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.
@article{arxiv.1610.07520,
title = {Nonlinear Adaptive Algorithms on Rank-One Tensor Models},
author = {Felipe C. Pinheiro and Cassio G. Lopes},
journal= {arXiv preprint arXiv:1610.07520},
year = {2016}
}