Spatial stochastic models for analysis of heterogeneous cellular networks with repulsively deployed base stations

Nakata, Itaru; Miyoshi, Naoto

doi:10.1016/j.peva.2014.05.002

Cited by 52 publications

(42 citation statements)

References 20 publications

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“…Further, since intra-tier coupling can be either attractive or repulsive, no single point process is the best choice for capturing it. For modeling repulsions, Matérn hard-core process [20], [21], Gauss-Poisson process [22], Strauss hardcore process [23], Ginibre point process [24], [25], and more general determinantal point processes [26] have been used for BS distributions. On the other hand, for modeling attraction, PCP [11] and Geyer saturation process [23] have been proposed.…”

Section: A Background and Related Workmentioning

confidence: 99%

Unified Analysis of HetNets Using Poisson Cluster Processes Under Max-Power Association

Saha

Dhillon

Miyoshi

et al. 2019

IEEE Trans. Wireless Commun.

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Owing to its flexibility in modeling real-world spatial configurations of users and base stations (BSs), the Poisson cluster process (PCP) has recently emerged as an appealing way to model and analyze heterogeneous cellular networks (HetNets). Despite its undisputed relevance to HetNets -corroborated by the models used in industry -the PCP's use in performance analysis has been limited. This is primarily because of the lack of analytical tools to characterize performance metrics such as the coverage probability of a user connected to the strongest BS. In this paper, we develop an analytical framework for the evaluation of the coverage probability, or equivalently the complementary cumulative density function (CCDF) of signal-to-interference-and-noise-ratio (SINR), of a typical user in a K-tier HetNet under a max power-based association strategy, where the BS locations of each tier follow either a Poisson point process (PPP) or a PCP. The key enabling step involves conditioning on the parent PPPs of all the PCPs which allows us to express the coverage probability as a product of sum-product and probability generating functionals (PGFLs) of the parent PPPs. In addition to several useful insights, our analysis provides a rigorous way to study the impact of the cluster size on the SINR distribution, which was not possible using existing PPP-based models. Index TermsHeterogeneous cellular network, 3GPP, Poisson cluster process, Thomas cluster process, Matérn cluster process.

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Section: A Background and Related Workmentioning

confidence: 99%

Unified Analysis of HetNets Using Poisson Cluster Processes Under Max-Power Association

Saha

Dhillon

Miyoshi

et al. 2019

IEEE Trans. Wireless Commun.

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“…Finally, when we use the Ginibre and other determinantal point processes as the models of BS deployments, we might face to a computation problem. Although the obtained formulas are indeed numerically computable, as seen in (16)- (19) and (24a)-(24d), they include infinite sums and infinite products, which may lead to the time-consuming computation. One direction to avoid this problem could be some kinds of asymptotics and/or approximation (see, e.g., [18,21,38,39,40] for this direction).…”

Section: Resultsmentioning

confidence: 99%

“…For α ∈ (0, 1], a determinantal point process Φ α on C (≃ R 2 ) is said to be an α-Ginibre point process when its kernel K α on C × C is given by right) point processes with the same intensity. [19] with respect to the modified Gaussian measure…”

Section: α-Ginibre Point Processesmentioning

confidence: 99%

Spatial Modeling and Analysis of Cellular Networks Using the Ginibre Point Process: A Tutorial

Miyoshi

Shirai

2016

IEICE Trans. Commun.

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SUMMARY Spatial stochastic models have been much used for performance analysis of wireless communication networks. This is due to the fact that the performance of wireless networks depends on the spatial configuration of wireless nodes and the irregularity of node locations in a real wireless network can be captured by a spatial point process. Most works on such spatial stochastic models of wireless networks have adopted homogeneous Poisson point processes as the models of wireless node locations. While this adoption makes the models analytically tractable, it assumes that the wireless nodes are located independently of each other and their spatial correlation is ignored. Recently, the authors have proposed to adopt the Ginibre point process -one of the determinantal point processes -as the deployment models of base stations (BSs) in cellular networks. The determinantal point processes constitute a class of repulsive point processes and have been attracting attention due to their mathematically interesting properties and efficient simulation methods. In this tutorial, we provide a brief guide to the Ginibre point process and its variant, α-Ginibre point process, as the models of BS deployments in cellular networks and show some existing results on the performance analysis of cellular network models with α-Ginibre deployed BSs. The authors hope the readers to use such point processes as a tool for analyzing various problems arising in future cellular networks.

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“…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].…”

Section: B Related Workmentioning

confidence: 99%

Simple Approximations of the SIR Meta Distribution in General Cellular Networks

Kalamkar

Haenggi

2019

IEEE Trans. Commun.

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Compared to the standard success (coverage) probability, the meta distribution of the signal-to-interference ratio (SIR) provides much more fine-grained information about the network performance. We consider general heterogeneous cellular networks (HCNs) with base station tiers modeled by arbitrary stationary and ergodic non-Poisson point processes. The exact analysis of non-Poisson network models is notoriously difficult, even in terms of the standard success probability, let alone the meta distribution. Hence we propose a simple approach to approximate the SIR meta distribution for non-Poisson networks based on the ASAPPP ("approximate SIR analysis based on the Poisson point process") method. We prove that the asymptotic horizontal gap G0 between its standard success probability and that for the Poisson point process exactly characterizes the gap between the bth moment of the conditional success probability, as the SIR threshold goes to 0. The gap G0 allows two simple approximations of the meta distribution for general HCNs: 1) the per-tier approximation by applying the shift G0 to each tier and 2) the effective gain approximation by directly shifting the meta distribution for the homogeneous independent Poisson network. Given the generality of the model considered and the finegrained nature of the meta distribution, these approximations work surprisingly well.Index Terms-Interference, heterogeneous cellular networks, meta distribution, Poisson point process, signal-to-interference ratio, stochastic geometry S. S. Kalamkar is with INRIA, Paris, France. M. Haenggi is with the

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Spatial stochastic models for analysis of heterogeneous cellular networks with repulsively deployed base stations

Cited by 52 publications

References 20 publications

Unified Analysis of HetNets Using Poisson Cluster Processes Under Max-Power Association

Unified Analysis of HetNets Using Poisson Cluster Processes Under Max-Power Association

Spatial Modeling and Analysis of Cellular Networks Using the Ginibre Point Process: A Tutorial

Simple Approximations of the SIR Meta Distribution in General Cellular Networks

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