L0-Norm Adaptive Volterra Filters

The paper addresses adaptive algorithms for Volterra filter identification capable of exploiting the sparsity of nonlinear systems. While the l
₁
-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 l
₀
-norm.Thus, in this paper, the Geman-McClure function is adopted to approximate the l
₀
-norm and to derive l
₀
-norm adaptiveVolterra 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 l
₁
-norm solutions.