Future wireless deployments will increasingly rely on HetNets to satisfy society's demands for high data rates coupled with high cell capacities. We argue that the design and deployment of such HetNets present many challenges, which, because of the much larger space of system deployment parameters relative to a single-tier network, cannot be feasibly addressed by the traditional approaches of measurement and simulation alone.

We show that techniques and results from stochastic geometry can relieve system designers from the burden of having to perform exhaustive simulations of all feasible combinations of deployment parameters, because they yield analytical results for key performance metrics such as coverage probability, thereby permitting (a) a uniform comparison across architectures and (b) quick rejection of certain combinations of deployment parameters without needing to simulate their performance. These theoretical results are illustrated with examples of their application to transmission scenarios specified in the LTE standard.

These analytical results for coverage probability have, until now, mostly been derived for independent Poisson deployments of base stations in tiers, a scenario for which there are tractable derivations of exact expressions. Although it is well known that real-world base station deployments do not behave like Poisson deployments, we show that the Poisson model is nonetheless fundamental to an analytical treatment of all deployments, for the following reasons: (a) the set of propagation losses to the typical location in an arbitrary network deployment converge asymptotically to that from a Poisson deployment of base stations and (b) long before this asymptotic limit is reached, the coverage results for a Poisson deployment can be employed to obtain very accurate approximations to the coverage results for various regular deployments. The present work is the first book-length treatment of these results.

We also provide the first book-level exposition of exact results on coverage for certain non-Poisson deployment models that are analytically tractable. Such models include the Ginibre point process and determinantal point processes. We also discuss the challenges of understanding and evaluating the complex analytical expressions so obtained.

For future work, in addition to stochastic geometry and point process theory covered in this book, other tools from probability may also be employed to analyze cellular networks.