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

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 explicity 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.