On the performance of adaptive pruned Volterra filters

Because of the high computational burden required by adaptive Volterra filters, several of their practical implementations consider some type of sparseness for complexity reduction. Such implementations are obtained using application-oriented strategies to prune a standard Volterra filter by zeroing some of its coefficients. In this context, the main challenge is to choose a pruning strategy that leads to minimum loss of performance. Meeting this challenge is not a trivial task because of the variety of strategies available for obtaining pruned Volterra filters as well as due to the lack of a theoretical framework describing these strategies in a general scenario. Thus, the primary objective of this research work is to establish a basis for assessing adaptive pruned Volterra filters. For such, a unifying scheme describing the input vectors of different pruned Volterra implementations is proposed along with an extended version of a constrained approach used to represent sparseness in adaptive filters. Based on this foundation, an analysis of the performance of adaptive pruned Volterra filters in terms of the minimum mean-square error is carried out. Simulation results are presented attesting the effectiveness of the proposed approach.

► A new foundation for the analysis of adaptive pruned Volterra filters is proposed.
► The different pruned Volterra filters are described using a novel unifying scheme.
► An extension of a constrained approach for analyzing adaptive filters is introduced.
► A minimum mean-square-error analysis is performed based on the proposed foundation.
► Results of numerical simulation attest the effectiveness of the presented theory.