Affine projection algorithms for sparse system identification

Abstract

We propose two versions of affine projection (AP) algorithms tailored for sparse system identification (SSI). Contrary to most adaptive filtering algorithms devised for SSI, which are based on the l <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> norm, the proposed algorithms rely on homotopic l <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> norm minimization, which has proven to yield better results in some practical contexts. The first proposal is obtained by direct minimization of the AP cost function with a penalty function based on the l <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> norm of the coefficient vector, whereas the second algorithm is a simplified version of the first proposal. Simulation results are presented in order to evaluate the performance of the proposed algorithms considering three different homotopies to the l <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> norm as well as competing algorithms.