A Shrinkage L1-Norm Constrained LMS Algorithm for Adaptive Sparse Array Beamforming

A constrained least-mean-square (CLMS) algorithm using shrinkage method and l
₁
-norm penalty, namely, the shrinkage l
₁
-norm penalized CLMS (SL
₁
-CLMS) algorithm is proposed for adaptive beamforming. The introduced algorithm can successfully exploit the sparse characteristics of the antenna array utilized in beamformer. Besides, the new algorithm maintains the desired performance, i.e., greeting main lobe and nulls corresponding to the signal of interest (SO
₁
) and interferences. The SL
₁
-CLMS algorithm employs an alterable step step which is acquired through the l
₁
-l
₂
minimization method to accelerate the convergence rate. Simulation results attest the validity of the SL
₁
-CLMS algorithm.