An L1-Norm Linearly Constrained LMS Algorithm Applied to Adaptive Beamforming

We propose in this work an L-1-norm Linearly-Constrained Least-Mean-Square (L-1-CLMS) algorithm. In addition to the linear constraints present in the CLMS algorithm, the L-1-CLMS algorithm takes into account an L-1-norm penalty on the filter coefficients. The performance of the L-1-CLMS algorithm is evaluated for a time-varying system identification under Gaussian noise and for an adaptive beamforming scenario. The effectiveness of the L-1-CLMS algorithm is demonstrated by comparing, via computer simulations, its results with the CLMS algorithm. When employed in a sensor array, the L-1-norm constraint increases the convergence rate making the proposed algorithm a good candidate for adaptive beamforming applications.