L0-norm adaptive Volterra filters

The paper addresses adaptive algorithms for Volterra filter identification capable of exploiting the sparsity of nonlinear systems. While the l1-norm of the coefficient vector is often employed to promote sparsity, it has been shown in the literature that superior results can be achieved using an approximation of the l0-norm. Thus, in this paper, the Geman-McClure function is adopted to approximate the l0-norm and to derive l0-norm adaptive Volterra filters. It is shown through experimental results, also involving a real-world system, that the proposed adaptive filters can obtain improved performance in comparison with classical approaches and l1-norm solutions.