Improved adaptive sparse channel estimation using mixed square/fourth error criterion

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