New insights into the weight behaviour of the Affine Projection algorithm

This paper presents a new analytical model for the mean weight behaviour of the Affine Projection adaptive algorithm for autoregressive inputs and unity step-size. Deterministic recursive equations are derived which consider an initial transient phase not accounted for in previous analyses. This phase occurs at the very beginning of the adaptation process, and is due to the arbitrary initialization of the coefficients. It is a deterministic process that prevents the correct orthogonalization of the coefficient vector in relation to the subspace defined by the past input vectors. Monte Carlo simulations show improvements in the accuracy of the presented model when compared with a previously developed one.