Derivative based proportionate type adaptive filtering over sparse echo channels

Salman, Murat Babek
Adaptive filters are the intelligent mechanisms, which are extensively used in the various real world applications such as system identification and equalization problems. Therefore, many well established adaptive filtering algorithms were developed in the literature. In this thesis, adaptive filters will be considered as a tool to identify an unknown impulse response. Impulse responses that are considered in current identification problems have special characteristics. These impulse responses are long and they are mainly composed of zero coefficients, only a few number of non-zero coefficients present in the impulse response. Due to this fact, well known adaptive filtering algorithms such as NLMS, APA yield slow convergence. In order to combat this performance problem, proportionate type algorithms were developed. Main logic behind the proportionate algorithms is applying coefficient specific step-size by exploiting the sparse characteristics of the impulse response. In this thesis, previously proposed proportionate algorithms are investigated, their advantages and disadvantages are discussed. Furthermore, a novel approach using the dynamic behavior of each filter coefficients is presented. In this thesis, time derivatives of the filter coefficients are put into the adaptation process. Mathematical and geometrical analysis on the convergence of the proportionate algorithms are provided. The proposed algorithm is also extended to the situations in which non-Gaussian impulsive noise is present. In the presence of the non-Gaussian impulsive noise standard algorithms shows poor performance in terms of robustness. Therefore, developed approach is combined with the algorithms robust ag ainst non-Gaussian impulsive noise. Superiority of the proposed approach is observed via the computer simulations.