A simple set-membership affine projection algorithm for sparse system modeling

In this paper, we derive two algorithms, namely the Simple Set-Membership Affine Projection (S-SM-AP) and the improved S-SM-AP (IS-SM-AP), in order to exploit the sparsity of an unknown system while focusing on having low computational complexity. To achieve this goal, the proposed algorithms apply a discard function on the weight vector to disregard the coefficients close to zero during the update process. In addition, the IS-SM-AP algorithm reduces the overall number of computations required by the adaptive filter even further by replacing small coefficients with zero. Simulation results show similar performance when comparing the proposed algorithm with some existing state-of-the-art sparsity-aware algorithms while the proposed algorithms require lower computational complexity.