Efficient implementation of Volterra systems using a multilinear SVD

A large class of nonlinear systems have been successfully modeled using Volterra series techniques. The problem with Volterra series is that the number of parameters grows very rapidly with the order of the nonlinearity and the memory in the system. Techniques exist to efficiently model and compensate for Volterra systems but are often not practical to implement. One approach is to factor the Volterra kernels into a sum of simple terms that are easy to implement. Approaches utilizing the eigen-decomposition have been published for second order nonlinearities. This work proposes using a multilinear extension of the SVD to factor third and higher order kernels into terms that are easily implemented.