Exact characterization and performance analysis of wireless networks should incorporate dependencies or correlations in space and time, i.e., study how the network performance varies spatially and temporally while having prior information about the performance at previous locations and time slots. This spatio-temporal correlation in wireless networks is usually characterized by studying metrics such as joint coverage probability at two spatial locations/time slots or spatio-temporal correlation coefficient. While developing models and analytical expressions for studying the two extreme cases of spatio-temoral correlation - i) uncorrelated scenario and ii) fully correlated scenario are easier, studying the intermediate case is non-trivial. In this thesis, we develop realistic and tractable analytical frameworks based on random spatial models (using tools from stochastic geometry) for modeling and analysis of correlation in cellular networks.

With an ever increasing data demand, caching popular content in the storage of small cells (small cell caching) or the memory of user devices (device caching) is seen as a good alternative to offload demand from macro base stations and reduce backhaul loads. After providing generic results for traditional cellular networks, we study two applications exploiting spatio-temporal correlation in cache-enabled cellular networks. First, we determine the optimal cache content to be stored in the cache of a small cell network that maximizes the hit probability and minimizes the reception energy for the two extreme cases of correlation. Our results concretely demonstrate that the optimal cache contents are significantly different for the two correlation scenarios, thereby indicating the need of correlation-aware caching strategies. Second, we look at a distributed caching scenario in user devices and show that spatio-temporal correlation (user mobility) can be exploited to improve the network performance (in terms of coverage probability and local delay) significantly.