A study on improving the performance of robust adaptive filtering algorithms in impulsive noise environment

Abstract

In this thesis, improving the performance of robust adaptive filtering algorithms in impulsive noise environment is studied. Impulsive noise refers to noise that has discontinuous, irregular amplitudes and occurs at very high intensity relative to other signals. Most of the adaptive filtering algorithms update the adaptive filter using the error signal between the desired signal and the output signal from the adaptive filter. When the impulsive noise occurs, the error value instantaneously becomes very large, resulting in a false update of the adaptive filter. Therefore, in this paper, we study the adaptive filtering algorithm which can be robust under the environment of impulsive noise. In Chapter 1, the background of adaptive filter is introduced to help understand the thesis. First, the basic principle of adaptive filter is given. Second, the various adaptive filtering algorithms are explained briefly. Lastly, the organization of the thesis is given. In Chapter 2, a variable step-size (VSS) normalized subband adaptive filter (NSAF) using a step-size scaler to improve the robustness against impulsive measurement noise is introduced. When impulsive measurement noise appears, the step size of the proposed VSS NSAF is scaled down by the step-size scaler, which is suitable for application in the NSAF. This removes the possibility of updating weight estimates based on defective information of the subband output errors due to impulsive measurement noise. In the proposed VSS NSAF, the equations for updating the step size are constructed by interpreting the behavior of the mean square deviation (MSD) of the conventional NSAF and applying the step-size scaler. The step-size scaler utilizes the sum of the subband output errors, which can be influenced by impulsive measurement noise. Simulations using the proposed VSS NSAF show an excellent transient and steady-state behavior with colored input in impulsive-noise environments. In Chapter 3, a new approach for deriving a robust saturation algorithm against impulsive noises is proposed. The proposed approach presents the saturation algorithm by using the Lagrange multiplier approach to obtain an analytically the exact solution to the problem of optimizing the cost function: the l1 norm of a posteriori error with the l2 norm constraint on the update distance of weight vectors. In addition, a variable step size is designed by mean-square-deviation (MSD) analysis. The various simulation results show that the proposed algorithm has faster convergence rate and lower steady-state error than the existing algorithms in both impulsive and free-impulsive noises environments. In Chapter 4, a variable step-size robust affine projection algorithm against impulsive noises is proposed. The proposed algorithm is obtained by an analytically the exact solution to the problem of optimizing the cost function with l2-constrain. In addition, a variable step size is designed by mean-square-deviation (MSD) analysis of two cases of the proposed algorithm. The various simulation results show that the proposed algorithm has faster convergence rate and lower steady-state error than the existing algorithms in both impulsive and free-impulsive noises environments.