Cryptography Reference
In-Depth Information
residual interference at the output of the equalizer. As we will see, these two
parameterscanbeestimatedfromtheoutputoftheequalizer. Fromrelation
(11.46) again, we can show the general following result:
E
2
=
g
Δ
σ
x
|
z
i
|
(11.58)
Assuming that the variance of the transmitted data is normalized to unity, an
estimate of
g
Δ
is given by:
N
i
=0
|
−
1
1
N
2
g
Δ
=
z
i
|
(11.59)
Once we have estimated
g
Δ
, we immediately deduce the value of
σ
ν
thanks to
relation (11.47):
σ
ν
=
σ
x
g
Δ
(1
−
g
Δ
)
(11.60)
One particularity of adaptive MMSE turbo equalization concerns the deter-
mination of the estimated symbols. Indeed, in accordance with the remarks
of [11.20] and [11.55], using
a posteriori
information instead of extrinsic infor-
mation at the output of the channel decoder in (11.27) can yield significant
performance improvement.
We have therefore defined an adaptive MMSE turbo equalizer whose coe-
cients are obtained from a low complexity stochastic gradient descent algorithm,
making it possible to track the slow time variations of the transmission channel.
A drawback of this technique lies in the necessity to transmit training sequences,
which lower the spectral eciency. The size of training sequences can be signif-
icantly reduced by considering self-learning or blind algorithms. In particular,
the equalizer in the first iteration can be advantageously replaced by a self-
learning equalizer called
Self Adaptive Decision-Feedback Equalizer
(SADFE)
[11.32] that requires a very small transmission overhead. The work of Hélard
et al.
[11.26] has shown that such a turbo equalizer can reach performance
virtually identical to that of the adaptive MMSE turbo equalizer with learning
sequence, while operating at a higher spectral eciency. On the other hand, a
higher number of iterations is then required.
Examples of performance
For comparison purposes, the performance of the MMSE turbo equalizer has
been simulated by considering the same transmission scenario as for the turbo
MAP equalizer.
First, the parameters of the channel are assumed to be perfectly estimated.
The coecients are calculated once per frame by matrix inversion, by considering
a digital filter with
F
=15
coecients and a designed delay
Δ=9
.The
simulation results, obtained after 10 iterations, are presented in Figure 11.16.
