A study on the step size design to improve the performance of the adaptive filter in a noisy environment

Abstract

In this paper, various studies have been conducted to improve the performance of the adaptive filter in a noisy environment. Adaptive filter is a kind of estimation technique and is used in various signal processing fields such as system identification, echo cancellation, and active noise control today. These adaptive filters have various structures, and their performance is evaluated in terms of convergence rate, steady-state error, robustness to noise, and computational complexity. Factors affecting the performance of such an adaptive filter include input noise, impulsive measurement noise, and input characteristics. Therefore, in this paper, we present a meaningful study result for an adaptive filter algorithm that is robust to impulsive noise and has good performance in such a noisy environment. In Chapter 1, the background of the adaptive filter is explained to help the understanding of the discussed adaptive filter. First, the basic operating principle and types of adaptive filters will be described. Second, the concept of variable step size, which has been studied to improve the performance of such an adaptive filter, is explained.

In Chapter 2, a novel individual variable step-size subband adaptive filter algorithm robust to impulsive noises (NIVSS-NSAF) is introduced. A fixed step-size subband adaptive filter algorithm that is robust against impulsive noises is newly derived by obtaining the optimal solution from a constrained optimization problem through the Lagrange multiplier. In addition, in order to further improve the convergence performance of the proposed algorithm, the weight update formula with a single fixed step size is modified to have multiple individual step sizes. By analyzing its mean-square-deviation (MSD), the optimal individual step size is designed. Simulation results show that the proposed algorithm outperforms the algorithms robust to impulsive noises in the literature.

In Chapter 3, the result of extending the concept of variable multiple step size (VMSS) introduced in Chapter 2 to the affine projection sign algorithm (APSA) is presented. APSA has also been researched on variable step size in various ways, and in this dissertation, performance improvement is proposed through extended application of VMSS. The basic weight update formula of APSA is transformed from a single step size form to a multiple step size form. The optimal variable multiple step size is designed through MSD analysis. The simulation results show that the proposed algorithm has much better performance than the existing variable step size APSAs.

In Chapter 4, a scheduled step-size normalized subband adaptive filter algorithm is proposed. The mean-square deviation of the normalized subband adaptive filter according to the step size is analyzed geometrically to construct a pre-designed trajectory. The mean-square deviation learning curve of the normalized subband adaptive filter algorithm is forced to follow the pre-designed trajectory. This method removes the need for the normalized subband adaptive filter algorithm to introduce tuning parameters and does not add any additional online computation. The table of the scheduled step sizes can be reconstructed online in proportion to not only the number of taps but also the number of subbands once they are scheduled offline. The novel memory-efficient scheduling scheme minimizes the memory space required and simplifies operation without performance degradation. Because of these features, the proposed algorithm performs as well as the variable-step-size normalized subband adaptive filters studied previously, and is very suitable for chip level implementation in terms of computational complexity and memory space. Simulation results show that the proposed algorithm is robust against external environment change and has good performance compared to the existing variable step-size algorithms without any additional online computation and tuning parameter.