<s>
In	O
telecommunications	O
,	O
orthogonal	B-Protocol
frequency-division	I-Protocol
multiplexing	I-Protocol
(	O
OFDM	B-Protocol
)	O
is	O
a	O
type	O
of	O
digital	O
transmission	O
used	O
in	O
digital	O
modulation	B-Application
for	O
encoding	O
digital	O
(	O
binary	O
)	O
data	O
on	O
multiple	O
carrier	O
frequencies	O
.	O
</s>
<s>
OFDM	B-Protocol
has	O
developed	O
into	O
a	O
popular	O
scheme	O
for	O
wideband	O
digital	O
communication	O
,	O
used	O
in	O
applications	O
such	O
as	O
digital	B-Application
television	I-Application
and	O
audio	O
broadcasting	O
,	O
DSL	O
internet	O
access	O
,	O
wireless	B-General_Concept
networks	I-General_Concept
,	O
power	B-Device
line	I-Device
networks	I-Device
,	O
and	O
4G/5G	O
mobile	O
communications	O
.	O
</s>
<s>
OFDM	B-Protocol
is	O
a	O
frequency-division	B-Protocol
multiplexing	I-Protocol
(	O
FDM	B-Protocol
)	O
scheme	O
that	O
was	O
introduced	O
by	O
Robert	O
W	O
.	O
Chang	O
of	O
Bell	O
Labs	O
in	O
1966	O
.	O
</s>
<s>
In	O
OFDM	B-Protocol
,	O
the	O
incoming	O
bitstream	O
representing	O
the	O
data	O
to	O
be	O
sent	O
is	O
divided	O
into	O
multiple	O
streams	O
.	O
</s>
<s>
Multiple	O
closely	O
spaced	O
orthogonal	B-Algorithm
subcarrier	O
signals	O
with	O
overlapping	O
spectra	O
are	O
transmitted	O
,	O
with	O
each	O
carrier	O
modulated	B-Application
with	O
bits	O
from	O
the	O
incoming	O
stream	O
so	O
multiple	O
bits	O
are	O
being	O
transmitted	O
in	O
parallel	O
.	O
</s>
<s>
OFDM	B-Protocol
was	O
improved	O
by	O
Weinstein	O
and	O
Ebert	O
in	O
1971	O
with	O
the	O
introduction	O
of	O
a	O
guard	B-Protocol
interval	I-Protocol
,	O
providing	O
better	O
orthogonality	O
in	O
transmission	O
channels	O
affected	O
by	O
multipath	O
propagation	O
.	O
</s>
<s>
Each	O
subcarrier	O
(	O
signal	O
)	O
is	O
modulated	B-Application
with	O
a	O
conventional	O
modulation	B-Application
scheme	O
(	O
such	O
as	O
quadrature	B-Device
amplitude	I-Device
modulation	I-Device
or	O
phase-shift	B-General_Concept
keying	I-General_Concept
)	O
at	O
a	O
low	O
symbol	O
rate	O
.	O
</s>
<s>
This	O
maintains	O
total	O
data	O
rates	O
similar	O
to	O
conventional	O
single-carrier	O
modulation	B-Application
schemes	O
in	O
the	O
same	O
bandwidth	O
.	O
</s>
<s>
The	O
main	O
advantage	O
of	O
OFDM	B-Protocol
over	O
single-carrier	O
schemes	O
is	O
its	O
ability	O
to	O
cope	O
with	O
severe	O
channel	O
conditions	O
(	O
for	O
example	O
,	O
attenuation	O
of	O
high	O
frequencies	O
in	O
a	O
long	O
copper	O
wire	O
,	O
narrowband	O
interference	O
and	O
frequency-selective	O
fading	O
due	O
to	O
multipath	O
)	O
without	O
the	O
need	O
for	O
complex	O
equalization	B-Algorithm
filters	O
.	O
</s>
<s>
Channel	O
equalization	B-Algorithm
is	O
simplified	O
because	O
OFDM	B-Protocol
may	O
be	O
viewed	O
as	O
using	O
many	O
slowly	O
modulated	B-Application
narrowband	O
signals	O
rather	O
than	O
one	O
rapidly	O
modulated	B-Application
wideband	O
signal	O
.	O
</s>
<s>
The	O
low	O
symbol	O
rate	O
makes	O
the	O
use	O
of	O
a	O
guard	B-Protocol
interval	I-Protocol
between	O
symbols	O
affordable	O
,	O
making	O
it	O
possible	O
to	O
eliminate	O
intersymbol	O
interference	O
(	O
ISI	O
)	O
and	O
use	O
echoes	O
and	O
time-spreading	O
(	O
in	O
analog	O
television	O
visible	O
as	O
ghosting	O
and	O
blurring	O
,	O
respectively	O
)	O
to	O
achieve	O
a	O
diversity	B-Protocol
gain	I-Protocol
,	O
i.e.	O
</s>
<s>
This	O
mechanism	O
also	O
facilitates	O
the	O
design	O
of	O
single	B-Device
frequency	I-Device
networks	I-Device
(	O
SFNs	O
)	O
where	O
several	O
adjacent	O
transmitters	O
send	O
the	O
same	O
signal	O
simultaneously	O
at	O
the	O
same	O
frequency	O
,	O
as	O
the	O
signals	O
from	O
multiple	O
distant	O
transmitters	O
may	O
be	O
re-combined	O
constructively	O
,	O
sparing	O
interference	O
of	O
a	O
traditional	O
single-carrier	O
system	O
.	O
</s>
<s>
In	O
coded	B-Protocol
orthogonal	I-Protocol
frequency-division	I-Protocol
multiplexing	I-Protocol
(	O
COFDM	B-Protocol
)	O
,	O
forward	B-Error_Name
error	I-Error_Name
correction	I-Error_Name
(	O
convolutional	B-Error_Name
coding	I-Error_Name
)	O
and	O
time/frequency	O
interleaving	O
are	O
applied	O
to	O
the	O
signal	O
being	O
transmitted	O
.	O
</s>
<s>
COFDM	B-Protocol
was	O
introduced	O
by	O
Alard	O
in	O
1986	O
for	O
Digital	O
Audio	O
Broadcasting	O
for	O
Eureka	O
Project	O
147	O
.	O
</s>
<s>
In	O
practice	O
,	O
OFDM	B-Protocol
has	O
become	O
used	O
in	O
combination	O
with	O
such	O
coding	O
and	O
interleaving	O
,	O
so	O
that	O
the	O
terms	O
COFDM	B-Protocol
and	O
OFDM	B-Protocol
co-apply	O
to	O
common	O
applications	O
.	O
</s>
<s>
The	O
following	O
list	O
is	O
a	O
summary	O
of	O
existing	O
OFDM-based	O
standards	O
and	O
products	O
.	O
</s>
<s>
The	O
OFDM-based	O
multiple	O
access	O
technology	O
OFDMA	O
is	O
also	O
used	O
in	O
several	O
4G	B-Architecture
and	O
pre-4G	O
cellular	O
networks	O
,	O
mobile	O
broadband	O
standards	O
and	O
the	O
next	O
generation	O
WLAN	B-Architecture
:	O
</s>
<s>
High	O
spectral	B-Protocol
efficiency	I-Protocol
as	O
compared	O
to	O
other	O
double	O
sideband	O
modulation	B-Application
schemes	O
,	O
spread	B-Architecture
spectrum	I-Architecture
,	O
etc	O
.	O
</s>
<s>
Can	O
easily	O
adapt	O
to	O
severe	O
channel	O
conditions	O
without	O
complex	O
time-domain	O
equalization	B-Algorithm
.	O
</s>
<s>
Conceptually	O
,	O
OFDM	B-Protocol
is	O
a	O
specialized	O
frequency-division	B-Protocol
multiplexing	I-Protocol
(	O
FDM	B-Protocol
)	O
method	O
,	O
with	O
the	O
additional	O
constraint	O
that	O
all	O
subcarrier	O
signals	O
within	O
a	O
communication	O
channel	O
are	O
orthogonal	B-Algorithm
to	O
one	O
another	O
.	O
</s>
<s>
In	O
OFDM	B-Protocol
,	O
the	O
subcarrier	O
frequencies	O
are	O
chosen	O
so	O
that	O
the	O
subcarriers	O
are	O
orthogonal	B-Algorithm
to	O
each	O
other	O
,	O
meaning	O
that	O
crosstalk	O
between	O
the	O
sub-channels	O
is	O
eliminated	O
and	O
inter-carrier	O
guard	O
bands	O
are	O
not	O
required	O
.	O
</s>
<s>
This	O
greatly	O
simplifies	O
the	O
design	O
of	O
both	O
the	O
transmitter	O
and	O
the	O
receiver	O
;	O
unlike	O
conventional	O
FDM	B-Protocol
,	O
a	O
separate	O
filter	O
for	O
each	O
sub-channel	O
is	O
not	O
required	O
.	O
</s>
<s>
The	O
orthogonality	O
also	O
allows	O
high	O
spectral	B-Protocol
efficiency	I-Protocol
,	O
with	O
a	O
total	O
symbol	O
