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.