Nonlinear Adaptive Algorithms on Rank-One Tensor Models

TL;DR

This paper introduces a low-complexity nonlinear adaptive algorithm based on rank-one tensor models, demonstrating effective performance and stability in simulations compared to existing nonlinear processing methods.

Contribution

It develops a novel adaptive algorithm using a rank-one tensor model derived from Volterra kernels, with proven stability and convergence properties.

Findings

Algorithms show good performance in simulations.

Stable and convergent under certain conditions.

Outperforms some existing nonlinear methods.

Abstract

This work proposes a low complexity nonlinearity model and develops adaptive algorithms over it. The model is based on the decomposable---or rank-one, in tensor language---Volterra kernels. It may also be described as a product of FIR filters, which explains its low-complexity. The rank-one model is also interesting because it comes from a well-posed problem in approximation theory. The paper uses such model in an estimation theory context to develop an exact gradient-type algorithm, from which adaptive algorithms such as the least mean squares (LMS) filter and its data-reuse version---the TRUE-LMS---are derived. Stability and convergence issues are addressed. The algorithms are then tested in simulations, which show its good performance when compared to other nonlinear processing algorithms in the literature.