rate	O
near	O
the	O
Nyquist	O
rate	O
for	O
the	O
equivalent	B-Algorithm
baseband	I-Algorithm
signal	I-Algorithm
(	O
i.e.	O
,	O
near	O
half	O
the	O
Nyquist	O
rate	O
for	O
the	O
double-side	O
band	O
physical	O
passband	O
signal	O
)	O
.	O
</s>
<s>
OFDM	B-Protocol
generally	O
has	O
a	O
nearly	O
'	O
white	O
 '	O
spectrum	O
,	O
giving	O
it	O
benign	O
electromagnetic	O
interference	O
properties	O
with	O
respect	O
to	O
other	O
co-channel	O
users	O
.	O
</s>
<s>
If	O
a	O
guard	B-Protocol
interval	I-Protocol
is	O
applied	O
(	O
see	O
below	O
)	O
,	O
Nyquist	O
bandwidth	O
requirement	O
would	O
be	O
even	O
lower	O
.	O
</s>
<s>
If	O
no	O
guard	B-Protocol
interval	I-Protocol
was	O
applied	O
,	O
this	O
would	O
result	O
in	O
a	O
base	B-Algorithm
band	I-Algorithm
complex	O
valued	O
signal	O
with	O
a	O
sample	O
rate	O
of	O
1MHz	O
,	O
which	O
would	O
require	O
a	O
baseband	B-Algorithm
bandwidth	O
of	O
0.5MHz	O
according	O
to	O
Nyquist	O
.	O
</s>
<s>
However	O
,	O
the	O
passband	O
RF	O
signal	O
is	O
produced	O
by	O
multiplying	O
the	O
baseband	B-Algorithm
signal	I-Algorithm
with	O
a	O
carrier	O
waveform	O
(	O
i.e.	O
,	O
double-sideband	O
quadrature	O
amplitude-modulation	O
)	O
resulting	O
in	O
a	O
passband	O
bandwidth	O
of	O
1MHz	O
.	O
</s>
<s>
A	O
single-side	O
band	O
(	O
SSB	O
)	O
or	O
vestigial	O
sideband	O
(	O
VSB	O
)	O
modulation	B-Application
scheme	O
would	O
achieve	O
almost	O
half	O
that	O
bandwidth	O
for	O
the	O
same	O
symbol	O
rate	O
(	O
i.e.	O
,	O
twice	O
as	O
high	O
spectral	B-Protocol
efficiency	I-Protocol
for	O
the	O
same	O
symbol	O
alphabet	O
length	O
)	O
.	O
</s>
<s>
OFDM	B-Protocol
requires	O
very	O
accurate	O
frequency	O
synchronization	O
between	O
the	O
receiver	O
and	O
the	O
transmitter	O
;	O
with	O
frequency	O
deviation	O
the	O
subcarriers	O
will	O
no	O
longer	O
be	O
orthogonal	B-Algorithm
,	O
causing	O
inter-carrier	O
interference	O
(	O
ICI	O
)	O
(	O
i.e.	O
,	O
cross-talk	O
between	O
the	O
subcarriers	O
)	O
.	O
</s>
<s>
This	O
effect	O
typically	O
worsens	O
as	O
speed	O
increases	O
,	O
and	O
is	O
an	O
important	O
factor	O
limiting	O
the	O
use	O
of	O
OFDM	B-Protocol
in	O
high-speed	O
vehicles	O
.	O
</s>
<s>
In	O
order	O
to	O
mitigate	O
ICI	O
in	O
such	O
scenarios	O
,	O
one	O
can	O
shape	O
each	O
subcarrier	O
in	O
order	O
to	O
minimize	O
the	O
interference	O
resulting	O
in	O
a	O
non-orthogonal	O
subcarriers	O
overlapping	O
.	O
</s>
<s>
For	O
example	O
,	O
a	O
low-complexity	O
scheme	O
referred	O
to	O
as	O
WCP-OFDM	O
(	O
Weighted	O
Cyclic	B-Device
Prefix	I-Device
Orthogonal	B-Protocol
Frequency-Division	I-Protocol
Multiplexing	I-Protocol
)	O
consists	O
of	O
using	O
short	O
filters	O
at	O
the	O
transmitter	O
output	O
in	O
order	O
to	O
perform	O
a	O
potentially	O
non-rectangular	O
pulse	B-Algorithm
shaping	I-Algorithm
and	O
a	O
near	O
perfect	O
reconstruction	O
using	O
a	O
single-tap	O
per	O
subcarrier	O
equalization	B-Algorithm
.	O
</s>
<s>
The	O
orthogonality	O
allows	O
for	O
efficient	O
modulator	B-Application
and	O
demodulator	O
implementation	O
using	O
the	O
FFT	O
algorithm	O
on	O
the	O
receiver	O
side	O
,	O
and	O
inverse	O
FFT	O
on	O
the	O
sender	O
side	O
.	O
</s>
<s>
Although	O
the	O
principles	O
and	O
some	O
of	O
the	O
benefits	O
have	O
been	O
known	O
since	O
the	O
1960s	O
,	O
OFDM	B-Protocol
is	O
popular	O
for	O
wideband	O
communications	O
today	O
by	O
way	O
of	O
low-cost	O
digital	B-General_Concept
signal	I-General_Concept
processing	I-General_Concept
components	O
that	O
can	O
efficiently	O
calculate	O
the	O
FFT	O
.	O
</s>
<s>
As	O
a	O
comparison	O
an	O
Intel	B-General_Concept
Pentium	I-General_Concept
III	I-General_Concept
CPU	O
at	O
1.266GHz	O
is	O
able	O
to	O
calculate	O
a	O
FFT	O
in	O
using	O
FFTW	B-Application
.	O
</s>
<s>
Intel	B-Architecture
Pentium	I-Architecture
M	I-Architecture
at	O
1.6GHz	O
does	O
it	O
in	O
Intel	O
Core	O
Duo	O
at	O
3.0GHz	O
does	O
it	O
in	O
.	O
</s>
<s>
One	O
key	O
principle	O
of	O
OFDM	B-Protocol
is	O
that	O
since	O
low	O
symbol	O
rate	O
modulation	B-Application
schemes	O
(	O
i.e.	O
,	O
where	O
the	O
symbols	O
are	O
relatively	O
long	O
compared	O
to	O
the	O
channel	O
time	O
characteristics	O
)	O
suffer	O
less	O
from	O
intersymbol	O
interference	O
caused	O
by	O
multipath	O
propagation	O
,	O
it	O
is	O
advantageous	O
to	O
transmit	O
a	O
number	O
of	O
low-rate	O
streams	O
in	O
parallel	O
instead	O
of	O
a	O
single	O
high-rate	O
stream	O
.	O
</s>
<s>
Since	O
the	O
duration	O
of	O
each	O
symbol	O
is	O
long	O
,	O
it	O
is	O
feasible	O
to	O
insert	O
a	O
guard	B-Protocol
interval	I-Protocol
between	O
the	O
OFDM	B-Protocol
symbols	O
,	O
thus	O
eliminating	O
the	O
intersymbol	O
interference	O
.	O
</s>
<s>
The	O
guard	B-Protocol
interval	I-Protocol
also	O
eliminates	O
the	O
need	O
for	O
a	O
pulse-shaping	B-Algorithm
filter	I-Algorithm
,	O
and	O
it	O
reduces	O
the	O
sensitivity	O
to	O
time	O
synchronization	O
problems	O
.	O
</s>
<s>
A	O
simple	O
example	O
:	O
If	O
one	O
sends	O
a	O
million	O
symbols	O
per	O
second	O
using	O
conventional	O
single-carrier	O
modulation	B-Application
over	O
a	O
wireless	O
channel	O
,	O
then	O
the	O
duration	O
of	O
each	O
symbol	O
would	O
be	O
one	O
microsecond	O
or	O
less	O
.	O
</s>
<s>
Assume	O
that	O
a	O
guard	B-Protocol
interval	I-Protocol
of	O
1/8	O
of	O
the	O
symbol	O
length	O
is	O
inserted	O
between	O
each	O
symbol	O
.	O
</s>
<s>
Intersymbol	O
interference	O
can	O
be	O
avoided	O
if	O
the	O
multipath	O
time-spreading	O
(	O
the	O
time	O
between	O
the	O
reception	O
of	O
the	O
first	O
and	O
the	O
last	O
echo	O
)	O
is	O
shorter	O
than	O
the	O
guard	B-Protocol
interval	I-Protocol
(	O
i.e.	O
,	O
125	O
microseconds	O
)	O
.	O
</s>
<s>
The	O
cyclic	B-Device
prefix	I-Device
,	O
which	O
is	O
transmitted	O
during	O
the	O
guard	B-Protocol
interval	I-Protocol
,	O
consists	O
of	O
the	O
end	O
of	O
the	O
OFDM	B-Protocol
symbol	O
copied	O
into	O
the	O
guard	B-Protocol
interval	I-Protocol
,	O
and	O
the	O
guard	B-Protocol
interval	I-Protocol
is	O
transmitted	O
followed	O
by	O
the	O
OFDM	B-Protocol
symbol	O
.	O
</s>
<s>
The	O
reason	O
that	O
the	O
guard	B-Protocol
interval	I-Protocol
consists	O
of	O
a	O
copy	O
of	O
the	O
end	O
of	O
the	O
OFDM	B-Protocol
symbol	O
is	O
so	O
that	O
the	O
receiver	O
will	O
integrate	O
over	O
an	O
integer	O
