New Trends in Stochastic Geometry for Wireless Networks: A Tutorial and Survey Yassine Hmamouche, Mustapha Benjillali, Samir Saoudi, Halim Yanikomeroglu, Marco Di Renzo To cite this version: Yassine Hmamouche, Mustapha Benjillali, Samir Saoudi, Halim Yanikomeroglu, Marco Di Renzo. New Trends in Stochastic Geometry for Wireless Networks: A Tutorial and Survey. Proceedings of the IEEE, Institute of Electrical and Electronics Engineers, 2021, 10.1109/JPROC.2021.3061778. hal-03149285 HAL Id: hal-03149285 https://hal.archives-ouvertes.fr/hal-03149285 Submitted on 22 Feb 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. 1 New Trends in Stochastic Geometry for Wireless Networks: A Tutorial and Survey Yassine Hmamouche, Member, IEEE, Mustapha Benjillali, Senior Member, IEEE, Samir Saoudi, Senior Member, IEEE, Halim Yanikomeroglu, Fellow, IEEE, and Marco Di Renzo, Fellow, IEEE GLOSSARY Abstract—Next generation wireless networks are expected to be highly heterogeneous, multi-layered, with embedded intelligence µWave microwave at both the core and edge of the network. In such a context, 3GPP 3rd generation partnership project system-level performance evaluation will be very important to AF Amplify-and-forward formulate relevant insights into tradeoffs that govern such a AoI Age of information complex system. Over the past decade, stochastic geometry (SG) ASE Area spectral efficiency has emerged as a powerful analytical tool to evaluate system-level AtG Air-to-ground performance of wireless networks and capture their tendency AWGN Additive white Gaussian noise towards heterogeneity. However, with the imminent onset of this B5G Beyond 5G crucial new decade, where global commercialization of fifth- BBU Baseband unit generation (5G) is expected to emerge and essential research BPM Bounded path loss model BPP Binomial point process questions related to beyond fifth-generation (B5G) are intended CAPEX Capital expenditure to be identified, we are wondering about the role that a powerful CoMP Coordinated multipoint tool like SG should play. In this paper, we first aim to track C-plane Control plane and summarize the novel SG models and techniques developed CR Cognitive radio during the last decade in the evaluation of wireless networks. C-RAN Cloud radio access network Next, we will outline how SG has been used to capture the CRE Cell range expansion properties of emerging radio access networks (RANs) for 5G/B5G D2D Device-to-device and quantify the benefits of key enabling technologies. Finally, DAS Distributed antenna system we will discuss new horizons that will breathe new life into dcx Directionally convex the use of SG in the foreseeable future. For instance, using DF Decode-and-forward SG to evaluate performance metrics in the visionary paradigm DPP Determinantal point process of molecular communications. Also, we will review how SG is DUDA Decoupled uplink-downlink access envisioned to cooperate with machine learning seen as a crucial EE Energy effeciency component in the race towards ubiquitous wireless intelligence. EM Electromagnetic Another important insight is Grothendieck toposes considered eMBB enhanced mobile broadband as a powerful mathematical concept that can help to solve long- F-RAN Fog radio access network standing problems formulated in SG. FSO Free space optical Index Terms—Fifth-generation (5G) and beyond fifth- GPP Ginibre point process generation (B5G) networks, point process theory, signal-to- GSPP Geyer saturation point process interference-and-noise-ratio, stochastic geometry. HD Half duplex HetNet Heterogeneous network HPPP Homogeneous Poisson point process I. INTRODUCTION IBFD In-band full-duplex Stochastic geometry (SG) is a field of applied probabil- ICIC Intercell interference coordination IDT Inhomogeneous double thinning ity that aims to provide tractable mathematical models and IoT Internet of things appropriate statistical methods to study and analyze random IPPP Inhomogeneous Poisson point process phenomena on the plane R2 or in larger dimensions [1]. Its LED Light-emitting diode development was driven by applications in several scientific LGCP Log-Gaussian Cox process areas such as forestry, image analysis, geophysics, neurophys- LOS Line-of-sight MAC Medium access control iology, cardiology, finance, and economics. In the context MC Molecular communication MCMC Markov chain Monte Carlo Y. Hmamouche and S. Saoudi are with Mathematical and Electrical Engineering Department, IMT-Atlantique, Lab-STICC, UMR CNRS 6285, MCP Mat´ern cluster