Equalization of Volterra systems using a multilinear SVD based pseudo pth order inverse

Volterra series techniques have been used for some time to model nonlinear systems. The models are well defined, however the number of parameters grows exponentially with the order of the nonlinearity. Techniques exist to compensate a nonlinear system but are often not practical to implement. One approach to this problem is to factor the Volterra kernels into a sum of simple terms that are easy to implement. There are several approaches published in the literature 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. Also proposed here is an extension of the pseudo-inverse concept that utilizes the multilinear factorization and compensates for the most significant terms.