number	O
of	O
sinusoid	O
cycles	O
for	O
each	O
of	O
the	O
multipaths	O
when	O
it	O
performs	O
OFDM	B-Protocol
demodulation	O
with	O
the	O
FFT	O
.	O
</s>
<s>
In	O
some	O
standards	O
such	O
as	O
Ultrawideband	O
,	O
in	O
the	O
interest	O
of	O
transmitted	O
power	O
,	O
cyclic	B-Device
prefix	I-Device
is	O
skipped	O
and	O
nothing	O
is	O
sent	O
during	O
the	O
guard	B-Protocol
interval	I-Protocol
.	O
</s>
<s>
The	O
receiver	O
will	O
then	O
have	O
to	O
mimic	O
the	O
cyclic	B-Device
prefix	I-Device
functionality	O
by	O
copying	O
the	O
end	O
part	O
of	O
the	O
OFDM	B-Protocol
symbol	O
and	O
adding	O
it	O
to	O
the	O
beginning	O
portion	O
.	O
</s>
<s>
The	O
effects	O
of	O
frequency-selective	O
channel	O
conditions	O
,	O
for	O
example	O
fading	O
caused	O
by	O
multipath	O
propagation	O
,	O
can	O
be	O
considered	O
as	O
constant	O
(	O
flat	O
)	O
over	O
an	O
OFDM	B-Protocol
sub-channel	O
if	O
the	O
sub-channel	O
is	O
sufficiently	O
narrow-banded	O
(	O
i.e.	O
,	O
if	O
the	O
number	O
of	O
sub-channels	O
is	O
sufficiently	O
large	O
)	O
.	O
</s>
<s>
This	O
makes	O
frequency	O
domain	O
equalization	B-Algorithm
possible	O
at	O
the	O
receiver	O
,	O
which	O
is	O
far	O
simpler	O
than	O
the	O
time-domain	O
equalization	B-Algorithm
used	O
in	O
conventional	O
single-carrier	O
modulation	B-Application
.	O
</s>
<s>
In	O
OFDM	B-Protocol
,	O
the	O
equalizer	B-Algorithm
only	O
has	O
to	O
multiply	O
each	O
detected	O
subcarrier	O
(	O
each	O
Fourier	O
coefficient	O
)	O
in	O
each	O
OFDM	B-Protocol
symbol	O
by	O
a	O
constant	O
complex	O
number	O
,	O
or	O
a	O
rarely	O
changed	O
value	O
.	O
</s>
<s>
On	O
a	O
fundamental	O
level	O
,	O
simpler	O
digital	O
equalizers	B-Algorithm
are	O
better	O
because	O
they	O
require	O
fewer	O
operations	O
,	O
which	O
translates	O
to	O
fewer	O
round-off	O
errors	O
in	O
the	O
equalizer	B-Algorithm
.	O
</s>
<s>
Our	O
example	O
:	O
The	O
OFDM	B-Protocol
equalization	B-Algorithm
in	O
the	O
above	O
numerical	O
example	O
would	O
require	O
one	O
complex	O
valued	O
multiplication	O
per	O
subcarrier	O
and	O
symbol	O
(	O
i.e.	O
,	O
complex	O
multiplications	O
per	O
OFDM	B-Protocol
symbol	O
;	O
i.e.	O
,	O
one	O
million	O
multiplications	O
per	O
second	O
,	O
at	O
the	O
receiver	O
)	O
.	O
</s>
<s>
complex-valued	O
multiplications	O
per	O
OFDM	B-Protocol
symbol	O
(	O
i.e.	O
,	O
10	O
million	O
multiplications	O
per	O
second	O
)	O
,	O
at	O
both	O
the	O
receiver	O
and	O
transmitter	O
side	O
.	O
</s>
<s>
This	O
should	O
be	O
compared	O
with	O
the	O
corresponding	O
one	O
million	O
symbols/second	O
single-carrier	O
modulation	B-Application
case	O
mentioned	O
in	O
the	O
example	O
,	O
where	O
the	O
equalization	B-Algorithm
of	O
125	O
microseconds	O
time-spreading	O
using	O
a	O
FIR	O
filter	O
would	O
require	O
,	O
in	O
a	O
naive	O
implementation	O
,	O
125	O
multiplications	O
per	O
symbol	O
(	O
i.e.	O
,	O
125	O
million	O
multiplications	O
per	O
second	O
)	O
.	O
</s>
<s>
FFT	O
techniques	O
can	O
be	O
used	O
to	O
reduce	O
the	O
number	O
of	O
multiplications	O
for	O
an	O
FIR	O
filter-based	O
time-domain	O
equalizer	B-Algorithm
to	O
a	O
number	O
comparable	O
with	O
OFDM	B-Protocol
,	O
at	O
the	O
cost	O
of	O
delay	O
between	O
reception	O
and	O
decoding	O
which	O
also	O
becomes	O
comparable	O
with	O
OFDM	B-Protocol
.	O
</s>
<s>
If	O
differential	O
modulation	B-Application
such	O
as	O
DPSK	B-General_Concept
or	O
DQPSK	B-General_Concept
is	O
applied	O
to	O
each	O
subcarrier	O
,	O
equalization	B-Algorithm
can	O
be	O
completely	O
omitted	O
,	O
since	O
these	O
non-coherent	O
schemes	O
are	O
insensitive	O
to	O
slowly	O
changing	O
amplitude	O
and	O
phase	O
distortion	O
.	O
</s>
<s>
In	O
a	O
sense	O
,	O
improvements	O
in	O
FIR	O
equalization	B-Algorithm
using	O
FFTs	O
or	O
partial	O
FFTs	O
leads	O
mathematically	O
closer	O
to	O
OFDM	B-Protocol
,	O
but	O
the	O
OFDM	B-Protocol
technique	O
is	O
easier	O
to	O
understand	O
and	O
implement	O
,	O
and	O
the	O
sub-channels	O
can	O
be	O
independently	O
adapted	O
in	O
other	O
ways	O
than	O
varying	O
equalization	B-Algorithm
coefficients	O
,	O
such	O
as	O
switching	O
between	O
different	O
QAM	B-Device
constellation	O
patterns	O
and	O
error-correction	B-Error_Name
schemes	O
to	O
match	O
individual	O
sub-channel	O
noise	O
and	O
interference	O
characteristics	O
.	O
</s>
<s>
Some	O
of	O
the	O
subcarriers	O
in	O
some	O
of	O
the	O
OFDM	B-Protocol
symbols	O
may	O
carry	O
pilot	O
signals	O
for	O
measurement	O
of	O
the	O
channel	O
conditions	O
(	O
i.e.	O
,	O
the	O
equalizer	B-Algorithm
gain	O
and	O
phase	O
shift	O
for	O
each	O
subcarrier	O
)	O
.	O
</s>
<s>
OFDM	B-Protocol
was	O
initially	O
used	O
for	O
wired	O
and	O
stationary	O
wireless	O
communications	O
.	O
</s>
<s>
Over	O
the	O
last	O
decade	O
,	O
research	O
has	O
been	O
done	O
on	O
how	O
to	O
equalize	O
OFDM	B-Protocol
transmission	O
over	O
doubly	O
selective	O
channels	O
.	O
</s>
<s>
OFDM	B-Protocol
is	O
invariably	O
used	O
in	O
conjunction	O
with	O
channel	O
coding	O
(	O
forward	B-Error_Name
error	I-Error_Name
correction	I-Error_Name
)	O
,	O
and	O
almost	O
always	O
uses	O
frequency	O
and/or	O
time	O
interleaving	O
.	O
</s>
<s>
The	O
reason	O
why	O
interleaving	O
is	O
used	O
on	O
OFDM	B-Protocol
is	O
to	O
attempt	O
to	O
spread	O
the	O
errors	O
out	O
in	O
the	O
bit-stream	O
that	O
is	O
presented	O
to	O
the	O
error	B-Error_Name
correction	I-Error_Name
decoder	O
,	O
because	O
when	O
such	O
decoders	O
are	O
presented	O
with	O
a	O
high	O
concentration	O
of	O
errors	O
the	O
decoder	O
is	O
unable	O
to	O
correct	O
all	O
the	O
bit	O
errors	O
,	O
and	O
a	O
burst	O
of	O
uncorrected	O
errors	O
occurs	O
.	O
</s>
<s>
A	O
classical	O
type	O
of	O
error	B-Error_Name
correction	I-Error_Name
coding	O
used	O
with	O
OFDM-based	O
systems	O
is	O
convolutional	B-Error_Name
coding	I-Error_Name
,	O
often	O
concatenated	O
with	O
Reed-Solomon	B-Error_Name
coding	I-Error_Name
.	O
</s>
<s>
The	O
choice	O
for	O
Reed-Solomon	B-Error_Name
coding	I-Error_Name
as	O
the	O
outer	O
error	B-Error_Name
correction	I-Error_Name
code	O
is	O
based	O
on	O
the	O
observation	O
that	O
the	O
Viterbi	O
decoder	O
used	O
for	O
inner	O
convolutional	O
decoding	O
produces	O
short	O
error	O
bursts	O
when	O
there	O
is	O
a	O
high	O
concentration	O
of	O
errors	O
,	O
and	O
Reed-Solomon	B-Error_Name
