Tensor modelling of MIMO communication systems with performance analysis and Kronecker receivers

•A new algorithm based on the ALS method, denoted KALS, is proposed for solving the Kronecker product approximation problem.•Eight tensor-based MIMO systems are presented in a unified way.•A comparative theoretical performance analysis is carried out and the maximum diversity gain is derived for the considered tensor-based systems.•Five new receivers exploiting a Kronecker product of the channel and symbol matrices are derived for jointly estimating these matrices.•Extensive Monte Carlo simulation results are shown to compare the performance of three tensor-based systems, and of five proposed Kronecker receivers for the TSTF system. The purpose of this paper is manifold. In a first part, we present a new alternating least squares (ALS)-based method for estimating the matrix factors of a Kronecker product, the so-called Kronecker ALS (KALS) method. Four other methods are also briefly described. In a second part, we consider the design of multiple-input multiple-output (MIMO) wireless communication systems using tensor modelling. Eight systems are presented in a unified way, and their theoretical performance is compared in terms of maximal diversity gain. Exploiting a Kronecker product of symbol and channel matrices, and applying the algorithms introduced in the first part, we propose three semi-blind and two supervised receivers, called Kronecker receivers, for jointly estimating the channel and the transmitted symbols. Necessary identifiability conditions are established. Finally, extensive Monte Carlo simulation results are provided to compare the performance of three tensor-based systems, on the one hand, and of the five proposed Kronecker receivers for the tensor space-time-frequency (TSTF) coding system, on the other hand.