Sparse channel estimation with lp-norm and reweighted l1-norm penalized least mean squares

The least mean squares (LMS) algorithm is one of the most popular recursive parameter estimation methods. In its standard form it does not take into account any special characteristics that the parameterized model may have. Assuming that such model is sparse in some domain (for example, it has sparse impulse or frequency response), we aim at developing such LMS algorithms that can adapt to the underlying sparsity and achieve better parameter estimates. Particularly, the example of channel estimation with sparse channel impulse response is considered. The proposed modifications of LMS are the l
p
-norm and reweighted l
1
-norm penalized LMS algorithms. Our simulation results confirm the superiority of the proposed algorithms over the standard LMS as well as other sparsity-aware modifications of LMS available in the literature.