${{\bf L}_1}$ -Constrained Normalized LMS Algorithms for Adaptive Beamforming

We detail in this paper an L1-norm Linearly constrained normalized least-mean-square (L1-CNLMS) algorithm and its weighted version (L1-WCNLMS) applied to solve problems whose solutions have some degree of sparsity, such as the beamforming problem in uniform linear arrays, standard hexagonal arrays, and (non-standard) hexagonal antenna arrays. In addition to the linear constraints present in the CN...