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Ill-convergence of Godard blind equalizers in data communicationsystems
Ding, Z.   Kennedy, R.A.   Anderson, B.D.O.   Johnson, C.R., Jr.  
Dept. of Electr. Eng., Auburn Univ., AL;

This paper appears in: Communications, IEEE Transactions on
Publication Date: Sep 1991
Volume: 39,  Issue: 9
On page(s): 1313-1327
ISSN: 0090-6778
References Cited: 13
CODEN: IECMBT
INSPEC Accession Number: 4057139
Digital Object Identifier: 10.1109/26.99137
Current Version Published: 2002-08-06

Abstract
The existence of stable undesirable equilibria for the Godard algorithm is demonstrated through a simple autoregressive (AR) channel model. These undesirable equilibria correspond to local but nonglobal minima of the underlying mean cost function, and thus permit the ill-convergence of the Godard algorithms which are stochastic gradient descent in nature. Simulation results confirm predicted misbehavior. For channel input of constant modulus, it is shown that attaining the global minimum of the mean cost necessarily implies correct equalization. A criterion is also presented for allowing a decision at the equalizer as to whether a global or nonglobal minimum has been reached

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