A complex version of the LASSO algorithm and its application to beamforming

Least Absolute Shrinkage and Selection Operator (LASSO) is a useful method to achieve coefficient shrinkage and data selection simultaneously. The central idea behind LASSO is to use the L1-norm constraint in the regularization step. In this paper, we propose an alternative complex version of the LASSO algorithm applied to beamforming aiming to decrease the overall computational complexity by zeroing some weights. The results are compared to those of the Constrained Least Squares and the Subset Selection Solution algorithms. The performance of nulling coefficients is compared to results from an existing complex version named the Gradient LASSO method. The results of simulations for various values of coefficient vector L1-norm are presented such that distinct amounts of null values appear in the coefficient vector. In this supervised beamforming simulation, the LASSO algorithm is initially fed with the optimum LS weight vector.