Bayesian Cramer–Rao Bound, Extended and Unscented Kalman Filters Based Tracking Through Non-Ideal Transceivers in 5G and Beyond

This work investigates the tracking process and its performance in milliwave (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$mm$</tex-math></inline-formula>wave) systems implementing orthogonal frequency-division multiplexing (OFDM). We aim to track a single-antenna mobile station (MS) based on well-known pilots broadcast from a multiple-antenna base station (BS). We have a particular interest in the practical scenario where the MS and BS are equipped with hardware-impaired transceivers that distort the pilots. To this end, the extended Kalman-filter-based tracker (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EKFT</i>) and the unscented Kalman-filter-based tracker (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">UKFT</i>) are proposed to accomplish the tracking process. We pay special attention in its design to the accuracy degradation caused by these hardware impairments (HWIs) as well as to the MS transition uncertainty. Afterwards, this work derives the performance analysis in the Bayesian Cramer-Rao bound (BCRB) term, which considers the information conveyed by the distorted pilot and the transition uncertainty model. Moreover, this analysis is not only for assessment purposes but also for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EKFT</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">UKFT</i> design. Furthermore, this work enhances the tracking accuracy by adopting the Monte Carlo (MC) approach. Lastly, extensive computer simulation is conducted for a comprehensive discussion of the proposed tracker's performance and the related theoretical bound. The results present the harmful impact of HWIs, non-line of sight paths reflected of unknown scatterers, and clock offset on the tracking process and the capabilities of the proposed trackers in improving tracking accuracy.