Design of Multi-Channel Equalizers via Linear
Matrix Inequalites:
Trade-Off between SNR and ISI
Design of Multi-Channel Equalizers via Linear
Matrix Inequalites:
Trade-Off between SNR and ISI
T. Settle, M. D. Zoltowski and V. Balakrishnan
Proc. University of California San Diego Conference
on Wireless Communications with IEEE Communications Society
San Diego, CA, March 1998
Abstract: Multi-channel linear equalizers are commonly
employed in digital communication systems to mitigate channel
distortions and thereby reduce inter-symbol interference
(ISI). Traditional multi-channel linear equalizer design for linear
time-invariant channels requires synthesis of equalizing filters such
that the frequency response of the overall system has unit magnitude
and linear phase. In this work, we investigate the efficacy of
deliberately allowing equalization errors, i.e., allowing deviations
from unit magnitude and linear phase of the overall frequency
response, with the goal of increasing the signal-to-noise ratio (SNR)
in the symbol decision statistics. Our approach relies on numerical
convex optimization based on linear matrix inequalities. Our
investigations reveal that as the allowable equalization error is
increased, the mean-square error (MSE) of the post-equalizer signal
constellation decreases despite the attendant increase in ISI. This
implies that the trade-off between SNR and ISI in the symbol decision
statistic weighs more heavily in favor of SNR improvement for a
surprisingly large range of allowable equalization error.
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