process F-29238, France. MGF Moment generating function (e-mail: {yassine.hmamouche, samir.saoudi}@imt-atlantique.fr). MHPP Mat´ern hard-core point process M. Benjillali is with the Department of Communication Systems, INPT, Rabat MIMO Multiple-input and multiple-output 10100, Morocco. (e-mail: [email protected]). ML Machine learning H. Yanikomeroglu is with the Department of Systems and Computer En- mmWave Millimeter wave gineering, Carleton University, Ottawa, ON K1S 5B6, Canada. (e-mail: NLOS Non-line-of-sight [email protected]). NOMA Non-orthogonal multiple access M. Di Renzo is with Universit´eParis-Saclay, CNRS, CentraleSup´elec, Lab- OPEX Operational expenditure oratoire des Signaux et Syst`emes, 3 Rue Joliot-Curie, 91192 Gif-sur-Yvette, PCP Poisson cluster process France. (e-mail: [email protected]). This work was supported by Pˆole de Recherche Avanc´ee en Communications PDF Probability density function (PRACOM) and the Regional Council of Brittany, France. PGFL Probability generating functional 2 PHCP Poisson hard-core process paradox3 (1889). A short historical outline of these early days PHP Poisson hole process PL Perturbed lattice of geometric probability may be found in [9]. PLP Poisson line process Since the 1950s, the framework of geometric probability PMF Probability mass function broadened substantially and framed as an academic area. In PP Point process particular, the focus mainly switched to models involving a PPP Poisson point process typical number of randomly selected geometric objects. As a RAN Radio access network RIS Reconfigurable intelligent surface consequence, the four distinguishable mathematical strands of RN Relay node integral geometry theory [10], random set theory [11], random ROI Return on investment measures theory [12], and point process (PP) theory [4]–[8] RRH Remote radio head started to play a prominent role in the geometric probability, RWP Random waypoint which since then was called stochastic geometry. Integral SDN Software-defined networking SG Stochastic geometry geometry gives a unified approach for defining integrands over SI Self interference curves, surfaces, volumes, and higher-dimensional manifolds SIC Successive interference cancellation by using tools from probability theory, group theory, and SINR Signal-to-interference-plus-noise ratio projective geometry. Random sets generalizes the concept of SPP Strauss point process random vectors, by addressing random entities whose number SSI Simple sequential inhibition SWIPT Simultaneous wireless information and power transfer of components is unknown. Random measures theory is fo- TCP Thomas cluster process cused on studying the properties of measures established on UAV Unmanned aerial vehicles random elements. In the special case where these measures UDN Ultra-dense network are integer-valued, random measures reduce to PPs considered UE User equipment as an important subclass of random measures. Discussions on U-plane User plane UPM Unbounded path loss model how early problems on geometrical probability have led to the URLLC Ultra-reliable and low latency communications construction of primary results on these pillar theories of SG, VAD Voronoi area distribution can be found in [13]. Moreover, for the sake of exploratory VANET Vehicular ad hoc network data analysis, parameter estimation, and model fitting, SG VLC Visible light communications has been endowed with a statistical theory in similarity with of communication networks, the location of user equipment the traditional probability theory. More statistical analysis and (UE) and base stations (BSs) are scattered randomly over an parameters estimation can be found in [14]. enormous number of possibilities, where designing the system In the context of communication networks, the paper [15] for every network realization would be time-consuming and is the first to consider tools from SG to evaluate connectivity resource-intensive [2], [3]. Instead, using tools from SG [1]– in a network of stations represented by a Poisson point [8], the location of nodes (i.e., UEs and/or BSs) is assessed process (PPP). In particular, it was only by the late 1990s statistically in order to study the interaction between them, that important ideas from SG found their way to modeling which inherently considers all possible network realizations and analysis of communication networks [2], [3], where tools and generally capture the main dependencies of the network based on Poisson Voronoi tessellations and Delaunay trian- performance