Digital Signal Processing Reference
In-Depth Information
h
11
h
21
h
12
h
22
,
g
11
g
12
=
=
.
(4.17)
g
21
g
22
Then (
4.12
) can be written as
⎛
⎝
⎞
⎠
+
c
1
y
1
y
2
E
s
h
11
h
11
n
1
n
2
g
11
g
11
c
2
=
.
(4.18)
h
21
h
21
g
21
g
21
s
1
s
2
Based on Eq. (
4.18
), it is easy to find a complex vector
g
satisfying
g
†
g
11
0
to remove the signals of User 2. Equation (
4.16
) represents the property that our
codebooks need in order to achieve interference cancellation.
Similarly, in time slot 2, our precoders should satisfy
=
g
21
A
2
A
2
B
2
B
2
(
1
)
=
(
2
),
(
1
)
=
(
2
).
(4.19)
1
and
2
, for Users 1 and 2, respectively, any matrix
Υ
1
[
Then using the codebook
Υ
Υ
i
]
Υ
1
Υ
2
[
Υ
2
in the codebook
and any matrix
j
]
in the codebook
have the following
properties:
Υ
1
[
)
=
Υ
1
[
Υ
2
[
)
=
Υ
2
[
i
]
(
1
i
]
(
2
),
j
]
(
1
j
]
(
2
).
(4.20)
Then (
4.13
) can be written as
⎛
⎝
⎞
⎠
+
c
1
(
E
s
(
h
12
)
∗
−
(
h
12
)
∗
(
(
(4.21)
y
1
)
∗
g
12
)
∗
−
(
g
12
)
∗
n
1
)
∗
c
2
=
y
2
)
∗
(
h
22
)
∗
−
(
h
22
)
∗
(
g
22
)
∗
−
(
g
22
)
∗
n
2
)
∗
(
s
1
(
s
2
4.2.2 Decoding
In what follows, based on Eqs. (
4.18
) and (
4.21
), we illustrate how to cancel the
interference of User 2 and decode in detail. First, we introduce some notation to
simplify the presentation. In Eqs. (
4.18
) and (
4.21
), we let
h
11
h
21
y
1
y
2
n
1
n
2
g
11
v
h
=
v
g
=
y
1
n
1
,
,
=
,
=
(4.22)
g
21
(
h
12
)
∗
(
h
22
)
∗
(
(
(
g
12
)
∗
(
y
1
)
∗
n
1
)
∗
v
h
=
v
g
=
y
2
n
2
,
,
=
,
=
(4.23)
g
22
)
∗
y
2
)
∗
n
2
)
∗
(
(
Then we introduce the following complex vectors
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