Cramér-Rao Bound for Direct Position Estimation in OFDM Based Cellular Systems

Abstract: Although direct position estimation (DPE) has been demonstrated to offer enhanced robustness in GNSS receivers, its theoretical limits and performance in OFDM based positioning systems remain largely unexplored. In this paper, the Cram\'er-Rao bound (CRB) for DPE using OFDM based cellular signals is derived and benchmarked against the conventional two-step positioning method to assess their relative performance in non-line-of-sight (NLOS) dominated multipath environments. Numerical results reveal that 1) the DPE method consistently outperforms the two-step approach in OFDM systems under all evaluated conditions; 2) a large bandwidth is crucial in both methods, and increasing subcarrier spacing is more beneficial for a fixed bandwidth; 3) utilizing multiple OFDM symbols for positioning leads to substantial improvements in localization accuracy compared to relying on a single symbol. However, further increasing the number of symbols yields marginal improvements while significantly increasing computational complexity.