Performance Limits of Single-Anchor mm-Wave Positioning.

The fundamental limits of single-anchor multi-antenna positioning are investigated. Exploiting the structure of the channel at millimeter-wave (mm-Wave) frequencies, the Cram\'er-Rao lower bound for the position, orientation and velocity estimation error is derived for transmitter and receiver localization under a static and dynamic scenario with or without knowledge of the time of transmission (KTT). After revisiting the relation of the observed multiple input-multiple output (MIMO)-orthogonal frequency division multiplexing (OFDM) channel with the underlying geometry of the channel, we present geometrically intuitive asymptotic expressions for the Fisher information for large bandwidth, large number of antennas and different levels of KTT. Based on our derived results, we show that the Fisher information matrix (FIM) on position and orientation parameters in the downlink (DL) and the uplink (UL) differ only by a scalar, which is equal to the ratio of the receive Signal-to-Noise Ratio (SNR) in the DL and UL.