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.