On the Convergence Behavior of the Affine Projection Algorithm for Adaptive Filters

The affine projection class of algorithms (APA) provides faster convergence than LMS-based adaptive filters. Its convergence analysis is not as extensively studied as Normalized LMS (NLMS), and remains an active area of research. For tractability, most works on APA make many assumptions on the statistics of the input, as well as correlation between signals. Here we consider the effect of the correlation between filter coefficients and past measurement noise on MSE error. The effect of this correlation was found to be dependent on step-size mu, increasing or decreasing the predicted MSE depending on whether mu is less than or greater than 1, irrespective of the input statistics. Simulations are used to verify the analysis results presented.