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.

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