A Set-Membership Approach to Improved Proportionate Affine Projection Algorithm

Abstract

The improved proportionate normalized least mean-square algorithm (IPNLMS) has been proposed with the objective of improving the adaptation convergence rate when modeling high-order sparse impulse response systems. However, the convergence performance of IPNLMS demonstrates slow convergence speed when the excitation signal is colored. The improved proportionate affine projection (IPAP) algorithm is an useful adaptive filter to improve the convergence speed of PNLMS-type filter by updating the weight vector based on several previous input vectors, Unfortunately, the IPAPA algorithm obtains a faster convergence of the PAPA comes at the expense of an increase in the computational complexity linked to the amount of reuses employed, In this paper, the improved proportionate affine projection algorithm combined with the framework of set-membership filtering(SMF) is proposed in an attempt to achieve the fastest convergence for a sparse impulse response with low computational complexity, The proposed algorithm is evaluated using impulse responses with various degrees of sparseness. Simulations show good results in terms of reduced number of updates, speed of convergence, and final mean-squared error.