Sparse least mean fourth adaptive algorithm for censored regression

In the linear systems, the conventional least mean fourth (LMF) algorithm has faster convergence and lower steady-state error than LMS algorithm, However, in many applications, the censored observations occur frequently. In this paper, a least mean fourth (LMF) algorithm with censored regression is proposed for adaptive filtering. When the identified system possesses a certain extent of sparsity, the least mean fourth algorithm for Censored Regression (CRLMF) algorithm may encounter performance degradation. Therefore, a reweighted zero-attracting LMF algorithm based on the censored regression model (RZA-CRLMF) is proposed further. Simulations are carried out in system identification and echo cancellation scenarios. The results verify the effectiveness of the proposed CRLMF and RZA-CRLMF algorithms. Moreover, in sparse system, the RZA-CRLMF algorithm improves further the filter performance in terms of the convergence speed and the mean squared deviation for the presence of sub-Gaussian noise.