Variable matrix-type step-size affine projection algorithm with orthogonalized input vectors

Abstract

This thesis proposes a variable matrix-type step-size affine projection algorithm (APA) with orthogonalized input vectors. We generate orthogonalized input vectors using theGram-Schmidt process so as to implement the weight update equation of the APA using the sum of normalized least mean square (NLMS)-like updating equations. This method allows us to use individual step sizes corresponding to each NLMS-like equation. This is equivalent to adopting the step size in the form of a diagonal matrix in the APA. A variable step-size scheme is adopted to improve the performance of the filter. The individual step sizes are determined to minimize the mean square deviation of the APA. The experimental results show that the proposed algorithm has a faster convergence rate and a smaller steady-state estimation error than the existing APAs.