Equivalence and comparison of heterogeneous cellular networks

TL;DR

This paper demonstrates that heterogeneous cellular networks with varying parameters can be equivalently represented by simpler models with constant parameters and adjusted base station density, facilitating analysis and comparison.

Contribution

The authors establish a framework showing the equivalence of complex heterogeneous networks to simplified models with constant parameters, enabling easier analytical comparisons.

Findings

Heterogeneous networks can be replaced by equivalent models with constant parameters.

The simplified models depend on a single moment of the original parameters.

Results extend to networks with random path-loss exponents.

Abstract

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.