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A new reweighted l1-norm penalized least mean square (LMS) algorithm forsparse channel estimation is proposed and studied in this paper. Since standardLMS algorithm does not take into account the sparsity information about thechannel impulse response (CIR), sparsity-aware modifications of the LMSalgorithm aim at outperforming the standard LMS by introducing a penalty termto the standard LMS cost function which forces the solution to be sparse. Ourreweighted l1-norm penalized LMS algorithm introduces in addition a reweightingof the CIR coefficient estimates to promote a sparse solution even more andapproximate l0-pseudo-norm closer. We provide in depth quantitative analysis ofthe reweighted l1-norm penalized LMS algorithm. An expression for the excessmean square error (MSE) of the algorithm is also derived which suggests thatunder the right conditions, the reweighted l1-norm penalized LMS algorithmoutperforms the standard LMS, which is expected. However, our quantitativeanalysis also answers the question of what is the maximum sparsity level in thechannel for which the reweighted l1-norm penalized LMS algorithm is better thanthe standard LMS. Simulation results showing the better performance of thereweighted l1-norm penalized LMS algorithm compared to other existing LMS-typealgorithms are given.

Reweighted l1-norm Penalized LMS for Sparse Channel Estimation and Its Analysis