Digital Signal Processing Reference
In-Depth Information
Multi−User, 2 bits/sec/Hz
10
0
Alamouti MUD
Our Scheme
No interference
10
−1
10
−2
10
−3
10
−4
10
−5
10
−6
0
5
10
15
20
25
30
Signal to Noise Ratio (dB)
Fig. 2.4
Comparison of our scheme and Alamouti MUD for 2 users each with 2 transmit antennas
method in Sect.
2.2
to detect the signals of User 2. In what follows, we show that the
method provides full diversity to User 2. There are two factors that result in error for
User 2. The first one is the fading in the channel of User 2 and the second one is
th
e
error in detecting the symbols of User 1, i.e., error propagation. Let Pr
d
2
)
denote the pairwise error probability for User 2, we separate these two events to have
(
→
d
2
Pr
(
d
2
→
d
2
)
=
Pr
{
d
2
→
d
2
|
σ
=
0
}
Pr
{
σ
=
0
}+
Pr
{
d
2
→
d
2
|
σ
=
0
}
Pr
{
σ
=
0
}
=
Pr
{
d
2
→
d
2
|
σ
=
0
}
(
1
−
Pr
{
σ
=
0
}
)
+
Pr
{
d
2
→
d
2
|
σ
=
0
}
Pr
{
σ
=
0
}
(2.107)
Since Pr
{
d
2
→
d
2
|
σ
=
0
}≤
1 and 1
−
Pr
{
σ
=
0
}≤
1, we have
Pr
(
d
2
→
d
2
)
≤
Pr
{
d
2
→
d
2
|
σ
=
0
}
(
1
−
Pr
{
σ
=
0
}
)
+
Pr
{
σ
=
0
}
≤
Pr
{
d
2
→
d
2
|
σ
=
0
}+
Pr
{
σ
=
0
}
(2.108)
Note that when
0, we can follow the steps in Sect.
2.2
to detect the signals of
User 2 and by the same technique used in Sect.
2.3
, we can easily derive
σ
=
2
}≤
(
8
)
−
6
)
|
−
6
=
τ
1
ρ
−
6
Pr
{
d
2
→
d
2
|
σ
=
0
1
|
Φ(
j
,
1
(2.109)
j
=
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