On the convergence of Constant Modulus Algorithm in Adaptive Equalization
Convergence des Algorithmes du Module Constant en Égalisation Adaptative
OPEN ACCESS
A direct approach is used to determine the conditions for the minimum mean-squared error and constant modulus criteria to lead to the same coefficient vector.The condition which is obtained,namely that the normalized kurtosis of the source signal be equal to 4/3,is nearly satisfied for the QAM constellations in digital transmission,which provides a theoretical justification for the Godard conjecture.Then,the performance of the adaptive algorithms is analyzed.It turns out that the CMA(2,2) algorithm is faster than the CMA(1,2) algorithm but much slower than the LMS algorithm.Finally, the importance of initialization for the constant modulus algorithms is underlined.
Résumé
Par une approche directe,on établit les conditions pour que le critère de l’erreur quadratique moyenne minimale et les critères du module constant conduisent au même vecteur de coefficients. La condition de kurtosis normalisé égal à 4/3 obtenue est presque satisfaite pour les constellations MAQ utilisées en transmission numérique,ce qui fournit la justification théorique de la conjecture de Godard. Ensuite,les performances des algorithmes adaptatifs sont analysées. Il apparaît que l’algorithme AMC(2,2) est plus rapide que l’algorithme AMC(1,2) mais beaucoup plus lent que l’algorithme du gradient avec signal de référence. L’importance de l’initialisation est soulignée,pour les algorithmes du module constant.
Constant modulus,self adaptive,equalization,convergence.
Mots clés
Module constant,adaptatif,égalisation,convergence.
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