On the convergence of Constant Modulus Algorithm in Adaptive Equalization. Convergence des Algorithmes du Module Constant en Égalisation Adaptative

On the convergence of Constant Modulus Algorithm in Adaptive Equalization

Convergence des Algorithmes du Module Constant en Égalisation Adaptative

Maurice Bellanger

CNAM, 292 rue Saint-Martin, 75141 Paris cedex 03

Corresponding Author Email: 
17 July 2007
31 August 2007
| Citation



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.


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.

2.Conditions d’Équivalence entre EQMM et MC(2,2)
3.Convergence de l’Algorithme AMC(2,2)
4.Étude de l’Algorithme AMC(1,2)
5.Initialisation des Algorithmes du Module Constant

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