New insights in the analysis of polynomial adaptive filters

New results are reported on the structure of the correlation matrix for the data vector in Volterra second order adaptive filters for a general colored Gaussian input process. The structure becomes apparent when the input to the quadratic part of the filter is represented as a Kronecker product of the vector of terms to the linear part, and the redundant terms in the product are not removed. This approach leads to bounds on the eigenvalues of the correlation matrix which characterize the performance of LMS algorithms, and suggestions for possibly improved nonlinear adaptive filtering algorithms.