Digital Signal Processing Reference
In-Depth Information
cyclic prefix,
L
samples
M
samples
bottom
L
samples
repeated
x
(
n
)
y
(
n
)
0
y
(
n
)
C
(
z
)
P
M
samples
P
z
−
1
z
−
1
z
−
1
z
channel
y
(
n
)
L
−
1
discard
prefix
P
P
noise
q
(
n
)
z
s
(
n
)
0
s(n)
P
M
P
y
(
n
)
0
z
−
1
z
z
s
(
n
)
1
retain
and
process
M
P
CP
P
z
y
(
n
)
1
z
−
1
advance
chain
delay chain
s
(
n
)
M
−
1
y
(
n
)
M
−
1
z
z
z
−
1
M
P
P
advance
chain
P = M+L
blocked
version of
s
(
n
)
blocked
version of
y
(
n
)
Figure 7.12
. The cyclic-prefix transceiver shown in terms of multirate building block
notation.
Since
B
[
k
]=
C
[
k
]
A
[
k
] (ignoring noise for a moment), it then follows that
⎡
⎤
⎡
⎤
⎡
⎤
y
0
(
n
)
C
[0]
0
...
0
s
0
(
n
)
s
1
(
n
)
.
s
M−
1
(
n
)
y
1
(
n
)
.
0
C
[1]
...
0
⎣
⎦
⎣
⎦
⎣
⎦
W
=
W
,
(7
.
19)
.
.
.
.
.
.
y
M−
1
(
n
)
0
0
...
C
[
M
−
1]
call this
Λ
c
which shows that
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
y
0
(
n
)
s
0
(
n
)
s
1
(
n
)
.
s
M−
1
(
n
)
y
1
(
n
)
.
=
W
−
1
Λ
c
W
.
(7
.
20)
y
M−
1
(
n
)
Thus the channel output in block number
n
depends only on the symbol stream
transmitted at block number
n.
This is because interblock interference has been
elimimated, as we have already seen. Assuming
C
[
k
]
=0
,
(7
.
21)
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