7
{
x
0
,
x
1
,…,
x
N2
,
x
N1
}:
x
n
=
1
N
X
k
e
j
2
π
nk
/
N
k
=
0
N
−
1
∑
where
0
≤
n
≤
(
N
−
1)
…(E1)
These
N
timedomain symbols can collectively be considered as one OFDM symbol/block. Each
OFDM block has a duration of
T
s
seconds and is passed through the cyclic prefix (CP) block.
Assume that the CP consists of
α
timedomain symbols that have a total duration of
T
cp
seconds.
Then the CP
x
−
,
x
−
(
−
1)
,...,
x
−
2
,
x
−
1
{ }
is prefixed to the
N
timedomain samples to give the
combined symbol {
x
CP
+
OFDM
}:
x
CP
+
OFDM
{ } =
x
−
,
x
−
(
−
1)
,...,
x
−
2
,
x
−
1
,
x
0
,
x
1
,...,
x
N
−
2
,
x
N
−
1
{ }
…(E2)
where
x
−
=
x
N
−
;
x
−
(
−
1)
=
x
N
−
(
−
1)
;…;
x
−
2
=
x
N
−
2
;
x
−
1
=
x
N
−
1
…(E3)
and hence:
x
CP
+
OFDM
{ } =
x
N
−
,
x
N
−
(
−
1)
,...,
x
N
−
2
,
x
N
−
1
,
x
0
,
x
1
,...,
x
N
−
2
,
x
N
−
1
{ }
…(E4)
{
x
CP
+
OFDM
} has a time duration of
T = T
s
+
T
cp
seconds. Notice that the duration of the combined
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 Spring '09
 Prof
 Xn, Orthogonal frequencydivision multiplexing, Multipath propagation, OFDM block, xCP + OFDM

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