Least Mean Square/Fourth Algorithm with Application to Sparse Channel Estimation

Broadband signal transmission over frequencyselective fading channel often requires accurate channel state information at receiver. One of the most attracting adaptive channel estimation methods is least mean square (LMS) algorithm. However, LMS-based method is often degraded by random scaling of input training signal. To improve the estimation performance, in this paper we apply the standard least mean square/fourth (LMS/F) algorithm to adaptive channel estimation (ACE). Since the broadband channel is often described by sparse channel model, such sparsity could be exploited as prior information. First, we propose an adaptive sparse channel estimation (ASCE) method using zero-attracting LMS/F (ZA-LMS/F) algorithm. To exploit the sparsity effectively, an improved channel estimation method is also proposed, using reweighted zero-attracting LMS/F (RZA-LMS/F) algorithm. We explain the reason why sparse LMS/F algorithms using -norm sparse constraint function can improve the estimation performance by virtual of geometrical interpretation. In addition, for different channel sparsity, we propose a Monte Carlo method to select a regularization parameter for RA-LMS/F and RZALMS/F to achieve approximate optimal estimation performance. Finally, simulation results show that the proposed ASCE methods achieve better estimation performance than the conventional one. Keywords—least mean square fourth (LMS/F), adaptive sparse channel estimation (ASCE), zero-zttracting LMS/F (ZA-LMS/F), re-weighted zero-attracting LMS/F (RZA-LMS/F).