In recent years, stochastic geometry theory has become a very promising tool to analyze the performance of wireless networks. By taking into account the spatial structure of the base stations (BSs) in homogeneous cellular networks, which plays a key role in evaluating the downlink performance, the theory gives direct insights about how the geometry of the BSs affects the network performance and enables tractable analyses on the signal-to-interference-plus-noise-ratio (SINR) distributions. In this dissertation, we mainly study the SINR distributions and their properties in cellular networks.
The BSs are usually assumed to form a lattice or a Poisson point process (PPP). In reality, however, they are deployed neither fully regularly nor completely randomly. For the first step of our analyses, we use different spatial stochastic models, including the PPP, the Poisson hard-core process (PHCP), the Strauss process (SP), and the perturbed triangular lattice, to model the spatial structure by fitting them to the locations of BSs in real cellular networks obtained from a public database. We provide two general approaches for fitting and find that fitted models can be obtained whose coverage performance matches that of the given data set very accurately.
For the second step, through observations of the model fittings, we discover that the shape of the complementary cumulative distribution function (CCDF) of the SINR for essentially all motion-invariant and ergodic point processes is the same, which means the SINR distribution for general point processes (i.e., general BS distributions) can be approximated by applying a horizontal shift to the corresponding (simple or maybe tractable) result of the PPP model. We demonstrate this finding by studying the lower tail of the CCDF of the SINR, or equivalently, its high-reliability regime.
For the third step, we extend our theoretical asymptotic analyses to the upper tail of the SINR and non-simple point processes (where points can be colocated).
For the fourth step, since the independent randomness in the positions of the BSs and the propagation conditions we usually assume does not comply with the real procedure of BS deployments, we propose a new class of cellular model, where BSs are deployed to make all users at cell edges achieve a minimum required signal power level from the serving BS. The equalized received signal power at cell edges is the outcome of both the spatial structure of the BSs and the propagation model of the signals. We call such system models joint spatial and propagation (JSP) models and provide two approaches to formulating the models. The SINR distribution is evaluated. Our results show that networks with Poisson distributed BSs appear to the user like lattice networks if the dependence between BS placement and propagation is accounted for.