A fast exact filtering approach to a family of affine projection-type algorithms

The affine projection (AP)-type algorithms produce a good tradeoff between convergence speed and complexity. As the projection order increases, the convergence rate of the AP algorithm is improved at a relatively high complexity. Many efforts have been made to reduce the complexity. However, most of the efficient versions of the AP-type algorithms are based on the fast approximate filtering (FAF) scheme originally proposed in the fast AP (FAP) algorithm. The approximation leads to degraded convergence performance. Recently, a fast exact filtering (FEF) AP (FEAP) algorithm was proposed by Y. Zakharov. In this paper, we propose a new FEF approach to further reduce the complexity of the FEAP algorithm given that the calculation of the weight vector is not the primary objective for the application at hand. The proposed FEF scheme is then extended to the dichotomous coordinate descent (DCD)-AP, affine projection sign (APS), and modified filtered-x affine projection (MFxAP) algorithms. The complexity of AP-type algorithms based on the proposed FEF approach is comparable to that based on the FAF scheme. Moreover, analysis results show that the complexity reduction of the new algorithms is achieved without any performance degradation.