codes	I-Error_Name
are	O
inherently	O
well	O
suited	O
to	O
correcting	O
bursts	O
of	O
errors	O
.	O
</s>
<s>
Newer	O
systems	O
,	O
however	O
,	O
usually	O
now	O
adopt	O
near-optimal	O
types	O
of	O
error	B-Error_Name
correction	I-Error_Name
codes	O
that	O
use	O
the	O
turbo	O
decoding	O
principle	O
,	O
where	O
the	O
decoder	O
iterates	O
towards	O
the	O
desired	O
solution	O
.	O
</s>
<s>
Examples	O
of	O
such	O
error	B-Error_Name
correction	I-Error_Name
coding	O
types	O
include	O
turbo	B-Error_Name
codes	I-Error_Name
and	O
LDPC	B-Error_Name
codes	I-Error_Name
,	O
which	O
perform	O
close	O
to	O
the	O
Shannon	O
limit	O
for	O
the	O
Additive	O
White	O
Gaussian	O
Noise	O
(	O
AWGN	O
)	O
channel	O
.	O
</s>
<s>
Some	O
systems	O
that	O
have	O
implemented	O
these	O
codes	O
have	O
concatenated	O
them	O
with	O
either	O
Reed-Solomon	B-Error_Name
(	O
for	O
example	O
on	O
the	O
MediaFLO	B-Device
system	O
)	O
or	O
BCH	O
codes	O
(	O
on	O
the	O
DVB-S2	O
system	O
)	O
to	O
improve	O
upon	O
an	O
error	B-Error_Name
floor	I-Error_Name
inherent	O
to	O
these	O
codes	O
at	O
high	O
signal-to-noise	O
ratios	O
.	O
</s>
<s>
Based	O
on	O
this	O
feedback	O
information	O
,	O
adaptive	B-Protocol
modulation	I-Protocol
,	O
channel	O
coding	O
and	O
power	O
allocation	O
may	O
be	O
applied	O
across	O
all	O
subcarriers	O
,	O
or	O
individually	O
to	O
each	O
subcarrier	O
.	O
</s>
<s>
In	O
the	O
latter	O
case	O
,	O
if	O
a	O
particular	O
range	O
of	O
frequencies	O
suffers	O
from	O
interference	O
or	O
attenuation	O
,	O
the	O
carriers	O
within	O
that	O
range	O
can	O
be	O
disabled	O
or	O
made	O
to	O
run	O
slower	O
by	O
applying	O
more	O
robust	O
modulation	B-Application
or	O
error	B-Error_Name
coding	I-Error_Name
to	O
those	O
subcarriers	O
.	O
</s>
<s>
The	O
term	O
(	O
DMT	O
)	O
denotes	O
OFDM-based	O
communication	O
systems	O
that	O
adapt	O
the	O
transmission	O
to	O
the	O
channel	O
conditions	O
individually	O
for	O
each	O
subcarrier	O
,	O
by	O
means	O
of	O
so-called	O
bit-loading	O
.	O
</s>
<s>
OFDM	B-Protocol
in	O
its	O
primary	O
form	O
is	O
considered	O
as	O
a	O
digital	O
modulation	B-Application
technique	O
,	O
and	O
not	O
a	O
multi-user	O
channel	O
access	O
method	O
,	O
since	O
it	O
is	O
used	O
for	O
transferring	O
one	O
bit	O
stream	O
over	O
one	O
communication	O
channel	O
using	O
one	O
sequence	O
of	O
OFDM	B-Protocol
symbols	O
.	O
</s>
<s>
However	O
,	O
OFDM	B-Protocol
can	O
be	O
combined	O
with	O
multiple	O
access	O
using	O
time	O
,	O
frequency	O
or	O
coding	O
separation	O
of	O
the	O
users	O
.	O
</s>
<s>
In	O
orthogonal	B-Algorithm
frequency-division	O
multiple	O
access	O
(	O
OFDMA	O
)	O
,	O
frequency-division	O
multiple	O
access	O
is	O
achieved	O
by	O
assigning	O
different	O
OFDM	B-Protocol
sub-channels	O
to	O
different	O
users	O
.	O
</s>
<s>
OFDMA	O
supports	O
differentiated	O
quality	O
of	O
service	O
by	O
assigning	O
different	O
number	O
of	O
subcarriers	O
to	O
different	O
users	O
in	O
a	O
similar	O
fashion	O
as	O
in	O
CDMA	B-Protocol
,	O
and	O
thus	O
complex	O
packet	O
scheduling	O
or	O
Media	B-Protocol
Access	I-Protocol
Control	I-Protocol
schemes	O
can	O
be	O
avoided	O
.	O
</s>
<s>
The	O
radio	O
interface	O
was	O
formerly	O
named	O
High	O
Speed	O
OFDM	B-Protocol
Packet	O
Access	O
(	O
HSOPA	O
)	O
,	O
now	O
named	O
Evolved	O
UMTS	O
Terrestrial	O
Radio	O
Access	O
(	O
E-UTRA	O
)	O
.	O
</s>
<s>
The	O
project	O
aims	O
at	O
designing	O
the	O
first	O
cognitive	O
radio-based	O
standard	O
operating	O
in	O
the	O
VHF-low	O
UHF	O
spectrum	O
(	O
TV	O
spectrum	O
)	O
.	O
</s>
<s>
In	O
multi-carrier	O
code-division	B-Protocol
multiple	I-Protocol
access	I-Protocol
(	O
MC-CDMA	O
)	O
,	O
also	O
known	O
as	O
OFDM-CDMA	O
,	O
OFDM	B-Protocol
is	O
combined	O
with	O
CDMA	B-Protocol
spread	B-Architecture
spectrum	I-Architecture
communication	I-Architecture
for	O
coding	O
separation	O
of	O
the	O
users	O
.	O
</s>
<s>
Co-channel	O
interference	O
can	O
be	O
mitigated	O
,	O
meaning	O
that	O
manual	O
fixed	B-Protocol
channel	I-Protocol
allocation	I-Protocol
(	O
FCA	O
)	O
frequency	O
planning	O
is	O
simplified	O
,	O
or	O
complex	O
dynamic	B-Protocol
channel	I-Protocol
allocation	I-Protocol
(	O
DCA	O
)	O
schemes	O
are	O
avoided	O
.	O
</s>
<s>
In	O
OFDM-based	O
wide-area	O
broadcasting	O
,	O
receivers	O
can	O
benefit	O
from	O
receiving	O
signals	O
from	O
several	O
spatially	O
dispersed	O
transmitters	O
simultaneously	O
,	O
since	O
transmitters	O
will	O
only	O
destructively	O
interfere	O
with	O
each	O
other	O
on	O
a	O
limited	O
number	O
of	O
subcarriers	O
,	O
whereas	O
in	O
general	O
they	O
will	O
actually	O
reinforce	O
coverage	O
over	O
a	O
wide	O
area	O
.	O
</s>
<s>
This	O
is	O
very	O
beneficial	O
in	O
many	O
countries	O
,	O
as	O
it	O
permits	O
the	O
operation	O
of	O
national	O
single-frequency	B-Device
networks	I-Device
(	O
SFN	O
)	O
,	O
where	O
many	O
transmitters	O
send	O
the	O
same	O
signal	O
simultaneously	O
over	O
the	O
same	O
channel	O
frequency	O
.	O
</s>
<s>
SFNs	O
use	O
the	O
available	O
spectrum	O
more	O
effectively	O
than	O
conventional	O
multi-frequency	O
broadcast	O
networks	O
(	O
MFN	B-Protocol
)	O
,	O
where	O
program	O
content	O
is	O
replicated	O
on	O
different	O
carrier	O
frequencies	O
.	O
</s>
<s>
SFNs	O
also	O
result	O
in	O
a	O
diversity	B-Protocol
gain	I-Protocol
in	O
receivers	O
situated	O
midway	O
between	O
the	O
transmitters	O
.	O
</s>
<s>
The	O
coverage	O
area	O
is	O
increased	O
and	O
the	O
outage	O
probability	O
decreased	O
in	O
comparison	O
to	O
an	O
MFN	B-Protocol
,	O
due	O
to	O
increased	O
received	O
signal	O
strength	O
averaged	O
over	O
all	O
subcarriers	O
.	O
</s>
<s>
Although	O
the	O
guard	B-Protocol
interval	I-Protocol
only	O
contains	O
redundant	O
data	O
,	O
which	O
means	O
that	O
it	O
reduces	O
the	O
capacity	O
,	O
some	O
OFDM-based	O
systems	O
,	O
such	O
as	O
some	O
of	O
the	O
broadcasting	O
systems	O
,	O
deliberately	O
use	O
a	O
long	O
guard	B-Protocol
interval	I-Protocol
in	O
order	O
to	O
allow	O
the	O
transmitters	O
to	O
be	O
spaced	O
farther	O
apart	O
in	O
an	O
SFN	O
,	O
and	O
longer	O
guard	B-Protocol
intervals	I-Protocol
allow	O
larger	O
SFN	O
cell-sizes	O
.	O
</s>
<s>
A	O
rule	O
of	O
thumb	O
for	O
the	O
maximum	O
distance	O
between	O
transmitters	O
in	O
an	O
SFN	O
is	O
equal	O
to	O
the	O
distance	O
