New Trends in Stochastic Geometry for Wireless Networks: A Tutorial and Survey

Next-generation wireless networks are expected to be highly heterogeneous, multilayered, with embedded intelligence at both the core and edge of the network. In such a context, system-level performance evaluation will be very important to formulate relevant insights into tradeoffs that govern such a complex system. Over the past decade, SG has emerged as a powerful analytical tool to evaluate the system-level performance of wireless networks and capture their tendency toward heterogeneity. However, with the imminent onset of this crucial new decade, where global commercialization of fifth generation (5G) is expected to emerge and essential research questions related to beyond 5G (B5G) are intended to be identified, we are wondering about the role that a powerful tool, such as SG, should play. In this article, we first aim to track and summarize the novel SG models and techniques developed during the last decade in the evaluation of wireless networks. Next, we will outline how SG has been used to capture the properties of emerging RANs for 5G/B5G and quantify the benefits of key enabling technologies. Finally, we will discuss new horizons that will breathe new life into the use of SG in the foreseeable future, for instance, using SG to evaluate performance metrics in the visionary paradigm of molecular communications. Also, we will review how SG is envisioned to cooperate with machine learning that is seen as a crucial component in the race toward ubiquitous wireless intelligence. Another important insight is Grothendieck's toposes, which is considered as a powerful mathematical concept that can help to solve long-standing problems formulated in SG.