Digital Signal Processing Reference
In-Depth Information
2
Q
real symbols, as done in [64]. To simplify the detector further, we may neglect the
RI and take into account only the noise variance. For not too large signal constellation
sizes, this simplification causes a negligible performance loss [65, 66].
4.4.3.3.3 Soft Estimation of Transmit Symbols
Each element γ˜
p
of the vector S
˜
is obtained by taking a summation over all the possible
values of the real part (or imaginary part) of the signal constellation, multiplied by the
corresponding probability calculated using the soft decoder output [62, 63]. It is prefer-
able to use the
a posteriori
information from the decoder output rather than extrinsic
information in the calculation of γ˜
p
. This has the advantage of permitting a better and
faster convergence of the Rx.
4.4.3.4 Case Study
As we focus here on the turbo-PIC detector as the suboptimal solution, we just compare
the performance of this detector with that of turbo-MAP. We consider the simplified
implementation of soft-PIC based on ZF filtering given in (4.20). For this comparison,
we consider the simple spatial multiplexing (V-BLAST) ST scheme and the case of four
transmit antennas,
M
T
= 4, while we take
M
R
between 1 and 4. he Tx and Rx schemes
correspond to
Figures 4.7
and
4.8
, respectively. We consider Gray bit/symbol mapping
and random interleaving, as well as the Rayleigh flat quasi-static channel model. The
nonrecursive and nonsystematic convolutional (NRNSC) channel code (5, 7)
8
(in octal
representation) is considered with rate
R
c
= 1/2. SNR is considered in the form of
E
b
/
N
0
,
where
E
b
is the average received energy per information bit and
N
0
is the unilateral noise
power spectral density;
E
b
/
N
0
includes the Rx array gain,
M
R
.
formances of turbo-PIC and turbo-MAP are relatively close to each other for
M
R
≥
M
T
.
Turbo-PIC can still be used for certain values of
M
R
<
M
T
, mostly for
M
R
>
M
T
/2 [63]. So,
for these
M
R
values where turbo-PIC converges properly, it would be preferred to turbo-
MAP due to its considerably lower complexity. Better performances are obtained for
turbo-PIC if the variance of the RI is taken into account in LLR calculation [63].
4.4.4 Orthogonal versus Nonorthogonal ST Schemes
In practice, to attain a desired spectral efficiency, we should adopt the most appropriate
scheme by fixing the degrees of freedom of the system, that is, the signal constellation,
the channel coding rate, and the ST coding scheme. The answer to the question “What
is the most suitable combination?” is not obvious for moderate to high spectral efficien-
cies. In effect, if a low spectral efficiency is required, an OSTBC scheme together with a
powerful turbo-code would be a suitable solution, as the reduction in the overall coding
rate is best invested in turbo channel codes [67]. To attain high spectral efficiencies with
OSTBC schemes, however, we have to use large signal constellations and increase the
channel coding rate by puncturing the encoder output bits. Use of larger signal constella-
tions complicates the tasks of synchronization and detection at the Rx and also results in
a higher SNR required to attain a desired BER. On the other hand, puncturing results in
a reduced channel code robustness against noise. Higher ST coding rates are offered
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