Inferring Direction and Orientation From Polarized Signals: Feasibility and Bounds

Polarization is a fundamental property of electromagnetic radio signals but often neglected in localization studies. In this paper, we study the potential benefits of integrating the polarization dimension into localization applications. We develop a three-dimensional (3D) geometric channel model between a base station (BS) and user equipment (UE), both equipped with dual-polarized (DP) antennas, which offers fundamental insights into the angles of departure (AoD) from the BS to the UE as well as the 3D orientation of the UE. From the model, we identify the degrees of freedom (DoF) provided by the polarization dimension for localization solutions by evaluating the rank of the equivalent Fisher information matrix. Subsequently, we leverage these DoF to introduce three distinct localization applications: (i) 3D orientation estimation, (ii) 2D AoD estimation, and (iii) mixed 2D position and 1D orientation estimation for vehicular scenarios. Furthermore, for the three localization applications we identify their regions of operation in terms of the ranges of the angles of interest, to avoid any ambiguity occurrence through the estimation process, thereby guaranteeing unique solutions. Finally, we derive the Cramér-Rao lower bounds and numerically establish the efficiency of the proposed estimators.