a	O
signal	O
travels	O
during	O
the	O
guard	B-Protocol
interval	I-Protocol
—	O
for	O
instance	O
,	O
a	O
guard	B-Protocol
interval	I-Protocol
of	O
200	O
microseconds	O
would	O
allow	O
transmitters	O
to	O
be	O
spaced	O
60km	O
apart	O
.	O
</s>
<s>
A	O
single	B-Device
frequency	I-Device
network	I-Device
is	O
a	O
form	O
of	O
transmitter	O
macrodiversity	B-Protocol
.	O
</s>
<s>
The	O
concept	O
can	O
be	O
further	O
used	O
in	O
dynamic	B-Protocol
single-frequency	I-Protocol
networks	I-Protocol
(	O
DSFN	B-Protocol
)	O
,	O
where	O
the	O
SFN	O
grouping	O
is	O
changed	O
from	O
timeslot	O
to	O
timeslot	O
.	O
</s>
<s>
OFDM	B-Protocol
may	O
be	O
combined	O
with	O
other	O
forms	O
of	O
space	O
diversity	O
,	O
for	O
example	O
antenna	O
arrays	O
and	O
MIMO	O
channels	O
.	O
</s>
<s>
This	O
is	O
done	O
in	O
the	O
IEEE	O
802.11	O
Wireless	B-Architecture
LAN	I-Architecture
standards	O
.	O
</s>
<s>
An	O
OFDM	B-Protocol
signal	O
exhibits	O
a	O
high	O
peak-to-average	O
power	O
ratio	O
(	O
PAPR	O
)	O
because	O
the	O
independent	O
phases	O
of	O
the	O
subcarriers	O
mean	O
that	O
they	O
will	O
often	O
combine	O
constructively	O
.	O
</s>
<s>
In	O
practical	O
OFDM	B-Protocol
systems	O
a	O
small	O
amount	O
of	O
peak	O
clipping	O
is	O
allowed	O
to	O
limit	O
the	O
PAPR	O
in	O
a	O
judicious	O
trade-off	O
against	O
the	O
above	O
consequences	O
.	O
</s>
<s>
Although	O
the	O
spectral	B-Protocol
efficiency	I-Protocol
of	O
OFDM	B-Protocol
is	O
attractive	O
for	O
both	O
terrestrial	O
and	O
space	O
communications	O
,	O
the	O
high	O
PAPR	O
requirements	O
have	O
so	O
far	O
limited	O
OFDM	B-Protocol
applications	O
to	O
terrestrial	O
systems	O
.	O
</s>
<s>
(	O
CFc	O
is	O
3.01dB	O
for	O
the	O
sine	O
waves	O
used	O
for	O
BPSK	O
and	O
QPSK	O
modulation	B-Application
)	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
DVB-T	O
signal	O
in	O
2K	O
mode	O
is	O
composed	O
of	O
1705	O
subcarriers	O
that	O
are	O
each	O
QPSK-modulated	O
,	O
giving	O
a	O
crest	O
factor	O
of	O
35.32dB	O
.	O
</s>
<s>
The	O
performance	O
of	O
any	O
communication	O
system	O
can	O
be	O
measured	O
in	O
terms	O
of	O
its	O
power	O
efficiency	O
and	O
bandwidth	B-Protocol
efficiency	I-Protocol
.	O
</s>
<s>
Bandwidth	B-Protocol
efficiency	I-Protocol
reflects	O
how	O
efficiently	O
the	O
allocated	O
bandwidth	O
is	O
used	O
and	O
is	O
defined	O
as	O
the	O
throughput	O
data	O
rate	O
per	O
hertz	O
in	O
a	O
given	O
bandwidth	O
.	O
</s>
<s>
where	O
is	O
the	O
symbol	O
rate	O
in	O
giga-symbols	O
per	O
second	O
(	O
Gsps	O
)	O
,	O
is	O
the	O
bandwidth	O
of	O
OFDM	B-Protocol
signal	O
,	O
and	O
the	O
factor	O
of	O
2	O
is	O
due	O
to	O
the	O
two	O
polarization	O
states	O
in	O
the	O
fiber	O
.	O
</s>
<s>
There	O
is	O
saving	O
of	O
bandwidth	O
by	O
using	O
multicarrier	O
modulation	B-Application
with	O
orthogonal	B-Protocol
frequency-division	I-Protocol
multiplexing	I-Protocol
.	O
</s>
<s>
So	O
the	O
bandwidth	O
for	O
multicarrier	O
system	O
is	O
less	O
in	O
comparison	O
with	O
single	O
carrier	O
system	O
and	O
hence	O
bandwidth	B-Protocol
efficiency	I-Protocol
of	O
multicarrier	O
system	O
is	O
larger	O
than	O
single	O
carrier	O
system	O
.	O
</s>
<s>
Transmission	O
type	O
M	O
in	O
M-QAM	O
No	O
.	O
</s>
<s>
There	O
is	O
only	O
1dB	O
increase	O
in	O
receiver	O
power	O
,	O
but	O
we	O
get	O
76.7	O
%	O
improvement	O
in	O
bandwidth	B-Protocol
efficiency	I-Protocol
with	O
using	O
multicarrier	O
transmission	O
technique	O
.	O
</s>
<s>
This	O
section	O
describes	O
a	O
simple	O
idealized	O
OFDM	B-Protocol
system	O
model	O
suitable	O
for	O
a	O
time-invariant	O
AWGN	O
channel	O
.	O
</s>
<s>
An	O
OFDM	B-Protocol
carrier	O
signal	O
is	O
the	O
sum	O
of	O
a	O
number	O
of	O
orthogonal	B-Algorithm
subcarriers	O
,	O
with	O
baseband	B-Algorithm
data	O
on	O
each	O
subcarrier	O
being	O
independently	O
modulated	B-Application
commonly	O
using	O
some	O
type	O
of	O
quadrature	B-Device
amplitude	I-Device
modulation	I-Device
(	O
QAM	B-Device
)	O
or	O
phase-shift	B-General_Concept
keying	I-General_Concept
(	O
PSK	B-General_Concept
)	O
.	O
</s>
<s>
This	O
composite	O
baseband	B-Algorithm
signal	I-Algorithm
is	O
typically	O
used	O
to	O
modulate	O
a	O
main	O
RF	O
carrier	O
.	O
</s>
<s>
By	O
inverse	B-Protocol
multiplexing	I-Protocol
,	O
these	O
are	O
first	O
demultiplexed	O
into	O
parallel	O
streams	O
,	O
and	O
each	O
one	O
mapped	O
to	O
a	O
(	O
possibly	O
complex	O
)	O
symbol	O
stream	O
using	O
some	O
modulation	B-Application
constellation	O
(	O
QAM	B-Device
,	O
PSK	B-General_Concept
,	O
etc	O
.	O
)	O
.	O
</s>
<s>
The	O
receiver	O
picks	O
up	O
the	O
signal	O
,	O
which	O
is	O
then	O
quadrature-mixed	O
down	O
to	O
baseband	B-Algorithm
using	O
cosine	O
and	O
sine	O
waves	O
at	O
the	O
carrier	O
frequency	O
.	O
</s>
<s>
The	O
baseband	B-Algorithm
signals	I-Algorithm
are	O
then	O
sampled	O
and	O
digitised	O
using	O
analog-to-digital	O
converters	O
(	O
ADCs	O
)	O
,	O
and	O
a	O
forward	O
FFT	O
is	O
used	O
to	O
convert	O
back	O
to	O
the	O
frequency	O
domain	O
.	O
</s>
<s>
This	O
returns	O
parallel	O
streams	O
,	O
each	O
of	O
which	O
is	O
converted	O
to	O
a	O
binary	O
stream	O
using	O
an	O
appropriate	O
symbol	O
detector	B-Algorithm
.	O
</s>
<s>
If	O
subcarriers	O
are	O
used	O
,	O
and	O
each	O
subcarrier	O
is	O
modulated	B-Application
using	O
alternative	O
symbols	O
,	O
the	O
OFDM	B-Protocol
symbol	O
alphabet	O
consists	O
of	O
combined	O
symbols	O
.	O
</s>
<s>
The	O
low-pass	B-Algorithm
equivalent	I-Algorithm
OFDM	B-Protocol
filter	O
is	O
expressed	O
as	O
:	O
</s>
<s>
where	O
are	O
the	O
data	O
symbols	O
,	O
is	O
the	O
number	O
of	O
subcarriers	O
,	O
and	O
is	O
the	O
OFDM	B-Protocol
symbol	O
time	O
.	O
</s>
<s>
The	O
subcarrier	O
spacing	O
of	O
makes	O
them	O
orthogonal	B-Algorithm
over	O
each	O
symbol	O
period	O
;	O
this	O
property	O
is	O
expressed	O
as	O
:	O
</s>
<s>
To	O
avoid	O
intersymbol	O
interference	O
in	O
multipath	O
fading	O
channels	O
,	O
a	O
guard	B-Protocol
interval	I-Protocol
of	O
length	O
is	O
inserted	O
prior	O
to	O
the	O
OFDM	B-Protocol
block	O
.	O
</s>
<s>
During	O
this	O
interval	O
,	O
a	O
cyclic	B-Device
prefix	I-Device
is	O
transmitted	O
such	O
that	O
the	O
signal	O
in	O
the	O
interval	O
equals	O
the	O
signal	O
in	O
the	O
interval	O
.	O
</s>
<s>
The	O
OFDM	B-Protocol
signal	O
with	O
