Kalman filter based channel tracking for RIS-assisted multi-user networks

In this paper, we investigate channel estimation in a reconfigurable intelligent surface (RIS) assisted multi-user network while considering the mobility of users. Based on a time-varying channel model, we utilize the Kalman filter (KF) that is able to exploit temporal correlation to track cascaded channels. In order to maintain a relatively low pilot overhead, we present a multiple sub-phases based transmission protocol where the number of pilot sequences in each sub-phase is less than the number of users, i.e., pilot contamination exists. For the sake of practicality, we directly utilize the discrete Fourier transform matrix as the RIS phase shift matrix during the training process. We analyze normalized mean square error and provide some asymptotic results. A more practical scenario with hardware impairments (HWI) at the transceiver and the RIS is considered. Since HWI is also part of the measurement matrix and is unknown to the base station, we propose a joint estimation of the channel and HWI. Under this joint estimation framework, the underlying state space model becomes nonlinear. We develop an extended KF (EKF) algorithm to tackle the nonlinearity through which the model can be linearized. Numerical results show that the proposed algorithms outperform benchmarks under various scenarios.