Fast implementation of a family of memory proportionate affine projection algorithm

Previously, a family of memory proportionate affine projection (MPAP) algorithms has been proposed by taking into account the “history” of the proportionate factors for sparse system identification. This paper presents a low-complexity implementation of this family of MPAP algorithms. Two most important ideas are used in the derivation of the fast algorithm. The first one is to update the auxiliary coefficient vector rather than the true coefficient vector. The second interesting idea is to calculate the error vector by using a recursive technique. Simulation results demonstrate the effectiveness of the fast algorithms.