Digital Signal Processing Reference
In-Depth Information
q
(
n
)
σ
2
covar
.
I
s
(
n
)
s
(
n
)
Σ
−
1
Σ
−
1
V
h
H
U
h
Σ
g
Λ
s
covar
.
unitary
matrix
channel
unitary
matrix
diagonal
matrix
(a)
diagonal
matrix
Σ
f
equalizer
precoder
q
(
n
)
s
(
n
)
s
(
n
)
W
M
W
M
−
1
θ
Σ
−
1
Σ
−
1
Λ
Σ
g
H
(b)
V
h
circulant
channel
U
h
Figure 17.10
. (a) General form of the transceiver optimized for minimum transmitted
power using bit allocation. Zero forcing is assumed. (b) Special case of the DMT system
with cyclic prefix where the channel
H
is circulant. All matrices in both figures are
M × M
.
q
(
n
)
σ
2
covar
.
I
s
(
n
)
s
(
n
)
W
M
W
M
Λ
−
1
H
Λ
s
covar
.
normalized
IDFT
circulant
channel
normalized
DFT
DFT domain
equalizers
Figure 17.11
. The DMT system optimized to minimize transmitted power. Zero
forcing and optimal bit allocation are assumed.
Thus the optimal DMT system (which minimizes power subject to optimum
bit allocation and zero forcing) is nothing but the “traditional DMT system”
introduced in Sec. 7.6, with the DFT and IDFT matrices [Lin and Phoong,
2001b]. The optimal bit allocation formula is as in Eq. (14.41), with
σ
h,k
=
|
C
[
k
]
|
.
Thus
σ
q
3
2
+log
2
|
Q
−
1
P
e
(
k
)
4
|
2
.
b
k
=
D
0
−
log
2
C
[
k
]
(17
.
47)
It is assumed here that the right-hand side of Eq. (17.47) yields su
ciently
large values for all
k
so that it can be truncated to positive integer values of
b
k
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