Quasi-Newton formulation and analysis of split LMS

A new filtering structure called split filtering was proposed by Ho and Ching (1992) and by Ching and Wan (1995). It was applied to the blind equalization domain and seems to speed up the adaptation and avoid local minima. Thanks to a reformulation of the split structure, we show that the adaptation belongs to the quasi-Newton algorithm class. Through the efficacy criterion proposed by Moustakides (1998), we show that it could be at least as efficient as the LMS method. Finally, we prove that the optimal normalization is not necessarily the power normalization of each sub-filter.