Convex cost functions in blind equalization
Vembu, S.
Verdu, S.
Kennedy, R.A.
Sethares, W.
Dept. of Electr. Eng., Princeton Univ., NJ;
This paper appears in: Signal Processing, IEEE Transactions on
Publication Date: Aug 1994
Volume: 42,
Issue: 8
On page(s): 1952-1960
ISSN: 1053-587X
References Cited: 27
CODEN: ITPRED
INSPEC Accession Number: 4763194
Digital Object Identifier: 10.1109/78.301833
Current Version Published: 2002-08-06
Abstract
Existing blind adaptive equalizers that use nonconvex cost
functions and stochastic gradient descent suffer from lack of global
convergence to an equalizer setup that removes sufficient ISI when an
FIR equalizer is used. The authors impose convexity on the cost function
and anchoring of the equalizer away from the all-zero setup. They
establish that there exists a globally convergent blind equalization
strategy for 1D pulse amplitude modulation (PAM) systems with bounded
input data (discrete or continuous) even when the equalizer is
truncated. The resulting cost function is a constrained l1
norm of the joint impulse response of the channel and the equalizer. The
results apply to arbitrary linear channels (provided there are no unit
circle zeros) and apply regardless of the initial ISI (that is whether
the eye is initially open or closed). They also show a globally
convergent stochastic gradient scheme based on an implementable
approximation of the l1 cost function
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