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

TL;DR

This paper develops an exact mathematical model for path-loss distribution in cellular systems with hexagonal coverage, improving simulation accuracy by addressing node placement and path-loss analysis.

Contribution

It introduces a precise random node scattering method within a hexagonal cell and derives a closed-form expression for path-loss distribution, enhancing cellular system modeling.

Findings

Validated the model with IEEE 802.20 standard data

Provided an exact path-loss density expression for hexagonal cells

Improved simulation accuracy for mobile node placement

Abstract

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 close-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.