Constrained ALS-based tensor blind receivers for multi-user MIMO systems

Abstract

Tensor factorizations has shown to be an efficient approach for symbols and/or channel estimation in multi-input multi-output (MIMO) systems, where the factor matrices of tensor that correspond to symbols, channel, code/diversity of signals, are often estimated by using alternating least squares (ALS) algorithm. Although the performance of tensor approaches strongly depend on the initializations of the factor matrices. However, due to the absence of a priori on channels, these initializations are done randomly in traditional ALS algorithm. This generally implies a slow convergence. Further, ALS does not take into account the potential orthogonal structure in the factor matrices, which can be exploited to improve the accuracy of factor matrices recovery. To address these insures, this paper proposes constrained ALS tensor blind receivers for multi-user MIMO systems. We show that the multi-user MIMO signals can be expressed as a third-order tensor model, where the matrices of users symbols, direction-of-arrival (DOA) and delay can be viewed as three factor matrices of the tensor model. Two constrained ALS blind algorithms that take into account the potential orthogonal and Vandermonde structures in the factor matrices, are proposed to learn the tensor model, where the users symbols, DOA and delay are joint estimated as three factor matrices. Besides provide the estimations for the factor matrices, the orthogonal and Vandermonde structures also give a better uniqueness results for the use of tensor model. Interestingly, these structures are the nature properties of the factor matrices in our system. This results in an efficient blind approach that has better performance and lower complexity compare with the traditional ALS.