Digital Signal Processing Reference
In-Depth Information
t
S=ℜ
{}
ℑ
{}
…
ℜ
{}
ℑ
{}
s
s
,
,
s
s
.
(4.12)
1
1
Q
Q
We have then X = F S, where the (2
M
T
T
× 2
Q
) matrix F depends on the actual ST
nel. Similar to X, we construct the (2
M
R
T
× 1) vector Y from
Y
. Vectors X and Y are then
related through a (2
M
R
T
× 2
M
T
T
) matrix H:
YHXN
=+
(4.13)
where N is the vector of real AWGN of zero mean and variance σ
n
2
. Matrix H is com-
posed of (2
T
× 2
T
) segments H
ij
,
i
= 1,
…
,
M
R
,
j
= 1,
…
,
M
T
, described below:
…
…
H
0
0
ij
0
H
0
ij
H
ij
=
(4.14)
…
0
0
H
ij
The (2 × 2) elements
H
ij
are obtained from each entry
H
ij
of the initial matrix
H
:
=
ℜ
{}
−ℑ
{}
ℑ
{}
ℜ
{}
H
H
ij
ij
H
ij
.
(4.15)
H
H
ij
ij
Now, we can describe the ST encoder and channel input/output relationship by consid-
ering an equivalent channel matrix H
eq
of dimension (2
M
R
T
× 2
Q
):
YHFS NHSN
=
+ =
+
.
(4.16)
eq
4.4.3 Iterative Detection for Nonorthogonal ST Schemes
We assume that H
eq
and σ
n
2
are known at the Rx. Having received the vector Y, we
should extract from it the transmitted data S. As we perform channel coding together
with ST coding, the idea of iterative detection comes to mind. Indeed, by profiting in
this way from the channel coding gain, we can obtain a good performance after only a
few iterations and approach the optimal ST decoder + channel decoder performance.
This is, of course, the case for nonorthogonal ST schemes. In what follows, we explain
the principle of iterative detection and explain in detail the ST decoding part.
The block diagram of such an Rx is shown in
Figure 4.8
. Soft-input soft-output sig-
nal detection and channel decoding are performed. For MIMO signal detection or ST
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