A gradient search interpretation of the super-exponential algorithm

This article reviews the super-exponential algorithm proposed by Shalvi and Weinstein (1993) for blind channel equalization. The principle of this algorithm-Hadamard exponentiation, projection over the set of attainable combined channel-equalizer impulse responses followed by a normalization-is show...

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Bibliographic Details
Published in:IEEE transactions on information theory 2000-11, Vol.46 (7), p.2731-2734
Main Authors: Mboup, M., Regalia, P.A.
Format: Article
Language:English
Subjects:
Algorithms
Blinds
Channels
Communication channels
Convergence
Cost function
Engineering Sciences
Entropy
Equalization
Search methods
Searching
Signal and Image processing
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Summary:This article reviews the super-exponential algorithm proposed by Shalvi and Weinstein (1993) for blind channel equalization. The principle of this algorithm-Hadamard exponentiation, projection over the set of attainable combined channel-equalizer impulse responses followed by a normalization-is shown to coincide with a gradient search of an extremum of a cost function. The cost function belongs to the family of functions given as the ratio of the standard l/sub 2p/ and l/sub 2/ sequence norms, where p>1. This family is very relevant in blind channel equalization, tracing back to Donoho's (1981) work on minimum entropy deconvolution and also underlying the Godard (1980) (or constant modulus) and the earlier Shalvi-Weinstein algorithms. Using this gradient search interpretation, which is more tractable for analytical study, we give a simple proof of convergence for the super-exponential algorithm. Finally, we show that the gradient step-size choice giving rise to the super-exponential algorithm is optimal.
ISSN:0018-9448
1557-9654
DOI:10.1109/18.887889