  In coverage-oriented networks, base stations (BSs) are deployed in a way such
that users at the cell boundaries achieve sufficient signal strength. The shape
and size of cells vary from BS to BS, since the large-scale signal propagation
conditions differ in different geographical regions. This work proposes and
studies a joint spatial-propagation (JSP) model, which considers the
correlation between cell radii and the large-scale signal propagation (captured
by shadowing). We first introduce the notion of the directional radius of
Voronoi cells, which has applications in cellular networks and beyond. The
directional radius of a cell is defined as the distance from the nucleus to the
cell boundary at an angle relative to the direction of a uniformly random
location in the cell. We study the distribution of the radii in two types of
cells in the Poisson Voronoi tessellations: the zero-cell, which contains the
origin, and the typical cell. The results are applied to analyze the JSP model.
We show that, even though the Poisson point process (PPP) is often considered
as a pessimistic spatial model for BS locations, the JSP model with the PPP
achieves coverage performance close to the most optimistic one -- the standard
triangular lattice model. Further, we show that the network performance depends
critically on the variance of the large-scale path loss along the cell
boundary.
