Optimal Passive Beamforming for Cooperative Localization with RIS-Assisted mmWave Systems

Localization is an essential service for numerous applications. In particular, cooperative localization is a widely used technique for improving performance by utilizing information obtained from several base stations. In this paper, we study the potential of reconfigurable intelligent surfaces (RIS) for cooperative localization performance in mmWave MIMO systems. Firstly, we obtain the fundamental cooperative localization performance limit, i.e., Cramer-Rao lower bound (CRLB) based on the Fisher information. Then, we propose an optimal phase design at RIS to optimize the position accuracy. In particular, to handle the phase only constraints of RIS, an optimal passive beamforming (PBF) algorithm based on manifold optimization is proposed to minimize the CRLB, which, however, has a high complexity. Then, under mild conditions, we show that the CRLB minimization problem can be cast as a joint channel gain maximization problem, which enables a low-complexity closed-form PBF design at RIS. The simulation results show that the proposed optimal PBF for cooperative localization significantly improves the localization accuracy. Moreover, the proposed low-complexity PBF achieves near optimal performance with very low computational complexity.