An Exact Path-Loss Density Model for Mobiles in a Cellular System

In trying to emulate the spatial position of wireless nodes for purpose of analysis, we rely on stochastic simulation. And, it is customary, for mobile systems, to consider a base-station radiation coverage by an ideal cell shape. For cellular analysis, a hexagon contour is always preferred mainly because of its tessellating nature. Despite this fact, largely due to its intrinsic simplicity, in literature only random dispersion model for a circular shape is known. However, if considered, this will result an unfair nodes density specifically at the edges of non-circular contours. As a result, in this paper, we showed the exact random number generation technique required for nodes scattering inside a hexagon. Next, motivated from a system channel perspective, we argued the need for the exhaustive random mobile dropping process, and hence derived a generic closed-form expression for the path-loss distribution density between a base-station and a mobile. Last, simulation was used to reaffirm the validity of the theoretical analysis using values from the new IEEE 802.20 standard.