Lower bounds for the MSE convergence of APA

It is well known that the least mean square (LMS) algorithm convergence speed degrades considerably when the input signal is correlated. On the other hand, the affine projection algorithm (APA) was recently developed and has faster convergence for correlated inputs compared to LMS. Convergence analysis done on APA to date has been based on either a modification of the independence assumption, a special regression model, or a Gaussian regression data model. In this paper, an analysis of the standard APA algorithm under the assumption of a finite strong memory and finite moments for the regression data is done. We prove that under steady state conditions, the weight error covariance is lower bounded and dependent on the step size and not the correlation of the input regression matrix