Nonlinear echo cancelling using look-up tables and Volterra systems

Two classical approaches to nonlinear echo cancellation are to use look-up tables combined with FIR filters and Volterra systems; their practical interest is higher when adapted with LMS-type algorithms, because results are easily implementable and offer good tracking capabilities. A complete analysis of look-up-table-based schemes is presented, and a new one is introduced which offers near optimal characteristics but without requiring variable steps: in practice a piecewise-constant adaptation algorithm is enough. The theoretical equivalence of these schemes with those based on Volterra kernels is established; a comparison of operational characteristic is then made. The important option of applying growing Volterra structures is proposed for the first time, and its possibilities are verified (as well as the previous analysis) by means of simulation examples. The paper ends with suggestions to be explored to obtain more efficient nonlinear echo cancellers