  In next-generation wireless communications systems, accurate sparse channel
estimation (SCE) is required for coherent detection. This paper studies SCE in
terms of adaptive filtering theory, which is often termed as adaptive channel
estimation (ACE). Theoretically, estimation accuracy could be improved by
either exploiting sparsity or adopting suitable error criterion. It motivates
us to develop effective adaptive sparse channel estimation (ASCE) methods to
improve estimation performance. In our previous research, two ASCE methods have
been proposed by combining forth-order error criterion based normalized least
mean fourth (NLMF) and L1-norm penalized functions, i.e., zero-attracting NLMF
(ZA-NLMF) algorithm and reweighted ZA-NLMF (RZA-NLMF) algorithm. Motivated by
compressive sensing theory, an improved ASCE method is proposed by using
reweighted L1-norm NLMF (RL1-NLMF) algorithm where RL1 can exploit more
sparsity information than ZA and RZA. Specifically, we construct the cost
function of RL1-NLMF and hereafter derive its update equation. In addition,
intuitive figure is also given to verify that RL1 is more efficient than
conventional two sparsity constraints. Finally, simulation results are provided
to confirm this study.
