<s>
In	O
telecommunications	O
,	O
the	O
term	O
cyclic	B-Device
prefix	I-Device
refers	O
to	O
the	O
prefixing	O
of	O
a	O
symbol	O
,	O
with	O
a	O
repetition	O
of	O
the	O
end	O
.	O
</s>
<s>
The	O
receiver	O
is	O
typically	O
configured	O
to	O
discard	O
the	O
cyclic	B-Device
prefix	I-Device
samples	O
,	O
but	O
the	O
cyclic	B-Device
prefix	I-Device
serves	O
two	O
purposes	O
:	O
</s>
<s>
It	O
provides	O
a	O
guard	B-Protocol
interval	I-Protocol
to	O
eliminate	O
intersymbol	O
interference	O
from	O
the	O
previous	O
symbol	O
.	O
</s>
<s>
It	O
repeats	O
the	O
end	O
of	O
the	O
symbol	O
so	O
the	O
linear	O
convolution	B-Language
of	O
a	O
frequency-selective	O
multipath	O
channel	O
can	O
be	O
modeled	O
as	O
circular	B-Algorithm
convolution	I-Algorithm
,	O
which	O
in	O
turn	O
may	O
transform	O
to	O
the	O
frequency	O
domain	O
via	O
a	O
discrete	B-Algorithm
Fourier	I-Algorithm
transform	I-Algorithm
.	O
</s>
<s>
For	O
the	O
cyclic	B-Device
prefix	I-Device
to	O
serve	O
its	O
objectives	O
,	O
it	O
must	O
have	O
a	O
length	O
at	O
least	O
equal	O
to	O
the	O
length	O
of	O
the	O
multipath	O
channel	O
.	O
</s>
<s>
The	O
concept	O
of	O
a	O
cyclic	B-Device
prefix	I-Device
is	O
traditionally	O
associated	O
with	O
OFDM	B-Protocol
systems	O
,	O
however	O
the	O
cyclic	B-Device
prefix	I-Device
is	O
now	O
also	O
used	O
in	O
single	O
carrier	O
systems	O
to	O
improve	O
the	O
robustness	O
to	O
multipath	O
propagation	O
.	O
</s>
<s>
A	O
cyclic	B-Device
prefix	I-Device
is	O
often	O
used	O
in	O
conjunction	O
with	O
modulation	O
to	O
retain	O
sinusoids	O
 '	O
properties	O
in	O
multipath	O
channels	O
.	O
</s>
<s>
It	O
is	O
well	O
known	O
that	O
sinusoidal	O
signals	O
are	O
eigenfunctions	B-Algorithm
of	O
linear	O
,	O
and	O
time-invariant	B-Algorithm
systems	I-Algorithm
.	O
</s>
<s>
Therefore	O
,	O
if	O
the	O
channel	O
is	O
assumed	O
to	O
be	O
linear	O
and	O
time-invariant	B-Algorithm
,	O
then	O
a	O
sinusoid	O
of	O
infinite	O
duration	O
would	O
be	O
an	O
eigenfunction	B-Algorithm
.	O
</s>
<s>
So	O
,	O
to	O
mimic	O
the	O
infinite	O
behavior	O
,	O
prefixing	O
the	O
end	O
of	O
the	O
symbol	O
to	O
the	O
beginning	O
makes	O
the	O
linear	O
convolution	B-Language
of	O
the	O
channel	O
appear	O
as	O
though	O
it	O
were	O
circular	B-Algorithm
convolution	I-Algorithm
,	O
and	O
thus	O
,	O
preserve	O
this	O
property	O
in	O
the	O
part	O
of	O
the	O
symbol	O
after	O
the	O
cyclic	B-Device
prefix	I-Device
.	O
</s>
<s>
OFDM	B-Protocol
uses	O
cyclic	B-Device
prefixes	I-Device
to	O
combat	O
multipath	O
by	O
making	O
channel	O
estimation	O
easy	O
.	O
</s>
<s>
As	O
an	O
example	O
,	O
consider	O
an	O
OFDM	B-Protocol
system	O
that	O
has	O
subcarriers	O
.	O
</s>
<s>
The	O
OFDM	B-Protocol
symbol	O
is	O
constructed	O
by	O
taking	O
the	O
inverse	B-Algorithm
discrete	I-Algorithm
Fourier	I-Algorithm
transform	I-Algorithm
(	O
IDFT	O
)	O
of	O
the	O
message	O
symbol	O
,	O
followed	O
by	O
a	O
cyclic	O
prefixing	O
.	O
</s>
<s>
Prefixing	O
it	O
with	O
a	O
cyclic	B-Device
prefix	I-Device
of	O
length	O
,	O
the	O
OFDM	B-Protocol
symbol	O
obtained	O
is	O
:	O
</s>
<s>
which	O
is	O
circular	B-Algorithm
convolution	I-Algorithm
,	O
as	O
becomes	O
.	O
</s>
<s>
where	O
is	O
the	O
discrete	B-Algorithm
Fourier	I-Algorithm
transform	I-Algorithm
of	O
.	O
</s>
