Analysis of LMS Algorithm Behavior with Subspace Inputs

This paper studies the behavior of the LMS algorithm for a special system identification problem when partial wavelet transformations restrict the algorithm´s input vector to a subspace of the unknown system´s input vector space. It is shown that the independence theory is not applicable in this case. A new theoretical model for the weight mean and fluctuation behaviors is developed which incorporates the correlation between successive data vectors (as opposed to using the independence theory model). Comparison of the new model predictions with Monte Carlo simulations shows good-to-excellent agreement, certainly much better than predicted by the independence theory model.