Distribution of the uplink multipaths' arrival delay and azimuth-elevation arrival angle because of 'bad urban' scatterers distributed cylindrically above the mobile

For radiowave landmobile cellular wireless communication in 'bad urban' environments dominated by high rises, this paper analytically derives closed-form expressions for the trivariate and bivariate joint distributions of the time-of-arrival and two-dimensional azimuth-elevation direction-of-arrival of the uplink multipaths. These expressions are explicitly in terms of the parameters of a 'geometrical' model of the three-dimensional spatial relationships among the mobile station, the scatterers and the base station. This present 'geometric model' idealises the scatterers as uniformly located within the volume of a three-dimensional vertical above-ground cylinder whose flat bottom circular base centres at the mobile.