A lattice predictor based adaptive Volterra filter and its convergence property analysis

This paper proposes a lattice predictor based adaptive Volterra filter (Lattice-AVF), and its convergence property is analyzed. In the adaptive FIR Volterra filter (AVF), the eigen value 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. For stationary colored input signals, the Lattice-AVF can provide a fast convergence and the well reduced residual error. Its convergence is highly dependent on a time constant, used in updating the reflection coefficients. A very large time constant is required. In the case of nonstationary colored input signal, the eigen value spread after the Volterra polynomial is not so highly amplified. This means fast convergence will be expected, and effects of the whitening will be small. These properties are analyzed. A problem of asynchronous updating the reflection coefficients and the filter coefficients observed in linear lattice predictor based adaptive filters, is also observed in the Lattice-AVF.