Multi-Array 5G V2V Relative Positioning: Performance Bounds

We study the performance bounds of vehicle-to-vehicle (V2V) relative positioning for vehicles with multiple antenna arrays. The Cram\'{e}r-Rao bound for the estimation of the relative position and the orientation of the Tx vehicle is derived, when angle of arrival (AOA) measurements with or without time-difference of arrival (TDOA) measurements are used. In addition, geometrically intuitive expressions for the corresponding Fisher information are provided. The derived bounds are numerically evaluated for different carrier frequencies, bandwidths and array configurations under different V2V scenarios, i.e. overtaking and platooning. The significance of the AOA and TDOA measurements for position estimation is investigated. The achievable positioning accuracy is then compared with the present requirements of the 3rd Generation Partnership Project (3GPP) 5G New Radio (NR) vehicle-to-everything (V2X) standardization.