Time-of-arrival, angle-of-arrival, and angle-of-departure statistics of a novel simplistic disk channel model

This paper introduces a novel simplistic geometrical disk scattering model in which the local scatterers are uniformly distributed in polar coordinates within a disk centered on the mobile station (MS). The proposed joint uniform distribution in polar coordinates results in a higher concentration of scatterers around the disk center and a lower concentration far from it. Furthermore, it is assumed that the base station (BS) is elevated to a non-scattering region and that a wave transmitted from the BS reaches the MS after a single bounce by one of the randomly distributed scatterers. Under the above-mentioned assumptions, we derive closed-form expressions for the joint probability density function (PDF) of the time-of-arrival (ToA) and angle-of-arrival (AoA), as well as for the joint PDF of the angle-of-departure (AoD) and AoA. From the joint distributions, we derive the marginal PDFs of the ToA, AoA, and AoD. Finally, we analyze the average delay and the delay spread of the proposed disk scattering model. The results presented in this paper enable the designers of cutting-edge mobile communication systems to study the system performance under simple, yet realistic, scattering conditions.