Fixed-point error analysis of stochastic gradient adaptive lattice filters

A theoretical analysis is presented of the stochastic gradient adaptive lattice filter used as a linear, one-step predictor, when the effects of finite-precision arithmetic are taken into account. Only the fixed-point implementation is considered. Both the unnormalized and normalized adaptation algorithms are analyzed. Expressions of the steady-state mean-squared values of the accumulated numerical errors in the computation of the reflection coefficients and the prediction errors of different orders have been developed. The results show that the dominant term in the expressions for the mean-squared values of the numerical errors is inversely proportional to the convergence parameter. Furthermore, they indicate that the quantization errors associated with the reflection coefficients are more critical than those associated with representing the prediction-error sequences. Signals with high correlation among samples produce larger numerical errors in the adaptive lattice filter. The authors present several simulation examples that show close agreement with the theoretical results. They also show that the gradient adaptive lattice filters have better numerical properties than their transversal counterparts