Reconfigurable Intelligent Surface-Assisted Localization in OFDM Systems With Carrier Frequency Offset and Phase Noise

Reconfigurable intelligent surface (RIS)-assisted communication systems have been extensively studied for providing high-precision location services. However, most studies have overlooked the impact of carrier frequency offset (CFO) and phase noise (PN) resulting from hardware impairments on localization. This paper presents a novel, alternating optimization (AO)-based algorithm to jointly estimate the CFO, PN, and user equipment (UE) position in orthogonal frequency division multiplexing (OFDM) systems, where, provided the UE position, closed-form expressions for the CFO and PN are derived per iteration, significantly reducing the complexity and enhancing the stability of the algorithm. Another important aspect is a new RIS phase shift optimization algorithm developed to minimize the analytical lower bound of localization accuracy, hence benefiting localization. The semidefinite relaxation method and Schur complement are utilized to convexify this challenging non-convex optimization problem to a semidefinite program. Simulations demonstrate the effectiveness of the proposed algorithms, with the localization accuracy enhanced by two orders of magnitude. The localization accuracy of the proposed algorithm is close to the analytical lower bound, with a root mean square error of lower than $\rm 10^{-2} \: m$ .