Phase Optimization and Message Passing Algorithm for RIS-Aided RSS Fingerprint Localization

The received signal strength (RSS) fingerprint-based technique is extensively utilized for indoor localization, as it does not require time synchronization. However, conventional RSS fingerprint localization schemes require multiple access points (APs), leading to a high deployment cost. In this work, by employing a reconfigurable intelligent surface (RIS), we propose an RSS fingerprint localization scheme with only one AP. First, we show that the variances of the measurement errors of RSSs in decibel (dB) are nonidentical (in contrast to the assumption of identical error variances in the literature), which needs to be considered in developing the localization scheme. Then, we optimize the phases of the RIS by minimizing the Cramér-Rao Lower Bound (CRLB) of localization with a particle swarm optimization (PSO) algorithm. To deal with the nonidentical measurement error variances, we develop a factor graph-based message passing localization algorithm by employing an approximate linear relationship between the target coordinates and the corresponding RSS. Numerical results are provided to demonstrate the effectiveness of the proposed method. We show that the proposed method outperforms existing schemes, and the optimization of RIS phases can significantly improve the localization performance.