A stochastic model for the convergence behavior of the Affine Projection algorithm for Gaussian inputs

This paper presents an analytical model for predicting, the stochastic behavior of Affine Projection (AP) algorithm. 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 better agreement between theory and simulations in transient and steady-state than previous models described in the literature. The learning behavior of the AP algorithm is of great interest in applications such as acoustic echo cancellation.