A statistical analysis of the affine projection algorithm for unity step size and autoregressive inputs

This paper presents a new statistical analysis of the affine projection (AP) algorithm. An analytical model is derived for autoregressive (AR) inputs for unity step size (fastest convergence). Deterministic recursive equations are derived for the mean AP weight and mean-square error for large values of N (the number of adaptive taps). The value of N is also assumed large compared to the algorithm order (number of input vectors used to determine the weight update direction). The model predictions display better agreement with Monte Carlo simulations in both transient and steady-state than models previously presented in the literature. The model's accuracy is sufficient for most practical design purposes.