  A new reweighted l1-norm 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 l1-norm penalized LMS algorithm introduces in addition a reweighting
of the CIR coefficient estimates to promote a sparse solution even more and
approximate l0-pseudo-norm closer. We provide in depth quantitative analysis of
the reweighted l1-norm 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 l1-norm 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 l1-norm penalized LMS algorithm is better than
the standard LMS. Simulation results showing the better performance of the
reweighted l1-norm penalized LMS algorithm compared to other existing LMS-type
algorithms are given.
