Low complexity norm-adaption least mean square/fourth algorithm and its applications for sparse channel estimation

A low-complexity norm-adaption least-mean-square/fourth (LCNA-LMS/F) algorithm is proposed to exploit the sparse properties of the wireless multi-path channel in this paper. The proposed LCNA-LMS/F algorithm is realized by using a segment function instead of the reweighting factor in the reweighted norm-adaption least-mean-square/fourth (RNA-LMF) algorithm to remove the division operation, which can reduce the computational complexity. The channel estimation behaviors of the proposed LCNA-LMS/F algorithm are investigated over a sparse channel and the computer simulation results show that the proposed LCNA-LMS/F algorithm achieves superior performance with respect to the convergence speed and the steady-state error floor compared with the conventional least-mean-square/fourth (LMS/F) and its sparsity forms.