We address the localization of a reconfigurable intelligent surface (RIS) for a single-input single-output multicarrier system using bi-static sensing between a fixed transmitter and a fixed receiver. Due to the deployment of RISs with a large dimension, near-field (NF) scenarios are likely to occur, especially for indoor applications, and are the focus of this work. We first derive the Cramér-Rao bounds (CRBs) on the estimation error of the RIS position and orientation and the time of arrival (TOA) for the path transmitter-RIS-receiver. We propose a multi-stage low-complexity estimator for RIS localization purposes. In this proposed estimator, we first perform a line search to estimate the TOA. Then, we use the far-field approximation of the NF signal model to implicitly estimate the angle of arrival and the angle of departure at the RIS center. Finally, the RIS position and orientation estimate are refined via a quasi-Newton method. Simulation results reveal that the proposed estimator can attain the CRBs. We also investigate the effects of several influential factors on the accuracy of the proposed estimator like the RIS size, transmitted power, system bandwidth, and RIS position and orientation.

Radio localization is applied in high-frequency (e.g., mmWave and THz) systems to support communication and to provide location-based services without extra infrastructure. For solving localization problems, a simplified, stationary, narrowband far-field channel model is widely used due to its compact formulation. However, with increased array size in extra-large multiple-input-multiple-output (XL-MIMO) systems and increased bandwidth at upper mmWave bands, the effect of channel spatial non-stationarity (SNS), spherical wave model (SWM), and beam squint effect (BSE) cannot be ignored. In this case, localization performance will be affected when an inaccurate channel model deviating from the true model is adopted. In this work, we employ the misspecified Cramér-Rao lower bound to lower bound the localization error using a simplified mismatched model while the observed data is governed by a more complex true model. The simulation results show that among all the model impairments, the SNS has the least contribution, the SWM dominates when the distance is small compared to the array size, and the BSE has a more significant effect when the distance is much larger than the array size.

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Beamforming (BF) is the inevitable component of the recent communication systems, especially Millimeter wave (mmWave) systems. Thanks to the radio frequency (RF) and digital technologies, BF techniques are implemented in the both digital and analogue domains by using phase shifters (PS) networks. Adopting the digital PS, which has the finite resolution bits, leads to loss in the spectral efficiency (SE). Accordingly, in this paper, we extract the SE loss in a multi-user multiple inputs single output (MISO) system, which would be useful for practical prospective. To this end, we apply machine learning (ML) to extract the SE loss. Simulation results show that the extracted models have the desirable accuracy in the SE loss prediction.