Estimation of RIS Misorientation in both Near and Far Field Regimes

This paper presents a rigorous examination of the estimation of the misorientation of a reconfigurable intelligent surface (RIS) based on the received signal when the user equipment (UE) is in the near or far fields of the RIS. The Bayesian analysis views the location of the RISs as a priori system-level information. With incorrect a priori information, the position and orientation offsets of the RISs become parameters that need to be estimated and fed back to the Base station (BS) for correction. Two key insights are obtained from our Bayesian analysis. First, the Bayesian equivalent Fisher information matrix (EFIM) for the channel parameters indicates that the RIS orientation offset cannot be estimated when there is an unknown phase offset in the received signal in the far-field propagation regime. Second, the corresponding EFIM for the channel parameters in the received signal observed in the near-field shows that this unknown phase offset does not hinder the estimation of the RIS orientation offset when the UE has more than one receive antenna.