Tensor train representation of MIMO channels using the JIRAFE method

•From a fundamental perspective, the equivalence between CPD and TTD has been presented in [6,7] for full column rank factors. This equivalence is deeply reformulated in the sense that the structure of the TT-cores changes if the full column rank factor assumption is violated. This is precisely the case of the MIMO channel tensor considered in this work.•Comparatively with the channel model considered in [2], the one proposed in this work exploits an URA at the reception, inducing an increase of spatial diversity. This case has been first mentioned in [2], but in this work we detail the model when URAs are considered at both the transmitter and the receiver.•The MIMO channel is represented under a TT format, instead of the usual CPD representation, and the structure of the TT-cores is highlighted separately under the assumptions of full column rank and full row rank for the matrix factors.•The TT structure characterized by properties of coupling between two adjacent cores containing the same latent matrices, is exploited for dimensionality reduction and channel parameters estimation using the JIRAFE (Joint dImensionality Reduction And Factor rEtrieval) scheme. MIMO technology has been subject of increasing interest in both academia and industry for future wireless standards. However, its performance benefits strongly depend on the accuracy of the channel at the base station. In a recent work, a fourth-order channel tensor model was proposed for MIMO systems. In this paper, we extend this model by exploiting additional spatial diversity at the receiver, which induces a fifth order tensor model for the channel. For such high orders, there is a crucial need to break the initial high-dimensional optimization problem into a collection of smaller coupled optimization sub-problems. This paper exploits new results on the equivalence between the canonical polyadic decomposition (CPD) and the tensor train (TT) decomposition for the multi-path scenario. Specifically, we propose a Joint dImensionality Reduction And Factor rEtrieval (JIRAFE) method to find the transmit and receive spatial signatures as well as the complex path gains (which also capture the polarization effects). Monte Carlo simulations show that our proposed TT-based representation of the channel is more robust to noise and computationally more attractive than available competing tensor-based methods, for physical parameters estimation.