A stochastic model for the affine projection algorithm operating in a nonstationary environment

The paper presents an analytical model for predicting the stochastic behavior of the affine projection (AP) algorithm operating in a nonstationary environment. The model is derived for autoregressive (AR) Gaussian inputs and for unity step size (fastest convergence). Deterministic recursive equations are presented for the mean weight and mean square error for a large number of adaptive taps, N, as compared to the algorithm order, P. The model predictions show excellent agreement with Monte Carlo simulations in transient and steady-state. The learning behavior of the AP algorithm in nonstationary environments is of great interest in applications such as acoustic echo cancellation.