A Study on Mean-Square-Deviation Analysis of Normalized Subband Adaptive Filter-type Algorithm and the Performance Improvement

Abstract

This thesis proposes the mean-square-deviation (MSD) analysis of the normalized subband adaptive filter (NSAF)-type algorithm. The analysis provides useful guidelines to design the algorithm and allows the verification of the performance of the algorithm. In addition, the analysis gives us a way to improve the performance of the algorithm by varying step size or varying regularization parameter. Chapter 2 and 3 present the MSD analysis of the NSAF-type algorithm for long-length adaptive filter. Chapter 2 proposes a new approach to the MSD analysis of the NSAF algorithm by using the persistently exciting input and the practical assumption that the stopband attenuation of the prototype filter is high. Unlike the previous analysis, the proposed analysis is possible to be applied to the long-length adaptive filter such as the acoustic echo cancellation. The proposed analysis is also applied to a non-stationary model with a random walk of the optimal weight vector. The simulation results match with the theoretical results in both the transient-state and steady-state MSD. Chapter 3 proposes a general solution of steady-sate MSD analysis of the improved NSAF algorithm, which is based on the substitution of the past weight error vector in the weight error vector. The simulation shows that our theoretical results correspond closely with the computer simulation results in various environments.

Chapter 4 and 5 improve the performance of the NSAF algorithm by using the MSD analysis. Chapter 4 describes a variable step size for the NSAF is derived by minimizing the MSD at each instant of time. The variable step size is presented in terms of error variance. Therefore, the proposed algorithm is capable of tracking in non-stationary environments. The simulation results show good tracking ability and low misalignment of the proposed algorithm in system identification. Chapter 5 proposes a variable regularization scheme for the NSAF is derived on the basis of the relationship between the weight-error vector and weight vector update, and by using the calculated MSD. The performance of the variable regularization algorithm is evaluated in terms of MSD. Our simulation results exhibit fast convergence and low steady-state MSD when using the proposed algorithm.