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NLMS Algorithm Robust Against Noisy Input and Impulsive Noise in Sparse Systems

This paper proposes the NLMS algorithm which is filtering the impulsive noise adaptively and compensates for the bias caused by the input noise in the sparse system. The weight is updated by incorrect data in the impulsive noise environment. To reduce the influence of the impulsive noise, it is filtered using a modified Huber function and the step size scaler. The steady-state misalignment is negatively affected by the bias caused by the input noise. To eliminate the bias, the unbiasedness criterion is used to derive a bias compensation vector. Simulations in system identification with impulsive noise and input noise show that the proposed algorithms outperform other algorithms.