Digital Signal Processing Reference
In-Depth Information
C
S
Fig. 2.1
Channel model
b
11
b
12
b
21
b
22
b
11
b
12
b
21
b
22
B
1
B
2
=
,
=
(2.5)
denote the precoders of User 2 at time slots 1 and 2, respectively. We assume
||
A
i
2
B
i
2
1 in order to satisfy the normalization conditions [
1
].
Our goal is to design low-complexity precoders to realize interference cancellation
and full diversity for each user. The main idea is to design precoders such that the
two users transmit over two orthogonal spaces. As a result, the decoders can project
the received signals to each of the orthogonal spaces and decode the information
of each user without any interference from the other user. Later, we prove that the
resulted diversity is full for each user.
||
F
=||
||
F
=
2.2 Precoding Design
We first present the precoder design for time slot 1. Then, a similar design strategy
for time slot 2 is briefly discussed. We present our precoder design method through
the following four steps, which are also illustrated in the flow chart in Fig.
2.2
:
Step 1
: Deriving the equivalent channel equations:
At time slot 1, the signal model can be written as
E
s
HA
1
c
1
E
s
GB
1
s
1
y
1
W
1
=
+
+
(2.6)
c
2
s
2
At time slot 2, we have
E
s
HA
2
−
E
s
GB
2
−
c
2
c
1
s
2
s
1
y
2
W
2
=
+
+
(2.7)
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