Improved adaptive sparse channel estimation using re-weighted L1-norm normalized least mean fourth algorithm

In the frequency-selective fading broadband wireless communications systems, two adaptive sparse channel estimation (ASCE) methods using zero-attracting normalized least mean fourth (ZA-NLMF) algorithm and reweighted ZA-NLMF (RZA-NLMF) algorithm have been proposed to mitigate noise and to exploit channel sparsity. Motivated by compressive sensing, in this paper, 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 algorithm and hereafter derive its update equation. Intuitive illustration is also given to demonstrate that RL1 is more efficient than conventional two sparsity constraints. Finally, simulation results are provided to show that the proposed method achieves better estimation performance than the two conventional ones.