  We consider a general heterogeneous network in which, besides general
propagation effects (shadowing and/or fading), individual base stations can
have different emitting powers and be subject to different parameters of
Hata-like path-loss models (path-loss exponent and constant) due to, for
example, varying antenna heights. We assume also that the stations may have
varying parameters of, for example, the link layer performance (SINR threshold,
etc). By studying the propagation processes of signals received by the typical
user from all antennas marked by the corresponding antenna parameters, we show
that seemingly different heterogeneous networks based on Poisson point
processes can be equivalent from the point of view a typical user. These
neworks can be replaced with a model where all the previously varying
propagation parameters (including path-loss exponents) are set to constants
while the only trade-off being the introduction of an isotropic base station
density. This allows one to perform analytic comparisons of different network
models via their isotropic representations. In the case of a constant path-loss
exponent, the isotropic representation simplifies to a homogeneous modification
of the constant intensity of the original network, thus generalizing a previous
result showing that the propagation processes only depend on one moment of the
emitted power and propagation effects. We give examples and applications to
motivate these results and highlight an interesting observation regarding
random path-loss exponents.
