Lyapunov-based stability analysis of supervised and unsupervised adaptive algorithms

This work analyzes representative algorithms for adaptive equalization from the standpoint of Lyapunov stability. The proposed approach is valid for both supervised and unsupervised algorithms. Using this framework, we were able to obtain results that are applicable to the entire parameter space, and that, for certain conditions, are equivalent to bounds previously derived for the steepest descent and for the one-tap CMA. The proposed methodology also leads to a novel analysis of the maximum step-size for the N-tap CMA.