Steady-state Performance Analysis of Bayesian Adaptive Filtering

Adaptive filtering is in principle intended for tracking nonstationary systems. However, most adaptive filtering algorithms have been designed for converging to a fixed unknown filter. When actually confronted with a non-stationary environment, they possess just one parameter (stepsize, window size) to adjust their tracking capability. In the stationary case of non-stationarity, the optimal filter coefficients evolve as a stationary process. The Bayesian approach to adaptive filtering exploits the a priori information in this stationary parameter variation model to optimize adaptive filtering performance. The prior information contains two critical parameter characteristics: the variance (magnitude) of the various filter coefficients and their variation spectrum (power delay profile and Doppler spectrum in the case of wireless channel tracking). The practical tool for implementing Bayesian Adaptive Filtering (BAF) is the Kalman filter, which typically models the parameter variation as an AR(1) process. To further limit the complexity to the same order as the complexity of the RLS algorithm, a diagonal AR(1) model can be taken. In this paper, we analyze the effect of power delay profile and Doppler bandwidth on the steady-state performance of BAF and LMS and RLS algorithms. The approximation effects of using a simplified state model are also exhibited.