so what
is the basic principle behind o f d m and
the basic principle behind o f d m can be
explained as follows 
the basic principle of o f d m can be explained
as follows for instance if you look at a typical
communication system a communication system
as you all know has a certain bandwidth which
is b i have a communication system over a
bandwidth which is b and i have a single carrier
i have a carrier
so in a communication system i have a bandwidth
and i have a carrier a single carrier placed
at the center of the bandwidth at the carrier
frequency correct so let us say this is our
carrier frequency 
i have a single carrier let us take a simple
example let us say my bandwidth is ten megahertz
so this is a broadband system so this is 
this is a broadband system of bandwidth ten
megahertz now therefore if you are performing
communication the communication system that
is implemented over this bandwidth has a symbol
time t is equal to one over the bandwidth
b and one over the bandwidth b we know bandwidth
b is ten megahertz of this is one over ten
megahertz which is basically one over ten
into ten to the power of six hertz which is
point two one into ten to the power of minus
six seconds equals point one micro second
so therefore we have a symbol time there is
what we have saying is very considering a
communication system which has a bandwidth
of ten megahertz in this bandwidth b which
is ten megahertz the symbol time is t equals
one over b therefore the symbol time is one
over ten megahertz which is point one micro
second right
so so what we are saying is for communication
over this bandwidth of ten megahertz the symbol
time is point one micro seconds however you
might re remember from the initial modules
that is the delay spread if we look at a typical
outdoor channel the delay spread 
of the wireless channel is approximately two
to three micro seconds that is two to three
micro seconds so if i look at t d where t
d is my delay spread t d is approximately
of the order of two to three micro seconds
which means now if i look at the relation
between this symbol time now let us look at
this our symbol time is point one micro seconds
our delay spread is approximately let say
two micro seconds
therefore the symbol time t is much less than
what we are observing is the symbol time t
is much less than the delay spread the symbol
time 
the symbol time t is much less than the delay
spread what we are observing is the symbol
time is point one minus micro second the delay
spread is two micro about two micro second
so the delay spread is about twenty times
larger than the symbol time correct which
means now you might also remember from the
characteristics of the wireless channel that
when this delay spread is larger than the
symbol time we have inter symbol interference
of this what does this lead to this leads
to a problem what is the problem this leads
to i s i or inter what is also known as inter
so what we are observing is as the bandwidth
b increases as 
as bandwidth b increases what happens is our
symbol time 
one over b symbol time one over b decreases
correct and therefore as the bandwidth of
the sys[tems] systems becomes more and more
broadband that is the bandwidth b is increasing
is becoming larger and larger the symbol time
one over b is becoming smaller and smaller
ah since the symbol time is becoming smaller
it is going to become lower than the delay
spread of the channel once it is lower than
the delay spread of the channel this results
in inter symbol interference and when you
have interference this leads to a degradation
or this leads to a loss of performance of
the wireless communication system
so the inter symbol interference resulting
in a broadband wireless communication system
leads to a performance or leads to a degradation
of the performance and therefore this is a
significant challenge this is the significant
problem and addressing this problem addressing
this problem of inter symbol interference
is a significant challenge in a broadband
wireless communication system so this leads
to inter symbol interference leads to i s
i as we said i s i stands for inter symbol
interference and this is a significant challenge
significant challenge in a broadband 
this is a significant challenge in a 
this is a significant challenge in a broadband
this is a significant challenge in a broadband
wireless system so how to overcome i s i so
our main problem is to overcome the inter
symbol interference what is the challenge
the challenge is to overcome the inter symbol
interference the challenge is basically because
of this small symbol time that is as the bandwidth
is increasing the symbol time one over b is
decreasing which is leading to inter symbol
interference of the challenge is to overcome
this inter symbol interference and what is
the principle what is the what is the method
or the means to overcome this inter symbol
interference and the scheme is simple how
to overcome the inter symbol interference
so and the principle to overcome that is to
avoid inter symbol interference realize that
the inter symbol interference is arising in
the first place because of the large bandwidth
so what we do is when we have a large bandwidth
instead of using the entire bandwidth at once
what we do is we use it piecemeal what we
