A lattice predictor based adaptive Volterra filter and its convergence analysis

Abstract

This paper proposes a lattice predictor based adaptive Volterra filter, and its convergence property is analyzed. In the adaptive Volterra filter (AVF), the eigenvalue spread of a correlation matrix is extremely amplified, and its convergence is very slow for gradient methods. A lattice predictor is employed for whitening the input signal. Its convergence property is analyzed. For colored signals, generated using an AR model, it can fast converge to the well reduced level. However, the convergence is sensitive to error of the whitening. When the reflection coefficients are updated, convergence is highly dependent on a time constant parameter used in updating the reflection coefficients. In the case of using a time variant AR model, that is nonstationary input signals, almost the same convergence is obtained compared with the fixed AR model. Furthermore, update of the reflection coefficients and the filter coefficients is not synchronized in the conventional lattice predictor based adaptive filters. This effect is also analyzed.