Uninformed-to-Informed Estimation: A Ping-Pong Positioning Method for Multi-user Wideband MmWave Systems

To enhance the positioning and tracking performance of dynamic user equipment (UE) in wideband millimeter-wave (mmWave) systems, we propose a novel positioning error lower bound (PELB)-driven ping-pong positioning framework, where the base station (BS) and UE alternately transmit and receive adaptive beamforming signals for positioning. All beamformers are scheduled based on the locally evaluated PELB. In this framework, we exploit multi-dimensional information fusion to assist in positioning. Firstly, a multi-subcarrier collaborative positioning error lower bound (MSCPEB) is proposed to evaluate the positioning error limits of wideband mmWave systems, which quantifies the contribution of all subcarriers to positioning accuracy. Moreover, we prove that the MSCPEB does not exceed the arithmetic mean of the PELBs of the individual subcarriers. Subsequently, we develop an alternating optimization (AO) algorithm to optimize the hybrid beamformers targeted for MSCPEB minimization. By convexifying this problem, closed-form solutions of beamformers are derived. Finally, we develop a multipath collaborative positioning method that quantifies the impact of path reliability on positioning accuracy, with a closed-form solution for user position derived. The proposed method does not rely on path resolution and traditional triangular relationships. Numerical results validate that the proposed method improves estimation accuracy by at least 16% compared to potential schemes without optimized beam configurations, while requiring only approximately one-quarter of the slot resources.