Wireless Area Positioning in RIS-Assisted mmWave Systems: Joint Passive and Active Beamforming Design

This letter investigates a reconfigurable intelligent surface (RIS) assisted mmWave system for wireless area positioning. We aim to optimize the worst-case localization performance in terms of squared position error bound within the target region by jointly optimizing beamforming vectors at RIS and user equipment (UE), which leads to a nonconvex-nonconcave minimax problem. To tackle the challenging minimax problem, we propose a two-step algorithm with good convergence performance. Specifically, a joint array gain and path loss search (JAPS) algorithm is proposed to effectively find the exact solution of inner nonconcave maximization problem and a difference of convex (DC)-based algorithm is proposed to update the beamforming vectors at RIS and UE to improve the worst localization performance. Numerical results show that the proposed algorithm achieves significant performance gains over the benchmark schemes.