  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.