do is we take this large bandwidth b and we
split it into smaller bands or we split it
into what are known as we split it into what
are known as sub bands so i have a large bandwidth
which i said is ten megahertz i am splitting
this into smaller bands so i am splitting
this into each smaller bands which are termed
as sub bands so previously we had a single
carrier now we will have multiple carriers
one in each sub band this is termed as a sub
carriers so we will have smaller sub bands
in each sub band place ah sub place a sub
carrier now if you look at this if i lets
say have n sub bands so i am saying smaller
sub bands lets say n right then bandwidth
of each sub band is equal to 
is equal to b by n correct
so what we are doing is we are taking a large
bandwidth b we are diving it into n sub band
so the bandwidth of each sub band is b by
n let us take a simple example for example
b equals let say ten megahertz and n equals
thousand what is n n equals n is n is basically
equal to the number of the number of sub bands
is equals to thousand then the bandwidth per
sub band of each sub band bandwidth of each
sub 
band is equal to b by n which is equal to
ten megahertz divided by ah sorry bandwidth
of each sub band is b by n which is ten megahertz
divided by thousand which is equal which is
equal to ten into ten to the power of six
divided by ten to the power of three which
is equal to ten into ten to the power of three
which is equal to ten kilohertz so the bandwidth
of each sub band is equal to so bandwidth
of each sub band
so we are taking a bandwidth b of thousand
of ah ten megahertz we are dividing it into
thousand sub bands bandwidth of each sub band
is ten megahertz divided by thousand that
is ten kilohertz now if you look at the symbol
time in each sub band now therefore symbol
time in each sub band 
is equal to the symbol time is one over b
over n is equal to n over b that is in our
examples symbol time t becomes one over ten
megahertz divided by thousand that is basically
as we have seen one over ten kilo hertz which
is equal to one over ten into ten power three
which is basically point one millisecond which
is equal to hundred micro second now if you
look at this hundred micro second now if we
look at this new symbol time which is hundred
micro second so now let us look at this new
symbol time which is hundred micro second
and compare this now again with the delay
spread which is two micro second and now you
can see that t is much greater than the delay
spread that is we have hundred micro seconds
um is much greater than two micro second that
is new symbol time the new symbol time 
is much greater than 
and therefore now what we are seeing is basically
the new symbol time is one over b by n that
is one over the bandwidth of each sub carrier
and the bandwidth of each sub carrier is ten
kilohertz so the new symbol times is one over
ten kilohertz which is point one millisecond
or hundred micro seconds and the delay spread
is two micro second so the new symbol time
which is hundred micro second is significantly
greater than the delay spread therefore there
is no inter symbol interference in the system
where we are using multiple sub bands and
multiple sub carriers therefore the usage
of these multiple sub ah sub bands and sub
carriers therefore this means there is no
i s i in new system in the new system with
multiple sub bands and sub carrier in each
band 
sub carrier in each band such a system with
multiple so such a system with multiple sub
bands at a sub carrier in each band so what
are we do we are taking band with b dividing
into n sub bands in each sub bands that is
a sub carrier so there are n sub carrier such
a system with multiple sub bands and multiple
sub carriers is termed as a multi carrier
system so such a system with multiple sub
bands and multiple sub carriers 
is termed as a multi carrier modulated 
multi carrier modulate a modulated system
so this is known as an m c m system which
is basically a precursor for o f d m
so what we are seen here is that we have a
multiple sub carriers we have multiple sub
bands and in each sub band we have a sub carrier
therefore we have multiple sub carriers and
we are modulating this multiple sub carriers
such a system is known as a multi multi carrier
or multiple carrier modulated system that
is an m c m system and this is the basis for
o f d m this is the precursor or basis for
o f d m this is not exactly o f d m this is
a basis for o f d m so what is o f d m o f
d m is basically a multi carrier multi carrier
modulated system that is where we have multiple
sub bands and multiple sub carriers each sub
carrier representing a small sub band and
since the bandwidth of each sub band is small
therefore the symbol time is large once a
symbol time is large the symbol time is larger
than the delay spread therefore there is no
inter symbol interference or negligible inter
symbol interference in each sub band and this
enables transmission this enables smooth transmission
and smooth reception in a broadband wireless
communication system so that is the principle
behind m c m which forms a basis of o f d
m that is orthogonal frequency division multiplexing
and we are going to explore this idea in great
in greater detail in the subsequent modules
thank you very much
