Steady-state weights solution to affine projection algorithm

A new expression of the weights update equation for the affine projection algorithm (APA) is proposed that improves the convergence rate of an adaptive filter, particularly for highly colored input signals, and yields greater details of the internal structure. The steady-state weights solution to the APA algorithm is calculated in different step-sizes, which is significantly different from the iteration method. The weights error in steady-state is proved to be zero as the number of the input direction vector increases to infinity, ensuring that the estimated weights of the APA algorithm in steady-state are unbiased and consistent. The sensitivity of the step-size parameter for the steady-state weights is also analyzed. Simulation results show that the steady-state weights of the APA algorithm, obtained from the proposed method, are closer to the true weights than the estimated steady-state weights as determined by the traditional iteration method.