Digital Signal Processing Reference
In-Depth Information
∗
s
−
s
X
=
1
2
.
(4.22)
∗
s
s
2
1
For the OSTBC case, the decoding is performed once using (4.18). We also consider two
nonorthogonal schemes. The first one is the simple V-BLAST scheme described by
X
=
[
s
1
s
2
]
t
, for which
Q
= 2,
T
= 1, and
R
STC
= 2. The second one is the optimized scheme pro-
posed in [68] and called
Golden code
, which we denote by GLD. For this code that offers
full rate and full diversity with the property of nonvanishing determinant, we have
Q
=
2,
T
= 2, and
R
STC
= 2:
+
( )
+
( )
+
( )
+
( )
αθ γα θ
αθ αθ
s
s
s
s
1
5
1
2
3
4
X
=
,
(4.23)
s
s
s
s
3
4
1
2
where
=
+
15
2
θ
,
α
=+ −=−=+− ==−
11
j
(
θθ θα
),
1
,
1
j
(
1
θγ
),
j
1
.
The factor 1/ 5 ensures normalized transmit power per channel use. For η = 2 bps/Hz,
performance curves are shown in
Figure 4.11
, where again perfect channel knowledge
is assumed at the Rx. For V-BLAST and GLD schemes, BER curves are shown for the
second and fourth iterations, where almost full Rx convergence is attained. We see that,
by using the V-BLAST scheme, we gain about 3.3 and 3.75 dB in SNR at BER = 10
-4
ater
two and four iterations, respectively, compared to Alamouti coding. The corresponding
gains by using GLD code are about 3.5 and 4.3 dB, respectively. We note that even when,
for the reasons of complexity and latency, only two iterations are to be performed, the
gain in SNR compared to the Alamouti scheme is still considerable.
4.5
Advanced Polarization Diversity Techniques
for MIMO Systems
The initial research demonstrates that the MIMO channel capacity based on the uncor-
related channel model can be proportionally increased by increasing the number of
antennas. However, in practice, the performance of the MIMO communication channel
is affected by spatial correlation, which is dependent on antenna array configurations
(such as radiation pattern, antenna spacing, and array geometry), and propagation chan-
nel characteristics, which are dependent on the environment (such as number of channel
paths, distribution and properties of scatterers, angle spread, and cross-polarization dis-
crimination). Thus, the antenna arrays at Tx and Rx should be properly designed to
reduce the spatial correlation effects and to improve the communication performance.
However, it is possible to reduce these effects by increasing antenna array spacing, but
this solution is not always suitable in some wireless applications where the array size is
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