On the convergence of constant modulus algorithm in adaptive equalization

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.