Hybrid Vector Message Passing for Cascaded Channel Estimation in RIS-Aided Multi-User MIMO-OFDM Systems

This paper investigates the fundamental problem of cascaded channel estimation in reconfigurable intelligent surface (RIS) aided multi-user (MU) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. To address the high pilot overhead required by existing methods, we introduce appropriate auxiliary variables to decompose the received signal model into a subcarrier-wise bilinear sub-model and two linear sub-models with respect to the MU-to-RIS and RIS-to-base-station (BS) cascaded channels. The proposed model decomposition maintains the matrix factorization structure of the two cascaded channels and avoids the problem of parameter expansion in exiting methods. In the two linear sub-models, in addition, the cascaded channels are transformed into the delay-angle domain to leverage the joint sparsity. Based on the established models, we consider the problem of simultaneously estimating the MU-to-RIS and RIS-to-BS channel matrices as a bilinear estimation problem. To tackle this problem, we formulate a Bayesian inference framework and develop a hybrid message-passing (HVMP) algorithm to achieve approximate Bayesian inference by leveraging the Bethe method. Notably, the HVMP algorithm infers the two cascaded channels iteratively, where the covariance of each cascaded channel matrix is estimated to characterize the correlation of the matrix elements. Simulation results show that the proposed algorithm achieves accurate channel estimation with low pilot overhead while state-of-the-art baseline schemes exhibit poor performance. Furthermore, the proposed algorithm can approach the estimation oracle bound of the MU-to-RIS (or RIS-to-BS) channel which assumes perfect knowledge of the RIS-to-BS (or MU-to-RIS) channel.