Diffusion NLMS algorithm Robust to Impulsive Noise and Input Noise in Sparse Systems

This paper proposes a new diffusion normalized least mean square algorithm which is robust to impulsive noise and input noises in sparse systems. The algorithm adopts the concept of step-size scaler and modified Huber function to improve performance against impulsive noise. To compensate the bias induced by input noises in sparse systems, the bias compensation vector is derived. The novelty of this paper lies in applying that method to a sparse system where the cost function has an
$L_{0}$
-norm term. In sparse systems, simulation shows that the proposed algorithm indicates better performance than the conventional algorithms against to impulsive noise and input noises in sparse systems.