Blind identification of a second order Volterra-Hammerstein series using cumulant cubic tensor analysis

In this paper we deal with blind identification of second order Volterra-Hammerstein series based on the analysis of a third order tensor composed of the fourth order output cumulants. We demonstrate that this nonlinear identification problem can be reduced to a linear one having the form Ax + By = c. The resolution of this system can be made with many methods. In this work we have used two algorithms: the alternating least square algorithm (ALS) and the alternating QR factorization algorithm (AQR). Simulation results show a good estimation of kernels with little superiority of the AQR algorithm. This superiority is the result of the numerical stability of the algorithm.