Fast exact variable order affine projection algorithm

Variable order affine projection algorithms have been recently presented to be used when not only the convergence speed of the algorithm has to be adjusted but also its computational cost and its final residual error. These kind of affine projection (AP) algorithms improve the standard AP algorithm performance at steady state by reducing the residual mean square error. Furthermore these algorithms optimize computational cost by dynamically adjusting their projection order to convergence speed requirements. The main cost of the standard AP algorithm is due to the matrix inversion that appears in the coefficient update equation. Most efforts to decrease the computational cost of these algorithms have focused on the optimization of this matrix inversion. This paper deals with optimization of the computational cost of variable order AP algorithms by recursive calculation of the inverse signal matrix. Thus, a fast exact variable order AP algorithm is proposed. Exact iterative expressions to calculate the inverse matrix when the algorithm projection order either increases or decreases are incorporated into Partially supported by TEC2009-13741, PROMETEO 2009/0013, GV/2010/027, ACOMP/2010/006 and UPV PAID-06-09. ∗e-mail: [email protected], Tel.: +34-96-3877007-88272, Fax: +34-96-3877309 Preprint submitted to Signal Processing December 13, 2011 a variable order AP algorithm leading to a reduced complexity implementation. The simulation results show the proposed algorithm performs similarly to the variable order AP algorithms and it has a lower computational complexity.