On the correlation between the noise and a priori error vectors for standard and augmented affine projection algorithms

• Autores: Altieri, Andrés Oscar
• Año de publicación: 2024
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: ADAPTIVE FILTER; AFFINE PROJECTION ALGORITHM; WIDELY LINEAR MODEL; A PRIORI ERROR
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

This paper analyzes the correlation matrix between the a priori error and measurement noise vectors for standard and augmented affine projection algorithms using a unified approach. This correlation stems from the dependence between the filter tap estimates and the noise samples, and has a strong influence on the mean square behavior of the algorithm. We show that the correlation matrix is upper triangular, and compute the diagonal elements in closed form, showing that they are independent of the input process statistics. Also, for white inputs we show that the matrix is fully diagonal. These results are valid in the transient and steady states, considering a possibly variable step-size. Our only assumption is that the filter order is large compared to its projection order and that the input signal is stationary. Using these results, we perform a steady-state analysis for small step size and provide a new simple closed-form expression for the mean-square error, which has comparable or better accuracy to many preexisting expressions, and is much simpler to compute. Finally, we also obtain expressions for the steady-state energy of the other components of the error vector.
Fil: Altieri, Andrés Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Centro de Simulación Computacional para Aplicaciones Tecnológicas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Electronica; Argentina