Reweighted l1-norm penalized LMS for sparse channel estimation and its analysis

Omid Taheri, Sergiy A. Vorobyov
2014 Signal Processing  
A new reweighted l 1 Ànorm penalized least mean square (LMS) algorithm for sparse channel estimation is proposed and studied in this paper. Since standard LMS algorithm does not take into account the sparsity information about the channel impulse response (CIR), sparsity-aware modifications of the LMS algorithm aim at outperforming the standard LMS by introducing a penalty term to the standard LMS cost function which forces the solution to be sparse. Our reweighted l 1 Ànorm penalized LMS
more » ... thm introduces in addition a reweighting of the CIR coefficient estimates to promote a sparse solution even more and approximate l 0 ÀpseudoÀnorm closer. We provide in depth quantitative analysis of the reweighted l 1 Ànorm penalized LMS algorithm. An expression for the excess mean square error (MSE) of the algorithm is also derived which suggests that under the right conditions, the reweighted l 1 Ànorm penalized LMS algorithm outperforms the standard LMS, which is expected. However, our quantitative analysis also answers the question of what is the maximum sparsity level in the channel for which the reweighted l 1 Ànorm penalized LMS algorithm is better than the standard LMS. Simulation results showing the better performance of the reweighted l 1 Ànorm penalized LMS algorithm compared to other existing LMS-type algorithms are given.
doi:10.1016/j.sigpro.2014.03.048 fatcat:s4iledbvifhxvb3u3nsfc2tbcy