  Broadband signal transmission over frequency-selective 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 l_1-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 RZA-LMS/F to achieve
approximate optimal estimation performance. Finally, simulation results show
that the proposed ASCE methods achieve better estimation performance than the
conventional one.
