$$L_{0}$$ L 0 -norm constraint normalized logarithmic subband adaptive filter algorithm

Abstract

With the purpose of identifying sparse unknown system better, a novel sparsity-aware normalized logarithmic subband adaptive filter algorithm is developed by introducing the $$L_{0}$$ -norm constraint of the estimated coefficient vector into the normalized logarithmic cost function. The gradient descent technique is utilized in the derivation of the weight vector updating formula. The proposed algorithm not only acquires a lower steady-state error, but also possesses good robustness against impulsive noise for sparse system. Besides, the reason why its performance is improved is interpreted by rigorous mathematical analysis. Simulation results in the context of sparse system identification have revealed the advantage of the proposed algorithms over other existing algorithms in impulsive noise environments.