  Sparse channel estimation problem is one of challenge technical issues in
stable broadband wireless communications. Based on square error criterion
(SEC), adaptive sparse channel estimation (ASCE) methods, e.g., zero-attracting
least mean square error (ZA-LMS) algorithm and reweighted ZA-LMS (RZA-LMS)
algorithm, have been proposed to mitigate noise interferences as well as to
exploit the inherent channel sparsity. However, the conventional SEC-ASCE
methods are vulnerable to 1) random scaling of input training signal; and 2)
imbalance between convergence speed and steady state mean square error (MSE)
performance due to fixed step-size of gradient descend method. In this paper, a
mixed square/fourth error criterion (SFEC) based improved ASCE methods are
proposed to avoid aforementioned shortcomings. Specifically, the improved
SFEC-ASCE methods are realized with zero-attracting least mean square/fourth
error (ZA-LMS/F) algorithm and reweighted ZA-LMS/F (RZA-LMS/F) algorithm,
respectively. Firstly, regularization parameters of the SFEC-ASCE methods are
selected by means of Monte-Carlo simulations. Secondly, lower bounds of the
SFEC-ASCE methods are derived and analyzed. Finally, simulation results are
given to show that the proposed SFEC-ASCE methods achieve better estimation
performance than the conventional SEC-ASCE methods. 1
