Fast least mean M-estimate algorithms for robust adaptive filtering in impulse noise

Adaptive filters with suitable nonlinear devices are very effective in suppressing the adverse effect due to impulse noise. In a previous work, the authors have proposed a new class of nonlinear adaptive filters using the concept of robust statistics [1,2]. The robust M-estimator is used as the objective function, instead of the mean square errors, to suppress the impulse noise. The optimal coefficient vector for such nonlinear filter is governed by a normal equation which can be solved by a recursive least squares like algorithm with O(N
²
) arithmetic complexity, where N is the length of the adaptive filter. In this paper, we generalize the robust statistic concept to least mean square (LMS) and transform domain LMS algorithms. The new fast nonlinear adaptive filtering algorithms called the least mean M-estimate (LMM) and transform domain LMM (TLMM) algorithms are derived. Simulation results show that they are robust to impulsive noise in the desired and input signals with an arithmetic complexity of order O(N).