PARAFAC-based unified tensor modeling for wireless communication systems with application to blind multiuser equalization

In some antenna array-based wireless communication systems the received signal is multidimensional and can be treated as a tensor (3D array) instead of a matrix (2D array). In this paper, we make use of a generalized tensor decomposition known as constrained Block-PARAFAC and propose a tensor (3D) model for the signal received by three types of wireless communication systems. The considered wireless communication systems are multiuser systems subject to frequency-selective multipath and employing multiple receiver antennas together with (i) oversampling or (ii) direct-sequence spreading or (iii) multicarrier modulation. The proposed modeling approach aims at unifying the received signal model of these systems into a single PARAFAC model. We show that the proposed model has a constrained structure, where model constraints and associated dimensions depend on each particular system. The proposed constrained Block-PARAFAC model is demonstrated by expanding the tensor using Kronecker products of canonical vectors. As an application of this model to tensor signal processing, a new tensor-based receiver is proposed for blind multiuser equalization, which combines PARAFAC-based modeling with a subspace method. Simulation results are presented to illustrate the performance of the proposed blind receiver.