Blind joint identification and equalization of Wiener-Hammerstein communication channels using PARATUCK-2 tensor decomposition

In this paper, we consider the blind joint identification and equalization of Wiener-Hammerstein nonlinear communication channels. By considering a special design of the input signal, we show that output data can be organized into a third-order tensor. We show that the obtained tensor has a PARATUCK-2 representation. We derive new results on uniqueness of the PARATUCK-2 model by considering structural constraints such as Toeplitz and Vander-monde forms for some of its matrix factors. We also constrain the input signal to belong to a finite alphabet. Then an Alternating Least Squares (ALS) algorithm is proposed for estimating the factors of the PARATUCK-2 model and therefore the parameters of the Wiener-Hammerstein channel and the unknown input signal. The performances of the proposed joint identification and equalization method are illustrated by means of simulation results.