Digital Signal Processing Reference
In-Depth Information
Fig. 4.2
Precoder design
illustration
i
g
v
v
i
h
hg
v
i
g
⎧
⎨
⎛
⎞
⎫
⎬
v
g
)
†
(
y
1
⎝
v
g
|
⎠
|
U
†
H
Real
{
c
1
,
c
2
}=
arg min
Real
{
c
1
,
c
2
}
Real
v
g
)
†
⎩
(
⎭
y
2
v
g
|
|
⎛
⎝
⎞
⎠
2
v
g
)
†
v
h
(
v
g
)
†
(
Real
v
h
−
√
E
s
U
†
c
1
v
g
|
v
g
|
|
|
.
(4.35)
H
v
g
)
†
v
g
)
†
(
(
c
2
v
h
−
v
h
v
g
|
v
g
|
|
|
F
c
2
, and the signals of User 2.
Note that the decoding complexity is symbol-by-symbol.
Till now, we have presented our precoding, decoding methods, and some neces-
sary properties needed by our codebooks to cancel interference for each user. Note
that in order to achieve interference cancellation, the only properties needed by our
codebooks are (
4.16
) and (
4.20
). The remaining degrees of freedom will be used to
maximize diversity and coding gain as discussed in the next two sections.
Similarly, we can decode the imaginary parts of
c
1
,
4.3 Feedback Design and Diversity Analysis
In this section, we first propose our feedback scheme, i.e., how to choose an index
l
i
and send it back to User
i
. Then we prove that our feedback scheme can achieve
full diversity when our codebooks satisfy some conditions.
4.3.1 Feedback Design
First, as illustrated in Fig.
4.2
, we define
v
g
)
†
v
h
|
|
(
1
v
h
,
v
g
>
=
cos
θ
hg
=
<
(4.36)
v
g
|·|
v
h
|
|
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