Characterization of the undesirable global minima of the Godard cost function: case of noncircular symmetric signals

The deconvolution of a filtered version of a zero-mean normalized independent and identically distributed (i.i.d.) signal (s/sub n/)/sub n/spl isin/z/ having a strictly negative Kurtosis /spl gamma//sub 2/= E[|s/sub n/|/sup 4/]-2(E[|s/sub n/|/sup 2/])/sup 2/-|E[s/sub n//sup 2/|/sup 2/] is addressed....

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Bibliographic Details
Published in:IEEE transactions on signal processing 2006-05, Vol.54 (5), p.1917-1922
Main Authors: Houcke, S., Chevreuil, A.
Format: Article
Language:English
Subjects:
Computer aided software engineering
Computer Science
constant modulus algorithm
contrast function
Cost function
Deconvolution
Digital communication
Doppler shift
Filters
Frequency
Godard algorithm
Kurtosis
Minima
Signal and Image Processing
Signal processing
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Summary:The deconvolution of a filtered version of a zero-mean normalized independent and identically distributed (i.i.d.) signal (s/sub n/)/sub n/spl isin/z/ having a strictly negative Kurtosis /spl gamma//sub 2/= E[|s/sub n/|/sup 4/]-2(E[|s/sub n/|/sup 2/])/sup 2/-|E[s/sub n//sup 2/|/sup 2/] is addressed. This correspondence focuses on the global minimizers of the Godard function. A well-known result states that these minimizers achieve deconvolution at least if the input signal shows the symmetry E[s/sup 2/]=0. When this constraint is relaxed, (s/sub n/)/sub n/spl isin/z/ is said to be noncircular symmetric: It is shown that the minimizers achieve deconvolution if and only if 2|E[s/sub n//sup 2/]|/sup 2/
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2006.872584