CRB for a Generic Near-Field Positioning System Using Three Electric Field Types

The use of larger antenna arrays at higher frequency bands is envisioned in the beyond 5G wireless networks. This takes advantage of the near-field propagation regime where the wavefront is no longer plane but spherical, bringing both new opportunities and challenges for the high-precision positioning. In this paper, a generic near-field positioning model with different observation capabilities for three electric fields (vector, scalar, and overall scalar electric field) is proposed. For these three electric field types, the Cram\'er-Rao bound (CRB) is adopted to evaluate the achievable estimation accuracy. The expressions of the CRBs using different electric field observations are derived by combining electromagnetic theory with estimation theory. Closed-form expressions can be further obtained if the terminal is located on the central perpendicular line (CPL) of the receiving antenna surface. In addition, the above discussions are extended to the system with multiple distributed receiving antennas under the CPL assumption. The CRBs using various electric fields in this case are derived and the effect of different numbers of receiving antennas on estimation accuracy is investigated. Numerical results are provided to quantify the CRBs and validate the analytical results. Also, the impact of various system parameters, including different electric fields and multiple antennas, on the near-field positioning performance is evaluated.