Performance Analysis of ℓ0-Norm Constraint Variable Step Size Normalized Least Mean Square Algorithm

Abstract

This paper incorporates a ℓ0 –norm sparsity constraint into variable step size normalized least mean square (ℓ0 -VSSNLMS) algorithm for identification of sparse system corrupted by additive noise. The proposed ℓ0–VSSNLMS algorithm makes a good fairness between convergence characteristics, filter stability and steady state error. The proposed (ℓ0 -VSSNLMS) algorithm incorporates a variable step size that accelerates the convergence characteristics and lowers the mean square deviation (MSD) error than in ℓ0 - NLMS with constant value of step size. The inclusive theoretical performance of ℓ0 -VSSSNLMS algorithm is analyzed in this paper with white Gaussian input under some assumptions which are suitable for practical purpose. An expression for variant step size is derived under the stability condition of proposed algorithm. Finally the implementation of the proposed algorithm is carried out in MATLAB software to manifest the improved beavior in identification of sparse system.