Characterizing the First-Arriving Multipath Component in 5G Millimeter Wave Networks: TOA, AOA, and Non-Line-of-Sight Bias

Abstract

This paper presents a stochastic geometry-based analysis of propagation statistics for 5G millimeter wave (mm-wave) cellular. In particular, the time-of-arrival (TOA) and angle-of-arrival (AOA) distributions of the first-arriving multipath component (MPC) are derived. These statistics find their utility in many applications such as cellular-based localization, channel modeling, and link establishment for mm-wave initial access (IA). Leveraging tools from stochastic geometry, a Boolean model is used to statistically characterize the random locations, orientations, and sizes of reflectors, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , buildings. Assuming non-line-of-sight (NLOS) propagation is due to first-order ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , single-bounce) reflections, and that reflectors can either facilitate or block reflections, the distribution of the path length ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , absolute time delay) of the first-arriving MPC is derived. This result is then used to obtain the first NLOS bias distribution in the localization literature that is based on the absolute delay of the first-arriving MPC for outdoor time-of-flight (TOF) range measurements. This distribution is shown to match exceptionally well with commonly assumed gamma and exponential NLOS bias models in the literature, which were only attained previously through heuristic or indirect methods. Continuing under this analytical framework, the AOA distribution of the first-arriving MPC is derived, which gives novel insight into how environmental obstacles affect the AOA and also represents the first AOA distribution derived under the Boolean model.