Affine projection algorithms based on sigmoid cost function

Abstract

In this paper, two new algorithms are proposed using modified sigmoid activation function as the cost function and combining with affine projection (AP) method, which are sigmoid affine projection sign algorithm (SAPSA) and sigmoid affine projection algorithm (SAPA). Conventional AP-type algorithms converge fast but are susceptible to impulsive interference. The sigmoid function has an upper bound, thus reducing the effect of impulse interference. The proposed algorithms combine the advantages of fast convergence speed of the affine projection method and strong noise resistance of the sigmoid cost function. Meanwhile the L2-norm constraint is used to adjust the updating formula of the weight vector, which further improves noise resistance. Several simulation experiments show that SAPSA and SAPA are superior to other AP-type algorithms under impulse interference.