Joint Estimation of Direct and RIS-assisted Channels with Tensor Signal Modelling

We consider a narrowband multi-user MIMO reconfigurable intelligent surface (RIS)-assisted wireless communication system and use tensor signal modelling techniques to jointly estimate all communication channels including the RIS-assisted link and the direct-path link between the access point and user equipment. We model the received signal as a third-order tensor comprising two additive CANDECOMP/PARAFAC (CP) decomposition terms corresponding to the direct-path and the RIS-assisted links. Based on this model we propose an enhanced iterative alternating least squares (E-ALS) algorithm to simultaneously estimate both the direct-path and RIS channels, and we derive the corresponding Cramér-Rao Bounds (CRB). Numerical results show that compared to recent previous works which estimate the direct-path and RIS links during separate training stages, the E-ALS method provides a more accurate estimate by efficiently using all pilots transmitted throughout the full training duration without turning the RIS OFF. For a sufficient number of transmitted pilots, the E-ALS method’s accuracy comes close to the CRB for the RIS channels and attains the CRB for the direct-path channel.