Stochastic Geometry Analysis of Spatial-Temporal Performance in Wireless Networks: A Tutorial

The performance of wireless networks is fundamentally limited by the aggregate interference, which depends on the spatial distributions of the interferers, channel conditions, and user traffic patterns (or queueing dynamics). These factors usually exhibit spatial and temporal correlations and thus make the performance of large-scale networks environment-dependent (i.e., dependent on network topology, locations of the blockages, etc.). The correlation can be exploited in protocol designs (e.g., spectrum-, load-, location-, energy-aware resource allocations) to provide efficient wireless services. For this, accurate system-level performance characterization and evaluation with spatial-temporal correlation are required. In this context, stochastic geometry models and random graph techniques have been used to develop analytical frameworks to capture the spatial-temporal interference correlation in large-scale wireless networks. The objective of this article is to provide a tutorial on the stochastic geometry analysis of large-scale wireless networks that captures the spatial-temporal interference correlation (and hence the signal-to-interference ratio (SIR) correlation). We first discuss the importance of spatial-temporal performance analysis, different parameters affecting the spatial-temporal correlation in the SIR, and the different performance metrics for spatial-temporal analysis. Then we describe the methodologies to characterize spatial-temporal SIR correlations for different network configurations (independent, attractive, repulsive configurations), shadowing scenarios, user locations, queueing behavior, relaying, retransmission, and mobility. We conclude by outlining future research directions in the context of spatial-temporal analysis of emerging wireless communications scenarios.