Near-Field Localization with RIS via Two-Dimensional Signal Path Classification

In this paper, we propose two-dimensional signal path classification (2D-SPC) for reconfigurable intelligent surface (RIS)-assisted near-field (NF) localization. In the NF regime, multiple RIS-driven signal paths (SPs) can contribute to precise localization if these are decomposable and the reflected locations on the RIS are known, referred to as SP decomposition (SPD) and SP labeling (SPL), respectively. To this end, each RIS element modulates the incoming SP's phase by shifting it by one of the values in the phase shift profile (PSP) lists satisfying resolution requirements. By interworking with a conventional orthogonal frequency division multiplexing (OFDM) waveform, the user equipment can construct a 2D spectrum map that couples each SPs time of arrival (ToA) and PSP. Then, we design SPL by mapping SPs with the corresponding reflected RIS elements when they share the same PSP. Given two unlabeled SPs, we derive a geometric discriminant from checking whether the current label is correct. It can be extended to more than three SPs by sorting them using pairwise geometric discriminants between adjacent ones. From simulation results, it has been demonstrated that the proposed 2D SPC achieves consistent localization accuracy even if insufficient PSPs are given.