Set-membership affine projection algorithm

This letter presents a new data selective adaptive filtering algorithm, the set-membership affine projection (SM-AP) algorithm. The algorithm generalizes the idea of the set-membership NLMS (SM-NLMS) algorithm to include constraint sets constructed from the past input and desired signal pairs. The resulting algorithm can be seen as a set-membership version of the affine-projection (AP) algorithm with an optimized step size. Also, the SM-AP algorithm does not trade convergence speed with misadjustment and computational complexity as most adaptive filtering algorithms. Simulations show the good performance of the algorithm, especially for colored input signals, in terms of convergence, final misadjustment, and reduced computational complexity.