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

Abstract

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 spatio-temporal correlation are required. In this context, stochastic geometry models and random graph techniques have been used to develop analytical frameworks to capture the spatio-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 spatio-temporal interference correlation (and hence the signal-to-interference ratio (SIR) correlation). We first discuss the importance of spatiotemporal performance analysis, different parameters affecting the spatio-temporal correlation in the SIR, and the different performance metrics for spatio-temporal analysis. Then we describe the methodologies to characterize spatio-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 spatiotemporal analysis of emerging wireless communications scenarios.

Reliability and User-Plane Latency Analysis of mmWave Massive MIMO for Grant-Free URLLC Applications

“…Stochastic geometry has become the de facto tool for analyzing large networks [31]- [33], and has been successfully used to investigate the performance of MIMO systems for a while now [34]- [37]. In [38], a unified stochastic geometric mathematical model for MIMO cellular networks with retransmission is proposed.…”

“…The Laplace transform of the interference can be derived as (31), shown at the top of the next page. Unfortunately, obtaining a closed-form expression for the expectation in (31) is not mathematically tractable. Therefore, we first obtain a suitable approximation to the Fejer kernel.…”

“…The quadratic approximation in (32) renders the derivation of the expectation in (31) tractable. Furthermore, it ensures that f K (x) = 0 whenever x / ∈ −…”