Digital Signal Processing Reference
In-Depth Information
q
(
n
)
covar
.
R
qq
s
(
n
)
s
(
n
)
F
H
G
(a)
precoder
channel
equalizer
,
Ι
q
(
n
)
1
covar
.
s
(
n
)
s
(
n
)
R
−1
F
H
R
G
(b)
precoder
channel
equalizer
q
(
n
)
1
Ι
covar
.
s
(
n
)
s
(
n
)
F
H
1
G
1
(c)
precoder
new channel
new equalizer
Figure 12.3
. (a) The transceiver system with noise covariance
R
qq
. (b) An equivalent
system with noise covariance =
I
. (c) Simplification of part (b), where
H
1
=
R
−
1
H
and
G
1
=
GR
.
matrix of the form
⎡
⎤
σ
s
0
0
...
0
⎣
⎦
σ
s
1
0
...
0
R
ss
=
.
(12
.
6)
.
.
.
.
.
.
σ
s
M−
1
00
.
..
call this
Λ
s
It is common that the
M
components
s
k
(
n
)
,
0
1
,
arise from a
sin-
gle
user. For example,
s
k
(
n
) could be the
M
samples within one block of a
block-based system such as the zero-padded (ZP) or cyclic-prefix (CP) system
(Chap. 7). Since
s
(
n
) is usually assumed to be an iid (independent identically
distributed) sequence, it follows in these cases that
s
k
(
n
) are not only uncorre-
lated, but have identical powers, that is,
σ
s
k
=
σ
s
for all
k,
so that
R
ss
=
σ
s
I
.
≤
k
≤
M
−
(12
.
7)
The results derived in this and the following chapter are most appropriate for
this situation.
Another situation of interest is that the
M
signals
s
k
(
n
)are
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