cyclic	B-Device
prefix	I-Device
is	O
thus	O
:	O
</s>
<s>
Real-valued	O
low-pass	B-Algorithm
equivalent	I-Algorithm
signals	O
are	O
typically	O
transmitted	O
at	O
baseband	B-Algorithm
—	O
wireline	O
applications	O
such	O
as	O
DSL	O
use	O
this	O
approach	O
.	O
</s>
<s>
OFDM	B-Protocol
is	O
used	O
in	O
:	O
</s>
<s>
Key	O
features	O
of	O
some	O
common	O
OFDM-based	O
systems	O
are	O
presented	O
in	O
the	O
following	O
table	O
.	O
</s>
<s>
Standard	O
name	O
DAB	O
Eureka	O
147	O
DVB-T	O
DVB-H	B-Protocol
DMB-T/H	O
DVB-T2	B-Protocol
IEEE	O
802.11a	O
Year	O
ratified	O
1995	O
1997	O
2004	O
2006	O
2007	O
1999	O
Frequency	O
range	O
of	O
today	O
's	O
equipment	O
(	O
MHz	O
)	O
,	O
,	O
Channel	O
spacing	O
,	O
B	O
(	O
MHz	O
)	O
1.712	O
6	O
,	O
7	O
,	O
8	O
5	O
,	O
6	O
,	O
7	O
,	O
8	O
8	O
1.7	O
,	O
5	O
,	O
6	O
,	O
7	O
,	O
8	O
,	O
10	O
20	O
FFT	O
size	O
,	O
Mode	O
I	O
:	O
2kMode	O
II	O
:	O
512Mode	O
III	O
:	O
256Mode	O
IV	O
:	O
1k	O
2k	O
,	O
8k	O
2k	O
,	O
4k	O
,	O
8k	O
1	O
(	O
single-carrier	O
)	O
4k	O
(	O
multi-carrier	O
)	O
1k	O
,	O
2k	O
,	O
4k	O
,	O
8k	O
,	O
16k	O
,	O
32k	O
64	O
Number	O
of	O
non-silent	O
subcarriers	O
,	O
N	O
Mode	O
I	O
:	O
1,536	O
Mode	O
II	O
:	O
384Mode	O
III	O
:	O
192Mode	O
IV	O
:	O
768	O
2K	O
mode	O
:	O
1	O
,	O
7058K	O
mode	O
:	O
6,817	O
1	O
,	O
705	O
,	O
3	O
,	O
409	O
,	O
6,817	O
1	O
(	O
single-carrier	O
)	O
3,780	O
(	O
multi-carrier	O
)	O
853	O
–	O
27,841	O
(	O
1K	O
normal	O
to	O
32K	O
extended	O
carrier	O
mode	O
)	O
52	O
Subcarrier	O
modulation	B-Application
scheme	O
-DQPSK	O
QPSK	O
,	O
4QAM	B-Device
is	O
equivalent	O
to	O
QPSK	O
16QAM	B-Device
,	O
64QAM	B-Device
QPSK	O
,	O
16QAM	B-Device
,	O
64QAM	B-Device
4QAM	B-Device
,	O
4QAM-NR	O
,	O
NR	O
refers	O
to	O
Nordstrom-Robinson	O
code	O
16QAM	B-Device
,	O
32QAM	B-Device
,	O
64QAM	B-Device
QPSK	O
,	O
16QAM	B-Device
,	O
64QAM	B-Device
,	O
256QAM	B-Device
BPSK	O
,	O
QPSK	O
,	O
16QAM	B-Device
,	O
64QAM	B-Device
Useful	O
symbol	O
length	O
,	O
TU	O
( μs	O
)	O
Mode	O
I	O
:	O
1,000	O
Mode	O
II	O
:	O
250Mode	O
III	O
:	O
125Mode	O
IV	O
:	O
500	O
2K	O
mode	O
:	O
2248K	O
mode	O
:	O
896	O
224	O
,	O
448	O
,	O
896	O
500	O
(	O
multi-carrier	O
)	O
112	O
–	O
3,584	O
(	O
1K	O
to	O
32K	O
mode	O
on	O
8	O
MHz	O
channel	O
)	O
3.2	O
Additional	O
guard	B-Protocol
interval	I-Protocol
,	O
TG/TU	O
24.6	O
%	O
(	O
all	O
modes	O
)	O
,	O
,	O
,	O
,	O
,	O
,	O
,	O
,	O
1/128	O
,	O
1/32	O
,	O
1/16	O
,	O
19/256	O
,	O
1/8	O
,	O
19/128	O
,	O
1/4	O
(	O
for	O
32k	O
mode	O
maximum	O
1/8	O
)	O
Subcarrier	O
spacing	O
,	O
(	O
Hz	O
)	O
Mode	O
I	O
:	O
1,000	O
Mode	O
II	O
:	O
4,000	O
Mode	O
III	O
:	O
8,000	O
Mode	O
IV	O
:	O
2,000	O
2K	O
mode	O
:	O
4	O
,	O
4648K	O
mode	O
:	O
1,116	O
4	O
,	O
464	O
,	O
2	O
,	O
232	O
,	O
1,116	O
8	O
M	O
(	O
single-carrier	O
)	O
2,000	O
(	O
multi-carrier	O
)	O
279	O
–	O
8,929	O
(	O
32K	O
down	O
to	O
1K	O
mode	O
)	O
312.5	O
K	O
Net	O
bit	O
rate	O
,	O
R	O
(	O
Mbit/s	O
)	O
0.576	O
–	O
1.152	O
4.98	O
–	O
31.67	O
(	O
24.13	O
)	O
3.7	O
–	O
23.8	O
4.81	O
–	O
32.49	O
Typically	O
35.4	O
6	O
–	O
54	O
Link	B-Protocol
spectral	I-Protocol
efficiency	I-Protocol
,	O
R/B	O
(	O
bit/s	O
·Hz	O
)	O
0.34	O
–	O
0.67	O
0.62	O
–	O
4.0	O
(	O
3.0	O
)	O
0.62	O
–	O
4.0	O
0.60	O
–	O
4.1	O
0.87	O
–	O
6.65	O
0.30	O
–	O
2.7	O
Inner	O
FEC	B-Error_Name
Conv	O
.	O
</s>
<s>
coding	O
with	O
code	O
rates	O
:	O
,	O
,	O
,	O
,	O
or	O
LDPC	B-Error_Name
with	O
code	O
rates	O
:	O
0.4	O
,	O
0.6	O
,	O
or	O
0.8	O
LDPC	B-Error_Name
:	O
,	O
,	O
,	O
,	O
,	O
Conv	O
.	O
</s>
<s>
OFDM	B-Protocol
is	O
used	O
in	O
ADSL	O
connections	O
that	O
follow	O
the	O
ANSI	O
T1.413	O
and	O
G.dmt	O
(	O
ITU	O
G.992.1	O
)	O
standards	O
,	O
where	O
it	O
is	O
called	O
discrete	B-Protocol
multitone	I-Protocol
modulation	I-Protocol
(	O
DMT	O
)	O
.	O
</s>
<s>
OFDM	B-Protocol
is	O
also	O
used	O
in	O
the	O
successor	O
standards	O
ADSL2	O
,	O
ADSL2+	O
,	O
VDSL	O
,	O
VDSL2	O
,	O
and	O
G.fast	O
.	O
</s>
<s>
ADSL2	O
uses	O
variable	O
subcarrier	O
modulation	B-Application
,	O
ranging	O
from	O
BPSK	O
to	O
32768QAM	O
(	O
in	O
ADSL	O
terminology	O
this	O
is	O
referred	O
to	O
as	O
bit-loading	O
,	O
or	O
bit	O
per	O
tone	O
,	O
1	O
to	O
15	O
bits	O
per	O
subcarrier	O
)	O
.	O
</s>
<s>
The	O
fact	O
that	O
OFDM	B-Protocol
can	O
cope	O
with	O
this	O
frequency	O
selective	O
attenuation	O
and	O
with	O
narrow-band	O
interference	O
are	O
the	O
main	O
reasons	O
it	O
is	O
frequently	O
used	O
in	O
applications	O
such	O
as	O
ADSL	O
modems	B-Application
.	O
</s>
<s>
OFDM	B-Protocol
is	O
used	O
by	O
many	O
powerline	B-Device
devices	O
to	O
extend	O
digital	O
connections	O
through	O
power	O
wiring	O
.	O
</s>
<s>
Adaptive	B-Protocol
modulation	I-Protocol
is	O
particularly	O
important	O
with	O
such	O
a	O
noisy	O
channel	O
as	O
electrical	O
wiring	O
.	O
</s>
<s>
Some	O
medium	O
speed	O
smart	O
metering	O
modems	B-Application
,	O
"	O
Prime	O
"	O
and	O
"	O
G3	O
"	O
use	O
OFDM	B-Protocol
at	O
modest	O
frequencies	O
(	O
30	O
–	O
100kHz	O
)	O
with	O
modest	O
numbers	O
of	O
channels	O
(	O
several	O
hundred	O
)	O
in	O
order	O
to	O
overcome	O
the	O
intersymbol	O
interference	O
in	O
the	O
power	O
line	O
environment	O
.	O
</s>
<s>
The	O
IEEE	O
1901	O
standards	O
include	O
two	O
incompatible	O
physical	O
layers	O
that	O
both	O
use	O
OFDM	B-Protocol
.	O
</s>
<s>
The	O
ITU-T	B-General_Concept
G.hn	I-General_Concept
standard	O
,	O
which	O
provides	O
high-speed	O
local	O
area	O
networking	O
over	O
existing	O
home	O
wiring	O
(	O
power	O
lines	O
,	O
phone	O
lines	O
and	O
coaxial	O
cables	O
)	O
is	O
based	O
on	O
a	O
PHY	O
layer	O
that	O
specifies	O
OFDM	B-Protocol
with	O
adaptive	B-Protocol
modulation	I-Protocol
and	O
a	O
Low-Density	O
Parity-Check	O
(	O
LDPC	B-Error_Name
)	O
FEC	B-Error_Name
code	O
.	O
</s>
<s>
OFDM	B-Protocol
is	O
extensively	O
used	O
in	O
wireless	B-Architecture
LAN	I-Architecture
and	O
MAN	O
applications	O
,	O
including	O
IEEE	O
802.11a/g/n	O
and	O
WiMAX	O
.	O
</s>
<s>
Four	O
different	O
modulation	B-Application
schemes	O
are	O
used	O
:	O
BPSK	O
,	O
QPSK	O
,	O
16-QAM	B-Device
,	O
and	O
64-QAM	B-Device
,	O
along	O
with	O
a	O
set	O
of	O
error	O
correcting	O
rates	O
(	O
1/2	O
–	O
5/6	O
)	O
.	O
</s>
<s>
OFDM	B-Protocol
is	O
also	O
now	O
being	O
used	O
in	O
the	O
for	O
high-speed	O
wireless	B-General_Concept
personal	I-General_Concept
area	I-General_Concept
