Estimation of quadratically nonlinear systems with an i.i.d. input

The properties of higher-order moment sequences and higher-order spectral moments of an independent, identically distributed (i.i.d.) process up to fourth order are discussed. These properties are utilized to develop algorithms to identify time-invariant nonlinear systems, which can be represented by second-order Volterra series and which are subjected to an i.i.d. input, in both the time and frequency domain. A relatively simple solution for estimating the Volterra kernels, which requires neither the calculation of the moment sequences for various time lags (or higher-order spectral moments) of the input nor the calculation of the inverse matrix, is shown to exist, even though the second-order Volterra series is not an orthogonal model for an i.i.d. input (unless the input is a white Gaussian process)