Far-Field Localization for RIS Empowered Wireless Systems Leveraging Beamforming

Reconfigurable intelligent Surfaces (RISs) have lately received a lot of interest due to their capability of providing a smarter controlled radio environment. This paper investigates the use of RIS beamforming to attain user equipment (UE) localization in far-field propagation with two localization schemes in millimeter-wave (mmWave) with orthogonal frequency division multiplexing (OFDM) signaling. The first scheme adopts a single RIS that leverages the time of arrival (ToA) and angle of departure (AoD) measurements. For this model, the impact of various parameters on the localization accuracy are examined. In addition, the Cramer-Rao Lower Bound (CRLB) for the positioning, i.e., the position error bounds (PEB), is derived to be used as benchmark. Also, an efficient multi-RIS aided localization scheme is proposed, in which the use of only AoDs to estimate the UE position is shown to be possible, whereas this was challenging without using multi-RIS scenario. The main contribution of this paper is relieving the complexity of localization algorithm by eliminating the necessity of ToA estimation where consensus-based fusion of AoDs estimations is used. The estimation of AoD from the RIS to the UE is obtained by using the RIS as a beamformer to scan the working area with successive beams. The highest received signal at UE from a particular beam will determine the AoD. The performance of the two localization models - discussed in this paper - are evaluated via extensive numerical simulations. For the first model, the simulation results and PEB demonstrated that increasing the number of beams that swept the region of interest has a significant impact on the accuracy, while using RIS with a large number of elements demonstrated marginal influence on the localization accuracy for a large number of RIS elements. Furthermore, the results reveal that the localization accuracy of the proposed multi-RIS localization scheme outperforms the performance of the first model by increasing the number of RISs and the number of beams. In addition, the proposed scheme benefits from being computationally efficient due to the release of ToA estimation in the first model that requires the computation of inverse fast Fourier transform (IFFT) of the oversampled version of the received signal for a sufficient number of transmissions and fine-tuning using search optimization to attain accurate estimation