Cellular Networks with $$\alpha $$-Ginibre Configurated Base Stations

Miyoshi, Naoto; Shirai, Tomoyuki

doi:10.1007/978-4-431-54907-9_16

Cited by 37 publications

(54 citation statements)

References 13 publications

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“…It is an important example of the determinantal PP recently studied on the theoretical ground (see e.g. [11]) and considered in modeling applications (see [24]). Denote by G = {|X i | 2 : X i ∈ G }, the PP on R + of the squared radii of the points of G .…”

Section: 21mentioning

confidence: 99%

On Comparison of Clustering Properties of Point Processes

Błaszczyszyn

Yogeshwaran

2014

Adv. Appl. Probab.

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In this paper, we propose a new comparison tool for spatial homogeneity of point processes, based on the joint examination of void probabilities and factorial moment measures. We prove that determinantal and permanental processes, as well as, more generally, negatively and positively associated point processes are comparable in this sense to the Poisson point process of the same mean measure. We provide some motivating results on percolation and coverage processes, and preview further ones on other stochastic geometric models, such as minimal spanning forests, Lilypond growth models, and random simplicial complexes, showing that the new tool is relevant for a systemic approach to the study of macroscopic properties of non-Poisson point processes. This new comparison is also implied by the directionally convex ordering of point processes, which has already been shown to be relevant to the comparison of the spatial homogeneity of point processes. For this latter ordering, using a notion of lattice perturbation, we provide a large monotone spectrum of comparable point processes, ranging from periodic grids to Cox processes, and encompassing Poisson point processes as well. They are intended to serve as a platform for further theoretical and numerical studies of clustering, as well as simple models of random point patterns to be used in applications where neither complete regularity nor the total independence property are realistic assumptions.

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Section: 21mentioning

confidence: 99%

On Comparison of Clustering Properties of Point Processes

Błaszczyszyn

Yogeshwaran

2014

Adv. Appl. Probab.

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“…Poisson cluster process also seems a judicious model for hotspots, small cells, and device-to-device (D2D) communications. In [10], [11], the authors propose the Ginibre point process (GPP), which is one of the determinantal point processes, as a model for wireless networks whose nodes exhibit repulsion. The GPP is a softcore point process and is less regular than the lattice but more regular than the PPP.…”

Section: Introductionmentioning

confidence: 99%

Approximating the interference distribution in large wireless networks

Kountouris

Παππάς

2014

2014 11th International Symposium on Wireless Communications Systems (ISWCS)

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The spatial locations of transmitters play a cardinal role in evaluating the aggregate interference and hence the performance of large wireless networks. The most widely used approach for modeling the network geometry is the Poisson point process (PPP), mainly due to its analytical tractability. However, point process models with repulsion and inhibition, such as the Matérn hardcore process, the Strauss process, the Ginibre point process, and the Poisson cluster process, are more accurate and realistic models than the PPP for actual heterogeneous cellular network (HetNets) deployments. Nevertheless, the limited analytical tractability of the aforementioned point processes makes it difficult or even impossible to obtain closed-form analytical expressions for network performance. In this paper, we provide a framework for approximating the interference distribution in wireless networks with spatial randomness. Specifically, the distribution of aggregate interference is approximated by known probability density functions, as a means to provide simple and tractable expressions for key performance metrics, i.e. coverage probability, area spectral efficiency, and average rate. We show the effectiveness of the proposed approach in analyzing large wireless networks with nodes exhibiting attraction and inhibition.

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“…Third, many stationary DPP models can be easily simulated [8]. Fourth, DPPs have many nice mathematical properties, which lend them to the analysis of cellular network performance [10] [11].…”

Section: Introductionmentioning

confidence: 99%

Fitting determinantal point processes to macro base station deployments

Baccelli

Dhillon

et al. 2014

2014 IEEE Global Communications Conference

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The macro base station (BS) deployments in modern cellular networks are neither regular nor completely random. We use determinantal point process (DPP) models to study the repulsiveness among macro base stations observed in cellular networks. Three DPP models are fitted to base station location data sets from two major US cities. Hypothesis testing is used to validate the goodness-of-fit for these DPP models. Based on performance metrics including the K-function, the L-function and coverage probability, DPP models are shown to be accurate in modeling real BS deployments. On the contrary, the Poisson point process and perturbed hexagonal grid model are shown to be less realistic. Different DPP models are compared, and several computational properties of these models are also discussed.

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Cellular Networks with $$\alpha $$-Ginibre Configurated Base Stations

Cited by 37 publications

References 13 publications

On Comparison of Clustering Properties of Point Processes

On Comparison of Clustering Properties of Point Processes

Approximating the interference distribution in large wireless networks

Fitting determinantal point processes to macro base station deployments

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