Tensors have recently been exploited to solve problems in reconfigurable surfaces-assisted communications, including channel estimation, active/passive beamforming design, and feedback control signaling.

Figure 6: RIS-related signal processing problems benefiting from tensor decompositions.

The connection of tensor decompositions to RIS channel estimation revealed that the estimation of the composite channel can be effectively decoupled, and the constituent channels can be provably identified owing to the uniqueness of tensor decomposition. This link results in efficient algorithms for channel estimation with reduced pilot overhead and built-in blind estimation.

In addition, tensor decompositions also effectively control the overhead of reconfigurable surfaces by representing the (tensorized version of the) RIS phase shift vector as a low-rank tensor model, significantly reducing feedback requirements. Tensors also enable low-complexity optimization of joint active/passive beamformings by leveraging the geometrical structure of the propagation channels.

Figure 7: Low-rank tensor decomposition of the IRS phase shifts to reduce representation complexity.

[1] G. T de Araújo, A. L. F. de Almeida, R. Boyer, “Channel estimation for IRS-assisted MIMO systems: A tensor modeling approach,” IEEE Journal of Selected Topics in Signal Processing,  vol. 15, pp. 789-802, 2021.

[2] K. Ardah, S. Gherekhloo, A. L. F. de Almeida, M. Haardt, “TRICE: An efficient channel estimation framework for RIS-aided MIMO communications,” IEEE Signal Processing Letters, vol. 28, pp. 513-517, 2021.

[3] B. Sokal, P. R. B. Gomes, A. L. F. de Almeida, B. Makki, G. Fodor, “Reducing the control overhead of intelligent reconfigurable surfaces via a tensor-based low-rank factorization approach”, IEEE Transactions on Wireless Communications, vol. 22, no. 10, pp. 6578-6593, 2023.

[4] K. B. Benício, A. L. F. de Almeida, B. Sokal, F. E-. Asim, B. Makki, G. Fodor,  “Tensor-based channel estimation and data-aided tracking in IRS-assisted MIMO systems,” IEEE Wireless Communications Letters, vol. 13, no. 2, pp. 333-337, 2024.
[5] P. R. B. Gomes, G. T. Araújo, A. L. F. de Almeida, B. Makki, G. Fodor, “Channel estimation in RIS-assisted MIMO systems operating under imperfections,” IEEE Transactions on Vehicular Technology, vol. 72, no. 11, pp. 14200-14213, 2023.