Hammerstein Adaptive Filter with Single Feedback under Minimum Mean Square Error

This paper presents a novel nonlinear adaptive filter method, namely, Hammerstein adaptive filter with single feedback under minimum mean square error (HAF-SF-MMSE). A single delayed output is incorporated into the estimation of the current output based on minimum mean square error criterion, and therefore the history information of output is considered. Moreover, hybrid learning rates and adaptive learning rates with normalization factors are designed to guarantee the convergence and stability of HAF-SF-MMSE. Compared with the traditional Hammerstein adaptive filter which usually consists of a nonlinear filter followed by a linear part, HAF-SF-MMSE can achieve a faster convergence rate and higher filter accuracy. Theoretical analysis regarding convergence behavior is performed to acquire a sufficient condition on the convergence of weight. Simulation results show the excellent filtering performance of the proposed HAF-SF-MMSE.