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

Abstract

Next generation wireless networks are expected to be highly heterogeneous, multi-layered, 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, stochastic geometry (SG) has emerged as a powerful analytical tool to evaluate system-level performance of wireless networks and capture their tendency towards heterogeneity. However, with the imminent onset of this crucial new decade, where global commercialization of fifthgeneration (5G) is expected to emerge and essential research questions related to beyond fifth-generation (B5G) are intended to be identified, we are wondering about the role that a powerful tool like SG should play. In this paper, 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 radio access networks (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 seen as a crucial component in the race towards ubiquitous wireless intelligence. Another important insight is Grothendieck toposes considered as a powerful mathematical concept that can help to solve longstanding problems formulated in SG.

On the Topological Aspects of UAV-Assisted Post-Disaster Wireless Communication Networks

“…We model the locations of the nodes as point processes (PPs), which is a common assumption in literature [2], [15]. In relation to Sec.…”

Fresnel Line-of-Sight Probability With Applications in Airborne Platform-Assisted Communications

“…In addition, the role of airborne platforms in modern wireless networks is rapidly growing and emerging as a key enabler for 5G/B5G communication requirements [2]. Indeed, 3GPP has considered aerial platforms as a new radio access for 5G as embodied in the standardization documents TR 38.811 [3], TR 22.829 [4], and TS 22.125 [5]. In this way, unmanned aerial vehicles (UAVs) operating at low altitudes of a few hundred meters can act as flexible and agile relays, base stations (BSs), or user equipments (UEs) (e.g., cargo delivery, aerial surveillance, IoT data gathering), while high-altitude platform stations (HAPSs) operating at higher altitudes of 8 to 50 km above the ground can offer longer flight times compared to UAVs, wider coverage areas, and transmission links between BSs and the core network for the backhauling traffic [6].…”

“…In particular, such elaborate LoS probability expressions preclude a more thorough system-level performance evaluation of airborne platform-assisted communications. Actually, considering the abstraction under a powerful analytical tool such as stochastic geometry [22], these models fail to derive the following integral…”

“…which is necessary to obtain, based on the concept of independent thinning of the Poisson point process (PPP) [22], the spatial intensity of nodes in LoS and non lineof-sight (NLoS) conditions with the typical UE, and then to calculate the probability density function (PDF) of the horizontal distance between the typical UE and the nearest node in LoS and NLoS transmission. These PDFs are in turn essential for the evaluation of key performance metrics, such as coverage probability and ergodic rate.…”

“…The developed LoS probability enables to derive a closed-form expression of the PDF of the horizontal distance between the typical ground UE and the best aerial platform in terms of the lowest path loss association scheme. Using tools from stochastic geometry [22], we are able to evaluate the coverage probability for both fixed/deterministic and random PPP-distributed UAV/HAPS locations around the typical ground UE.…”