Performance analysis and adaptive Newton algorithms of multimodulus blind equalization criterion

This paper studies the stationary points of the multimodulus blind equalization criterion in a noiseless communication channel and proposes two adaptive Newton algorithms. It is shown in this paper that the stationary points of the multimodulus criterion can be grouped into two categories, according to the power of equalizer output. The stationary points having the same equalizer output power with that of the transmitted symbols are desirable global minima, while the stationary points having less equalizer output power than that of the transmitted symbols are saddle points. A pseudo Newton learning algorithm and a full Newton learning algorithm minimizing the multimodulus criterion are proposed. By using the matrix inversion lemma, both Newton algorithms can be efficiently implemented with a computational complexity of O(N2)O(N2), where NN is the tap length of equalizer. Computer experiment results are presented. It is found that the full Newton algorithm performs well in both static and time-varying communication channels, while the pseudo Newton algorithm performs well only in static communication channels.