A Sparse-Interpolated Scheme for Implementing Adaptive Volterra Filters

In most practical applications, the major drawback for using adaptive Volterra filters is the large number of coefficients to cope with. Several research works discussing strategies to reduce the computational burden of these structures have been presented in the open literature. For such, a common approach has been the use of some type of sparseness in Volterra filter kernels. In this work, a sparse-interpolated approach, with the interpolation having the purpose of recreating (in an approximate way) the elements disregarded for obtaining sparse kernels, is presented and discussed. Thus, for the adaptive sparse-interpolated Volterra filter, coefficient update expressions considering both least-mean-square (LMS) and normalized LMS (NLMS) algorithms are derived by using a constrained approach. In general, the proposed strategy outperforms other sparse schemes in terms of the tradeoff between computational complexity and mean-square error (MSE) performance, as shown through numerical simulations.