An L1-constrained normalized lms algorithm and its application to thinned adaptive antenna arrays

We propose in this work an L₁-norm Linearly Constrained Normalized Least-Mean-Square (L₁-CNLMS) algorithm applied to solve the beamforming problem in Standard Hexagonal Arrays (SHA) and (non-standard) Hexagonal Antenna Arrays (HAA). In addition to the linear constraints present in the CNLMS algorithm, the L₁-CNLMS algorithm takes into account an L₁-norm penalty on the filter coefficients which results in sparse solutions producing Thinned Hexagonal Arrays. The effectiveness of the L₁-CNLMS algorithm is demonstrated by comparing, via computer simulations, its results with those of the CNLMS algorithm. When employing the L₁-CNLMS algorithm to antenna array problems, the resulting effect of the L₁-norm constraint is perceived as a large aperture array with few active array elements.