Adaptive Volterra Filters With Evolutionary Quadratic Kernels Using a Combination Scheme for Memory Control

This paper proposes a new paradigm for adaptive Volterra filtering using a time-variant size of the quadratic kernel memory in order to optimally identify any unknown transversal second-order nonlinear system. To this end, competing Volterra structures of different sizes are employed in a hierarchical combination scheme so as to find the best configuration of the second-order kernel memory, using the already known diagonal-coordinate representation. The length and number of required quadratic kernel diagonals can be concurrently estimated by monitoring the combination performance. Subsequently, the memory size of the involved models is dynamically increased or decreased, following a set of intuitive rules. Since this automatic memory adaptation is performed along with the coefficient updates, an efficient Volterra filter is realized, offering great flexibility and minimizing the risk of under- or overmodeling any given quadratic nonlinearity. Besides the straightforward scheme, a simplified version is presented, greatly reducing the algorithmic demands. This efficient version is based on a virtualization of the competing Volterra filters by jointly using common coefficients and hence exhibits a computational complexity suitable for practical implementations. The robust estimation performance of the approach is demonstrated by various examples for a nonlinear acoustic echo cancellation scenario, involving stationary noise, real speech signals and realistic Volterra kernels.