Variational Bayesian Multiuser Tracking for Reconfigurable Intelligent Surface Aided MIMO-OFDM Systems

Reconfigurable intelligent surface (RIS) has attracted enormous interest for its potential advantages in assisting both wireless communication and environmental sensing. In this paper, we study a challenging multiuser tracking problem in the multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system aided by multiple RISs. In particular, we assume that a multi-antenna base station (BS) receives the OFDM symbols from single-antenna users reflected by multiple RISs and tracks the positions of these users. Considering the users' mobility and the blockage of light-of-sight (LoS) paths, we establish a probability transition model to characterize the tracking process, where the geometric constraints between channel parameters and multiuser positions are utilized. We further develop an online message passing algorithm, termed the Bayesian multiuser tracking (BMT) algorithm, to estimate the multiuser positions, the angles-of-arrivals (AoAs) at multiple RISs, and the time delay and the blockage of the LoS path. The Bayesian Cramer Rao bound (BCRB) is derived as the fundamental performance limit of the considered tracking problem. Based on the BCRB, we optimize the passive beamforming (PBF) of the multiple RISs to improve the tracking performance. Simulation results show that the proposed PBF design significantly outperforms the counterpart schemes, and our BMT algorithm can achieve up to centimeter-level tracking accuracy.