Blind equalization of nonlinear channels using a tensor decomposition with code/space/time diversities

In this paper, we consider the blind equalization problem for nonlinear channels represented by means of a Volterra model. We first suggest a precoding scheme inducing a three-dimensional (3-D) structure for the received data due to code, space, and time diversities. The tensor of received data admits a PARAFAC (parallel factors) decomposition with finite alphabet and Vandermonde structure constraints. We derive a uniqueness result taking such constraints into account. When one of the matrix factors, the code matrix, is known or belongs to a known finite set of matrices, we give new uniqueness results and three equalization algorithms are proposed. The performances of these algorithms are illustrated by means of simulation results.