A geometrical model for the toa distribution of uplink/downlink multipaths, assuming scatterers with a conical spatial density

Abstract

The time-of-arrival (TOA) distributions of the uplink and downlink multipath are analytically derived in this paper. This is based on geometrical models that simplify the spatial relationship among a mobile transceiver, the scatterers, and a base-station transceiver. These models idealize the scatterers as lying on a circular disc centered around the mobile transceiver, with these scatterers concentrating in a conically shaped spatial density. The base-station transceiver may lie either among these scatterers (in an indoor propagation environment) or outside this disc of scatterers (for an elevated base-station outdoor receiver). In contrast to the customary uniform-disc density, this "conical" scatterer density indirectly accounts for the multipath scattering power loss. These new TOA distribution formulas, herein derived explicitly in terms of the model's only two independent parameters, can better fit some empirical data than can all earlier models that also confine all scatterers to within a circular disc.

Time of Arrival and Angle of Arrival Statistics for Distant Circular Scattering Model

“…To identify the support region of θ at a specificτ, there exists a τ-constant spatial ellipse focusing at the base station's and the mobile station's spatial locations, any propagation path must bounce off a scatterer lying on this ellipse's rim, this elliptical rim intersects with the circle (within which the scatterers lie) at two points at most [12] , that is θ satisfying the following relation for a specific time delay τ:…”

“…Circular scattering model [4,5], the density of scatterers within a circular region about MS has been assumed to be uniform, this model was assumed to be most valid in macrocell environments where the antenna heights of the base station (BS) are relatively high without signal scattering from location near BS. Elliptical scattering model [6], where the scatterers are uniformly distributed within an elliptical region with foci at BS and MS respectively, this model was assumed valid in micro or picocell types of environments where the angular spread tends to be high and the delay spread tends to be low.…”