29-10-2012, 02:26 PM
Blind Channel Equalization with Amplitude Banded Godard and Sato Algorithms
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Abstract
The least-mean-squares (LMS) algorithm
which updates the filter coefficients by a stochastic gradient
descent approach is the most popular adaptive filtering one.
In this paper we propose a novel amplitude banded (AB)
technique with LMS on Godard (ABGodard) and Sato
(ABSato) algorithms for the equalization of communication
channels. The non-linear properties of the AB technique
with LMS algorithm are inherited into the ABGodard
and ABSato algorithms, resulting in an improvement of
equalization performance. These properties are validated
from a signal separation aspect based on decision boundary.
Mean square error (MSE) and bit error rate (BER) are
investigated on several communication channel models.
Observations on simulations show that the ABGodard and
ABSato algorithms provide better performance than the
standard Godard and Sato algorithms, respectively, and
that the ABSato algorithm is superior to the ABGodard
algorithm. As the division number used for the AB
technique is increased, the MSE and BER performances of
the ABSato algorithm are improved. A parallel structure
of the Sato and ABSato algorithms provides a further
improvement of the MSE and BER performances.
INTRODUCTION
The physical channel introduces a distortion to the
transmitted signal. To recover the original signal, the
principle of channel equalization plays an important role
in digital communication systems. To reduce or ideally
to eliminate completely the intersymbol interference (ISI)
induced by the channel, adaptive equalization [1] is
required. Although conventional equalization techniques
rely on training sequence based equalization, they suffer
from the trade-off between the sequence length and the
capacity of the link. To avoid this problem and when
the training sequence is not available, blind equalization
technique [2] can be used. Thus the blind channel equalization
is the great deal of attention for its importance in
digital communication systems. The Godard [3] and Sato
[4] adaptive algorithms are widely used blind algorithms
for equalization of a channel. They are commonly derived
based on measuring the output of the channel in case of
lacking explicit knowledge of the transmitted sequence.
Performance Evaluation
The performances of the parallel Sato-ABSato equalizer
were investigated on Channel 1. Figure 15 shows the
MSE convergence plots of the Sato, ABSato and parallel
Sato-ABSato equalizers with SNR=40 dB, M=8 and step
size ¹=0.025. The division number Q=4 was set for the
ABSato algorithm. Figure 15 clarifies that the parallel
structure of the Sato and ABSato algorithms provides
better performance than non-parallel structure algorithms.
Figure 16 shows the BER performances of the Sato,
ABSato and parallel Sato-ABSato algorithms with the
filter order M=8 and step size ¹=0.025. The division
number Q=4 was set for the ABSato algorithm. Figure
16 suggests that even for BER, the parallel combination
of the Sato and ABSato algorithms improves the performance.
From Figures 15 and 16, we can confirm that the
parallel structure enhances the performance of the ABSato
algorithm with the support of the Sato algorithm.
Additionally we checked the performance of the parallel
equalizer with the Godard and ABGodard algorithms,
which is constructed in the same way as in Figure 14. The
performance of the parallel Godard-ABGodard equalizer
was, however, worse than that of the parallel Sato-ABSato
equalizer. This result may be expected from those in
Figures 5 and 6.
CONCLUSION
In this paper, the ABGodard and ABSato algorithms
have been proposed for blind channel equalization. Simulation
results have demonstrated that the ABGodard
and ABSato algorithms perform better than the Godard
and Sato algorithms, respectively. The ABSato algorithm
behaves more accurately than the ABGodard algorithm,
and the increased division number leads to an improved
performance of the ABSato algorithm. The use of a
parallel structure enhances the performance of the ABSato
algorithm further. Future work will aim at developing a
transform-domain implementation technique of the proposed
blind equalizer.