Semi-Blind Tensor-Based Channel Estimation For Double RIS MIMO Systems

In this work, we propose a new joint (coupled) Tucker-2 decomposition method for semi-blind channel estimation in a double-reconfigurable intelligent surface (D-RIS)assisted MIMO communications system. In the D-RIS-assisted system, two RISs are considered; where the first RIS is placed close to the transmitter, and the other is placed close to the receiver for optimal performance. We demonstrate that the received signals in flat fading D-RIS-assisted MIMO systems can be effectively constructed using a 3-way Tucker-2 tensor model. By utilizing the Tucker factorization on the Tucker-2 received signals model, all the three channels i.e., $H_{T}$ channel between Tx-to-RIS 1, the HS channel between RIS 1-to-RIS 2, and the $H_{R}$ channel between RIS 2-to-Rx can be estimated effectively. Furthermore, compared with a single RIS (S-RIS) and the multiple RIS (M-RIS) case, we demonstrate how the system’s performance is influenced by parameters related to the transceiver, training overhead, and the number of elements considered in the RISs. A numerical performance evaluation depicts a fast convergence and underscores the improvement in the spectral efficiency of the D-RIS system compared to S-RIS and M-RIS systems. Index Terms-D-RIS-assisted MIMO, joint Tucker-2 decomposition, semi-blind channel estimation.