networks	I-General_Concept
in	O
the	O
3.1	O
–	O
10.6GHz	O
ultrawideband	O
spectrum	O
(	O
see	O
MultiBand-OFDM	O
)	O
.	O
</s>
<s>
Much	O
of	O
Europe	O
and	O
Asia	O
has	O
adopted	O
OFDM	B-Protocol
for	O
terrestrial	O
broadcasting	O
of	O
digital	B-Application
television	I-Application
(	O
DVB-T	O
,	O
DVB-H	B-Protocol
and	O
T-DMB	O
)	O
and	O
radio	O
(	O
EUREKA	O
147	O
DAB	O
,	O
Digital	O
Radio	O
Mondiale	O
,	O
HD	O
Radio	O
and	O
T-DMB	O
)	O
.	O
</s>
<s>
By	O
Directive	O
of	O
the	O
European	O
Commission	O
,	O
all	O
television	O
services	O
transmitted	O
to	O
viewers	O
in	O
the	O
European	O
Community	O
must	O
use	O
a	O
transmission	O
system	O
that	O
has	O
been	O
standardized	O
by	O
a	O
recognized	O
European	O
standardization	O
body	O
,	O
and	O
such	O
a	O
standard	O
has	O
been	O
developed	O
and	O
codified	O
by	O
the	O
DVB	O
Project	O
,	O
Digital	O
Video	O
Broadcasting	O
(	O
DVB	O
)	O
;	O
Framing	O
structure	O
,	O
channel	O
coding	O
and	O
modulation	B-Application
for	O
digital	O
terrestrial	O
television	O
.	O
</s>
<s>
Customarily	O
referred	O
to	O
as	O
DVB-T	O
,	O
the	O
standard	O
calls	O
for	O
the	O
exclusive	O
use	O
of	O
COFDM	B-Protocol
for	O
modulation	B-Application
.	O
</s>
<s>
DVB-T	O
is	O
now	O
widely	O
used	O
in	O
Europe	O
and	O
elsewhere	O
for	O
terrestrial	O
digital	B-Application
TV	I-Application
.	O
</s>
<s>
The	O
ground	O
segments	O
of	O
the	O
Digital	O
Audio	O
Radio	O
Service	O
(	O
SDARS	O
)	O
systems	O
used	O
by	O
XM	O
Satellite	O
Radio	O
and	O
Sirius	O
Satellite	O
Radio	O
are	O
transmitted	O
using	O
Coded	B-Protocol
OFDM	I-Protocol
(	O
COFDM	B-Protocol
)	O
.	O
</s>
<s>
The	O
word	O
"	O
coded	O
"	O
comes	O
from	O
the	O
use	O
of	O
forward	B-Error_Name
error	I-Error_Name
correction	I-Error_Name
(	O
FEC	B-Error_Name
)	O
.	O
</s>
<s>
The	O
question	O
of	O
the	O
relative	O
technical	O
merits	O
of	O
COFDM	B-Protocol
versus	O
8VSB	B-Device
for	O
terrestrial	B-Application
digital	I-Application
television	I-Application
has	O
been	O
a	O
subject	O
of	O
some	O
controversy	O
,	O
especially	O
between	O
European	O
and	O
North	O
American	O
technologists	O
and	O
regulators	O
.	O
</s>
<s>
The	O
United	O
States	O
has	O
rejected	O
several	O
proposals	O
to	O
adopt	O
the	O
COFDM-based	O
DVB-T	O
system	O
for	O
its	O
digital	B-Application
television	I-Application
services	O
,	O
and	O
for	O
many	O
years	O
has	O
opted	O
to	O
use	O
8VSB	B-Device
(	O
vestigial	O
sideband	O
modulation	B-Application
)	O
exclusively	O
for	O
terrestrial	B-Application
digital	I-Application
television	I-Application
.	O
</s>
<s>
However	O
,	O
in	O
November	O
2017	O
,	O
the	O
FCC	O
approved	O
a	O
voluntary	O
transition	O
to	O
ATSC	B-Device
3.0	I-Device
,	O
a	O
new	O
broadcast	O
standard	O
which	O
is	O
based	O
on	O
COFDM	B-Protocol
.	O
</s>
<s>
Unlike	O
the	O
first	O
digital	B-Application
television	I-Application
transition	O
in	O
America	O
,	O
TV	O
stations	O
will	O
not	O
be	O
assigned	O
separate	O
frequencies	O
to	O
transmit	O
ATSC	B-Device
3.0	I-Device
and	O
are	O
not	O
required	O
to	O
switch	O
to	O
ATSC	B-Device
3.0	I-Device
by	O
any	O
deadline	O
.	O
</s>
<s>
Televisions	O
sold	O
in	O
the	O
U.S.	O
are	O
also	O
not	O
required	O
to	O
include	O
ATSC	B-Device
3.0	I-Device
tuning	O
capabilities	O
.	O
</s>
<s>
Full-powered	O
television	O
stations	O
are	O
permitted	O
to	O
make	O
the	O
switch	O
to	O
ATSC	B-Device
3.0	I-Device
,	O
as	O
long	O
as	O
they	O
continue	O
to	O
make	O
their	O
main	O
channel	O
available	O
through	O
a	O
simulcast	O
agreement	O
with	O
another	O
in-market	O
station	O
(	O
with	O
a	O
similar	O
coverage	O
area	O
)	O
through	O
at	O
least	O
November	O
2022	O
.	O
</s>
<s>
One	O
of	O
the	O
major	O
benefits	O
provided	O
by	O
COFDM	B-Protocol
is	O
in	O
rendering	O
radio	O
broadcasts	O
relatively	O
immune	O
to	O
multipath	O
distortion	O
and	O
signal	O
fading	O
due	O
to	O
atmospheric	O
conditions	O
or	O
passing	O
aircraft	O
.	O
</s>
<s>
Proponents	O
of	O
COFDM	B-Protocol
argue	O
it	O
resists	O
multipath	O
far	O
better	O
than	O
8VSB	B-Device
.	O
</s>
<s>
Early	O
8VSB	B-Device
DTV	B-Application
(	O
digital	B-Application
television	I-Application
)	O
receivers	O
often	O
had	O
difficulty	O
receiving	O
a	O
signal	O
.	O
</s>
<s>
Also	O
,	O
COFDM	B-Protocol
allows	O
single-frequency	B-Device
networks	I-Device
,	O
which	O
is	O
not	O
possible	O
with	O
8VSB	B-Device
.	O
</s>
<s>
However	O
,	O
newer	O
8VSB	B-Device
receivers	O
are	O
far	O
better	O
at	O
dealing	O
with	O
multipath	O
,	O
hence	O
the	O
difference	O
in	O
performance	O
may	O
diminish	O
with	O
advances	O
in	O
equalizer	B-Algorithm
design	O
.	O
</s>
<s>
COFDM	B-Protocol
is	O
also	O
used	O
for	O
other	O
radio	O
standards	O
,	O
for	O
Digital	O
Audio	O
Broadcasting	O
(	O
DAB	O
)	O
,	O
the	O
standard	O
for	O
digital	O
audio	O
broadcasting	O
at	O
VHF	B-Algorithm
frequencies	O
,	O
for	O
Digital	O
Radio	O
Mondiale	O
(	O
DRM	O
)	O
,	O
the	O
standard	O
for	O
digital	O
broadcasting	O
at	O
shortwave	O
and	O
medium	B-Algorithm
wave	I-Algorithm
frequencies	O
(	O
below	O
30MHz	O
)	O
and	O
for	O
DRM+	O
a	O
more	O
recently	O
introduced	O
standard	O
for	O
digital	O
audio	O
broadcasting	O
at	O
VHF	B-Algorithm
frequencies	O
.	O
</s>
<s>
However	O
,	O
it	O
uses	O
COFDM	B-Protocol
as	O
the	O
underlying	O
broadcast	O
technology	O
to	O
add	O
digital	O
audio	O
to	O
AM	O
(	O
medium	B-Algorithm
wave	I-Algorithm
)	O
and	O
FM	O
broadcasts	O
.	O
</s>
<s>
Both	O
Digital	O
Radio	O
Mondiale	O
and	O
HD	O
Radio	O
are	O
classified	O
as	O
in-band	O
on-channel	O
systems	O
,	O
unlike	O
Eureka	O
147	O
(	O
DAB	O
:	O
Digital	O
Audio	O
Broadcasting	O
)	O
which	O
uses	O
separate	O
VHF	B-Algorithm
or	O
UHF	O
frequency	O
bands	O
instead	O
.	O
</s>
<s>
The	O
band-segmented	O
transmission	O
orthogonal	B-Protocol
frequency-division	I-Protocol
multiplexing	I-Protocol
(	O
BST-OFDM	O
)	O
system	O
proposed	O
for	O
Japan	O
(	O
in	O
the	O
ISDB-T	O
,	O
ISDB-TSB	B-Protocol
,	O
and	O
ISDB-C	O
broadcasting	O
systems	O
)	O
improves	O
upon	O
COFDM	B-Protocol
by	O
exploiting	O
the	O
fact	O
that	O
some	O
OFDM	B-Protocol
carriers	O
may	O
be	O
modulated	B-Application
differently	O
from	O
others	O
within	O
the	O
same	O
multiplex	O
.	O
</s>
<s>
Some	O
forms	O
of	O
COFDM	B-Protocol
already	O
offer	O
this	O
kind	O
of	O
