Geographic locations of cellular base stations sometimes can be well fitted
with spatial homogeneous Poisson point processes. In this paper we make a
complementary observation: In the presence of the log-normal shadowing of
sufficiently high variance, the statistics of the propagation loss of a single
user with respect to different network stations are invariant with respect to
their geographic positioning, whether regular or not, for a wide class of
empirically homogeneous networks. Even in perfectly hexagonal case they appear
as though they were realized in a Poisson network model, i.e., form an
inhomogeneous Poisson point process on the positive half-line with a power-law
density characterized by the path-loss exponent. At the same time, the
conditional distances to the corresponding base stations, given their observed
propagation losses, become independent and log-normally distributed, which can
be seen as a decoupling between the real and model geometry. The result applies
also to Suzuki (Rayleigh-log-normal) propagation model. We use
Kolmogorov-Smirnov test to empirically study the quality of the Poisson
approximation and use it to build a linear-regression method for the
statistical estimation of the value of the path-loss exponent
