Decoupling static nonlinearities in a parallel Wiener-Hammerstein system: A first-order approach

We present a method to decompose a static MIMO (multiple-input-multiple-output) nonlinearity into a set of SISO (single-input-single-output) polynomials acting on internal variables that are related to the inputs and outputs of the MIMO nonlinearity by linear transformations. The method is inspired on the small-signal analysis of nonlinear circuits and proceeds by collecting first-order information of the MIMO function into a set of Jacobian matrices. A simultaneous diagonalization of the set of Jacobian matrices is computed using a tensor decomposition, providing the required linear transformations, after which also the coefficients of the internal SISO polynomials can be computed. The method is validated on measurements of a parallel two-branch Wiener-Hammerstein identification setup.