hierarchical	B-Protocol
modulation	I-Protocol
,	O
though	O
BST-OFDM	O
is	O
intended	O
to	O
make	O
it	O
more	O
flexible	O
.	O
</s>
<s>
The	O
6MHz	O
television	O
channel	O
may	O
therefore	O
be	O
"	O
segmented	O
"	O
,	O
with	O
different	O
segments	O
being	O
modulated	B-Application
differently	O
and	O
used	O
for	O
different	O
services	O
.	O
</s>
<s>
Furthermore	O
,	O
these	O
may	O
be	O
modulated	B-Application
with	O
different	O
parameters	O
so	O
that	O
,	O
for	O
example	O
,	O
the	O
audio	O
and	O
data	O
services	O
could	O
be	O
optimized	O
for	O
mobile	O
reception	O
,	O
while	O
the	O
television	O
service	O
is	O
optimized	O
for	O
stationary	O
reception	O
in	O
a	O
high-multipath	O
environment	O
.	O
</s>
<s>
Ultra-wideband	O
(	O
UWB	O
)	O
wireless	B-General_Concept
personal	I-General_Concept
area	I-General_Concept
network	I-General_Concept
technology	O
may	O
also	O
use	O
OFDM	B-Protocol
,	O
such	O
as	O
in	O
Multiband	O
OFDM	B-Protocol
(	O
MB-OFDM	O
)	O
.	O
</s>
<s>
This	O
UWB	O
specification	O
is	O
advocated	O
by	O
the	O
WiMedia	O
Alliance	O
(	O
formerly	O
by	O
both	O
the	O
Multiband	O
OFDM	B-Protocol
Alliance	O
 [ MBOA ] 	O
and	O
the	O
WiMedia	O
Alliance	O
,	O
but	O
the	O
two	O
have	O
now	O
merged	O
)	O
,	O
and	O
is	O
one	O
of	O
the	O
competing	O
UWB	O
radio	O
interfaces	O
.	O
</s>
<s>
Fast	O
low-latency	O
access	O
with	O
seamless	O
handoff	O
orthogonal	B-Protocol
frequency-division	I-Protocol
multiplexing	I-Protocol
(	O
Flash-OFDM	O
)	O
,	O
also	O
referred	O
to	O
as	O
F-OFDM	O
,	O
was	O
based	O
on	O
OFDM	B-Protocol
and	O
also	O
specified	O
higher	O
protocol	B-Architecture
layers	I-Architecture
.	O
</s>
<s>
Flash-OFDM	O
was	O
marketed	O
as	O
a	O
packet-switched	O
cellular	O
bearer	O
,	O
to	O
compete	O
with	O
GSM	O
and	O
3G	B-Architecture
networks	I-Architecture
.	O
</s>
<s>
As	O
an	O
example	O
,	O
450MHz	O
frequency	O
bands	O
previously	O
used	O
by	O
NMT-450	O
and	O
C-Net	O
C450	O
(	O
both	O
1G	O
analogue	O
networks	O
,	O
now	O
mostly	O
decommissioned	O
)	O
in	O
Europe	O
are	O
being	O
licensed	O
to	O
Flash-OFDM	O
operators	O
.	O
</s>
<s>
In	O
Finland	O
,	O
the	O
license	O
holder	O
Digita	O
began	O
deployment	O
of	O
a	O
nationwide	O
"	O
@450	O
"	O
wireless	B-General_Concept
network	I-General_Concept
in	O
parts	O
of	O
the	O
country	O
since	O
April	O
2007	O
.	O
</s>
<s>
Slovak	O
Telekom	O
in	O
Slovakia	O
offers	O
Flash-OFDM	O
connections	O
with	O
a	O
maximum	O
downstream	O
speed	O
of	O
5.3Mbit/s	O
,	O
and	O
a	O
maximum	O
upstream	O
speed	O
of	O
1.8Mbit/s	O
,	O
with	O
a	O
coverage	O
of	O
over	O
70	O
percent	O
of	O
Slovak	O
population	O
.	O
</s>
<s>
The	O
Flash-OFDM	O
network	O
was	O
switched	O
off	O
in	O
the	O
majority	O
of	O
Slovakia	O
on	O
30	O
September	O
2015	O
.	O
</s>
<s>
T-Mobile	O
Germany	O
used	O
Flash-OFDM	O
to	O
backhaul	O
Wi-Fi	O
HotSpots	O
on	O
the	O
Deutsche	O
Bahn	O
's	O
ICE	O
high	O
speed	O
trains	O
between	O
2005	O
and	O
2015	O
,	O
until	O
switching	O
over	O
to	O
UMTS	O
and	O
LTE	O
.	O
</s>
<s>
American	O
wireless	O
carrier	O
Nextel	O
Communications	O
field	O
tested	O
wireless	B-General_Concept
broadband	I-General_Concept
network	O
technologies	O
including	O
Flash-OFDM	O
in	O
2005	O
.	O
</s>
<s>
Sprint	O
purchased	O
the	O
carrier	O
in	O
2006	O
and	O
decided	O
to	O
deploy	O
the	O
mobile	O
version	O
of	O
WiMAX	O
,	O
which	O
is	O
based	O
on	O
Scalable	O
Orthogonal	B-Algorithm
Frequency-Division	O
Multiple	O
Access	O
(	O
SOFDMA	O
)	O
technology	O
.	O
</s>
<s>
Citizens	O
Telephone	O
Cooperative	O
launched	O
a	O
mobile	O
broadband	O
service	O
based	O
on	O
Flash-OFDM	O
technology	O
to	O
subscribers	O
in	O
parts	O
of	O
Virginia	B-Application
in	O
March	O
2006	O
.	O
</s>
<s>
VOFDM	O
replaces	O
each	O
scalar	O
value	O
in	O
the	O
conventional	O
OFDM	B-Protocol
by	O
a	O
vector	O
value	O
and	O
is	O
a	O
bridge	O
between	O
OFDM	B-Protocol
and	O
the	O
single	O
carrier	O
frequency	O
domain	O
equalizer	B-Algorithm
(	O
SC-FDE	O
)	O
.	O
</s>
<s>
When	O
the	O
vector	O
size	O
is	O
,	O
it	O
is	O
OFDM	B-Protocol
and	O
when	O
the	O
vector	O
size	O
is	O
at	O
least	O
the	O
channel	O
length	O
and	O
the	O
FFT	O
size	O
is	O
,	O
it	O
is	O
SC-FDE	O
.	O
</s>
<s>
In	O
VOFDM	O
,	O
assume	O
is	O
the	O
vector	O
size	O
,	O
and	O
each	O
scalar-valued	O
signal	O
in	O
OFDM	B-Protocol
is	O
replaced	O
by	O
a	O
vector-valued	O
signal	O
of	O
vector	O
size	O
,	O
.	O
</s>
<s>
Clearly	O
,	O
when	O
the	O
vector	O
size	O
,	O
the	O
above	O
VOFDM	O
returns	O
to	O
OFDM	B-Protocol
and	O
when	O
and	O
,	O
it	O
becomes	O
the	O
SC-FDE	O
.	O
</s>
<s>
Also	O
note	O
that	O
there	O
exist	O
many	O
other	O
different	O
generalizations/forms	O
of	O
OFDM	B-Protocol
,	O
to	O
see	O
their	O
essential	O
differences	O
,	O
it	O
is	O
critical	O
to	O
see	O
their	O
corresponding	O
received	O
signal	O
equations	O
to	O
demodulate	O
.	O
</s>
<s>
OFDM	B-Protocol
has	O
become	O
an	O
interesting	O
technique	O
for	O
power	B-Device
line	I-Device
communications	I-Device
(	O
PLC	O
)	O
.	O
</s>
<s>
In	O
this	O
area	O
of	O
research	O
,	O
a	O
wavelet	O
transform	O
is	O
introduced	O
to	O
replace	O
the	O
DFT	O
as	O
the	O
method	O
of	O
creating	O
orthogonal	B-Algorithm
frequencies	O
.	O
</s>
<s>
An	O
example	O
of	O
W-OFDM	O
uses	O
the	O
Perfect	O
Reconstruction	O
Cosine	O
Modulated	B-Application
Filter	O
Bank	O
(	O
PR-CMFB	O
)	O
and	O
Extended	O
Lapped	O
Transform	O
(	O
ELT	O
)	O
is	O
used	O
for	O
the	O
wavelet	O
TF	O
.	O
</s>
<s>
Just	O
as	O
in	O
the	O
case	O
of	O
DFT	O
,	O
the	O
wavelet	O
transform	O
creates	O
orthogonal	B-Algorithm
waves	O
with	O
,	O
,	O
...	O
,	O
.	O
</s>
<s>
W-OFDM	O
is	O
an	O
evolution	O
of	O
the	O
standard	O
OFDM	B-Protocol
,	O
with	O
certain	O
advantages	O
.	O
</s>
<s>
Mainly	O
,	O
the	O
sidelobe	O
levels	O
of	O
W-OFDM	O
are	O
lower	O
.	O
</s>
<s>
A	O
comparison	O
between	O
the	O
two	O
modulation	B-Application
techniques	O
also	O
reveals	O
that	O
the	O
complexity	O
of	O
both	O
algorithms	O
remains	O
approximately	O
the	O
same	O
.	O
</s>
<s>
1957	O
:	O
Kineplex	O
,	O
multi-carrier	O
HF	O
modem	B-Application
(	O
R.R.	O
</s>
<s>
2000	O
:	O
Proprietary	O
fixed	O
wireless	O
access	O
(	O
V-OFDM	O
,	O
FLASH-OFDM	O
,	O
etc	O
.	O
)	O
</s>
<s>
May	O
2001	O
:	O
The	O
FCC	O
allows	O
OFDM	B-Protocol
in	O
the	O
2.4GHz	O
license	O
exempt	O
band	O
.	O
</s>
