3GPP-Inspired HetNet Model Using Poisson Cluster Process: Sum-Product Functionals and Downlink Coverage

Abstract

The growing complexity of heterogeneous cellular networks (HetNets) has necessitated a variety of user and base station (BS) configurations to be considered for realistic performance evaluation and system design. This is directly reflected in the HetNet simulation models proposed by standardization bodies, such as the third generation partnership project (3GPP). Complementary to these simulation models, stochastic geometry-based approach, modeling the locations of the users and the K tiers of BSs as independent and homogeneous Poisson point processes (PPPs), has gained prominence in the past few years. Despite its success in revealing useful insights, this PPP-based K-tier HetNet model is not rich enough to capture spatial coupling between user and BS locations that exists in real-world HetNet deployments and is included in 3GPP simulation models. In this paper, we demonstrate that modeling a fraction of users and arbitrary number of BS tiers alternatively with a Poisson cluster process (PCP) captures the aforementioned coupling, thus bridging the gap between the 3GPP simulation models and the PPP-based analytic model for HetNets. We further show that the downlink coverage probability of a typical user under maximum signal-to-interference-ratio (SIR) association can be expressed in terms of the sum-product functionals over PPP, PCP, and its associated offspring point process, which are all characterized as a part of our analysis. We also show that the proposed model converges to the PPP-based HetNet model as the cluster size of the PCPs tends to infinity. Finally, we specialize our analysis based on general PCPs for Thomas and Matérn cluster processes. Special instances of the proposed model closely resemble the different configurations for BS and user locations considered in 3GPP simulations. Index TermsHeterogeneous cellular network, Poisson point process, Poisson cluster process, Matérn cluster process, Thomas cluster process, 3GPP.The authors are with Wireless@VT,

Simple Approximations of the SIR Meta Distribution in General Cellular Networks

“…For HCNs with non-Poisson deployments, it is often the case that it is hard to perform an exact mathematical analysis of key performance metrics such as the SIR distribution (sometimes called the coverage probability). Even if an exact expression of the SIR distribution exists, it is available in a complex form that does not help gain insights about the performance of the network for different network parameters [11]- [15].…”

Coverage Probability Analysis Under Clustered Ambient Backscatter Nodes

“…With some assumptions to the distribution (such as PPP) of the node locations, the system performance of a HetNet can be expressed by quickly computable integrals with a small number of parameters [14]. Recent studies have found that simply using a PPP based geometric model is not rich enough to analyze the increasingly complex HetNet, yet the Poisson cluster process (PCP) based analysis is more capable [15]. Some quantitative properties of PCP and PCP based device-to-device (D2D) network can be found in [15]- [18].…”

“…Recent studies have found that simply using a PPP based geometric model is not rich enough to analyze the increasingly complex HetNet, yet the Poisson cluster process (PCP) based analysis is more capable [15]. Some quantitative properties of PCP and PCP based device-to-device (D2D) network can be found in [15]- [18]. Specifically, the coverage probabilities of several HetNet configurations based on the 3rd generation partnership project (3GPP) model were studied in [15].…”

Coverage Analysis of Integrated Sub-6GHz-mmWave Cellular Networks With Hotspots

“…Although PPP is tractable in modeling random networks, it is not rich enough in capturing spatial coupling between UE and BS locations that exists in traffic hotspots [18], [19], which can be better modeled by Poisson cluster process (PCP). The PCP-based modeling and performance analysis of HetNet has gained much attention in these years [19]- [21].…”

“…The PCP-based modeling and performance analysis of HetNet has gained much attention in these years [19]- [21]. A complete characterization of the downlink coverage probability for a PCP-based HetNet model under max-SINR based association scheme is investigated in [18]. The BS-centric cellular network was analyzed in [22], in which the locations of BSs are modeled as a PPP, and the UEs are modeled as a PCP around BSs.…”