This dissertation takes a probabilistic approach to analyze cellular networks, with an emphasis on the spatial aspect. This approach is substantiated by the increasingly dense and irregular deployment of base stations as well as the need for tractability for advanced network analysis. For instance, in recent developments, the ultra-reliable and low-latency communications (URLLC) is introduced as a keystone to support mission-critical applications; there is also a shift of emphasis from the average/peak performance to a seamless user experience. These developments require guaranteed performance at the link level under varied propagation conditions, interference, and so on. To model these variations, the framework of stochastic geometry is developed, with the primary goal of refining the network analysis to the link level.
Previously, network metrics are often analyzed in ways that obscure the effects of multiple sources of spatial and temporal randomness. An important example is the success probability, defined through the distribution of the signal-to-interference-plus-noise ratio (SINR). The SINR is subject to randomness both temporally and spatially, including the small-scale fading and the large-scale propagation loss. Distinguishing their effects is a crucial step towards the analysis of next-generation networks.
The dissertation consists of three parts. In the first part, we study the SINR meta distribution, which defines the individual link reliability by first conditioning on the spatial locations of base stations. Exploiting the independence between the small-scale fading and large-scale path loss, we derive the separability of the meta distributions for arbitrary fading. In the second part, we quantify the performance gap between the typical user and the cell edge users; then we investigate cooperative transmissions to improve the performance of the latter. The last part focuses on the correlation between the irregular base station deployment and the large-scale propagation conditions. We show that properly accounting for this correlation reveals a critical deployment gain over models that ignore the dependence.