Norm-adaption penalized least mean square/fourth algorithm for sparse channel estimation

•Norm-adaption penalized LMS/F (NA-LMS/F) algorithm is proposed for channel estimation.•Reweighting NA-LMS/F (RNA-LMS/F) algorithm is proposed and analyzed in detail.•Simulations verify the performance of the proposed NA-LMS/F and RNA-LMS/F algorithms.•RNA-LMS/F algorithm has fastest convergence and best channel estimation performance.

A type of norm-adaption penalized least mean square/fourth (NA-LMS/F) algorithm is proposed for sparse channel estimation applications. The proposed NA-LMS/F algorithm is realized by incorporating a p-norm-like into the cost function of the conventional least mean square/fourth (LMS/F) which acts as a combination of the l0- and l1-norm constraints. A reweighted NA-LMS/F (RNA-LMS/F) algorithm is also developed by adding a reweighted factor in the NA-LMS/F algorithm. The proposed RNA-LMS/F algorithm exhibits an improved performance in terms of the convergence speed and the steady-state error, which can provide a zero attractor to further exploit the sparsity of the channel by the use of the norm adaption penalty and the reweighting factor. The simulation results obtained from the sparse channel estimations are given to verify that our proposed RNA-LMS/F algorithm is superior to the previously reported sparse-aware LMS/F and the conventional LMS/F algorithms in terms of both the convergence speed and the steady-state behavior.