Digital Signal Processing Reference
In-Depth Information
Receiver 1
User 1
C
1
Signal
Processing
ML
detection
C
11
Codewords
Precoder
C
2
S
1
Receiver 2
User 2
Signal
Processing
ML
detection
Codewords
Precoder
CS
S
2
22
Fig. 5.1
X channel
A
t
1
||
2
A
t
2
||
2
F
=
2
. Similarly, User 2 sends the fol-
||
||
In this chapter, we assume that
F
=
lowing codewords
S
t
B
t
1
S
1
(
B
t
2
S
2
(
=
)
+
)
t
t
(5.5)
with the power constraint
B
t
1
||
2
B
t
2
||
2
||
F
+||
F
=
1
(5.6)
where
B
l
b
l
(
=[
i
,
j
)
]
N
×
4
,
t
=
1
,
2
,
3
,
4
,
l
=
1
,
2
(5.7)
are
the
precoders
we
need
to
design
for
User
2.
Also
we
assume
that
B
t
1
||
B
t
2
||
1
2
F
2
F
||
2
. The channels are quasi-static flat Rayleigh fading and
keep unchanged during four time slots. Then we let
=||
=
H
l
=[
h
l
(
i
,
j
)
]
M
×
N
,
l
=
1
,
2
(5.8)
denote the channel matrix between User 1 and Receivers
l
, respectively. Similarly,
we use
G
l
=[
g
l
(
i
,
j
)
]
M
×
N
,
l
=
1
,
2
(5.9)
to denote the channel matrix between User 2 and Receiver
l
, respectively. Then the
received signals at Receiver 1 at time slot
t
can be denoted by
y
t
1
=
H
1
A
t
1
C
1
(
H
1
A
t
2
C
2
(
G
1
B
t
1
S
1
(
G
1
B
t
2
S
2
(
n
t
1
)
+
)
+
)
+
)
+
t
t
t
t
(5.10)
where
y
t
1
=[
y
1
(
n
t
1
=[
n
t
1
(
i
,
1
)
]
M
×
1
,
i
,
1
)
]
M
×
1
(5.11)
denote the received signals and the noise at Receiver 1, respectively, at time slot
t
.
Similarly, at time slot
t
, Receiver 2 will receive the following signals
y
t
2
=
H
2
A
t
1
C
1
(
H
2
A
t
2
C
2
(
G
2
B
t
1
S
1
(
G
2
B
t
2
S
2
(
n
t
2
t
)
+
t
)
+
t
)
+
t
)
+
(5.12)
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