Digital Signal Processing Reference
In-Depth Information
Chapter 5
Interference-Free Transmission for X channels
5.1 Channel Model
We introduce our channel model as shown in Fig.
5.1
. We assume there are 2 users
each with
N
transmit antennas and 2 receivers each with
M
receive antennas. Both
users want to send different codewords to Receivers 1 and 2 on the same frequency
band at the same time. As shown in Fig.
5.1
, User 1 wants to send codeword
C
1
to
Receiver 1 and
C
2
to Receiver 2. User 2 wants to send codeword
S
1
to Receiver 1
and
S
2
to Receiver 2. We also assume that full channel information is available at
each user and receiver. The problem we want to solve is how to derive interference-
free codewords from each user at each receiver with full diversity and rate 1. We let
each user transmit Quasi Orthogonal Space-Time Block Codes (QOSTBCs) [
1
]as
follows:
⎛
⎞
⎛
⎞
s
j
2
s
j
4
c
i
2
c
i
4
s
j
1
−
s
j
3
−
c
i
1
−
c
i
3
−
s
j
2
s
j
1
s
j
4
s
j
3
⎝
c
i
2
c
i
1
c
i
4
c
i
3
⎠
,
⎝
⎠
C
i
=
S
j
=
(5.1)
c
i
4
c
i
2
s
j
4
s
j
2
c
i
3
−
c
i
1
−
s
j
3
−
s
j
1
−
c
i
4
c
i
3
c
i
2
c
i
1
s
j
4
s
j
3
s
j
2
s
j
1
,
=
,
where
i
2. Note that we can also use other space-time codes with rate one
and QOSTBC is just one example. Since User 1 needs to send
C
1
to Receiver 1 and
C
2
to Receiver 2 at the same time, we can let User 1 transmit the following combined
codewords at time slot
t
j
1
C
t
A
t
1
C
1
(
A
t
2
C
2
(
=
t
)
+
t
)
(5.2)
where
A
l
a
1
(
=[
i
,
j
)
]
N
×
4
,
t
=
1
,
2
,
3
,
4
,
l
=
1
,
2
(5.3)
are the precoders we need to design for User 1. Note that in order to satisfy the power
constraint, we need
A
t
1
||
2
A
t
2
||
2
||
F
+||
F
=
1
(5.4)
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