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

We propose in this work an L
₁
-norm Linearly Constrained Normalized Least-Mean-Square (L
₁
-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 L
₁
-CNLMS algorithm takes into account an L
₁
-norm penalty on the filter coefficients which results in sparse solutions producing Thinned Hexagonal Arrays. The effectiveness of the L
₁
-CNLMS algorithm is demonstrated by comparing, via computer simulations, its results with those of the CNLMS algorithm. When employing the L
₁
-CNLMS algorithm to antenna array problems, the resulting effect of the L
₁
-norm constraint is perceived as a large aperture array with few active array elements.