A fully LMS/NLMS adaptive scheme applied to sparse-interpolated Volterra filters with removed boundary effect

Adaptive implementations of Volterra filters have been used successfully in several practical applications involving nonlinear systems. Such implementations are mostly based on reduced-complexity Volterra structures aiming to circumvent the high computational burden usually required by standard Volterra filters. One of these structures is the sparse-interpolated Volterra filter, which uses kernel sparseness to reduce computational cost as well as interpolation to compensate for the loss of performance. The aim of this work is to improve both convergence and steady-state mean-square error (MSE) performance of the adaptive sparse-interpolated Volterra filter with only a small increase in computational complexity. For such, a novel fully adaptive scheme is devised using a combination of the least-mean-square (LMS) and the normalized LMS (NLMS) algorithms to update the coefficients of the sparse-interpolated Volterra structure with removed boundary effect. The obtained algorithm achieves superior performance as compared with other adaptive sparse-interpolated implementations. Numerical simulation results corroborate the effectiveness of the proposed approach.

► An approach to implement adaptive sparse-interpolated Volterra filters is proposed.
► An LMS/NLMS adaptive setup is used to keep the computational cost at low level.
► A rigorous mathematical approach is used to develop the proposed algorithm.
► The proposed scheme outperforms other sparse-interpolated Volterra implementations.