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Journal ArticleDOI

Modeling Heterogeneous Network Interference Using Poisson Point Processes

01 Aug 2013-IEEE Transactions on Signal Processing (IEEE)-Vol. 61, Iss: 16, pp 4114-4126
TL;DR: This paper proposes to analyze downlink performance in a fixed-size cell, which is inscribed within a weighted Voronoi cell in a Poisson field of interferers, using recent applications of stochastic geometry to analyze cellular systems.
Abstract: Cellular systems are becoming more heterogeneous with the introduction of low power nodes including femtocells, relays, and distributed antennas. Unfortunately, the resulting interference environment is also becoming more complicated, making evaluation of different communication strategies challenging in both analysis and simulation. Leveraging recent applications of stochastic geometry to analyze cellular systems, this paper proposes to analyze downlink performance in a fixed-size cell, which is inscribed within a weighted Voronoi cell in a Poisson field of interferers. A nearest out-of-cell interferer, out-of-cell interferers outside a guard region, and cross-tier interferers are included in the interference calculations. Bounding the interference power as a function of distance from the cell center, the total interference is characterized through its Laplace transform. An equivalent marked process is proposed for the out-of-cell interference under additional assumptions. To facilitate simplified calculations, the interference distribution is approximated using the Gamma distribution with second order moment matching. The Gamma approximation simplifies calculation of the success probability and average rate, incorporates small-scale and large-scale fading, and works with co-tier and cross-tier interference. Simulations show that the proposed model provides a flexible way to characterize outage probability and rate as a function of the distance to the cell edge.
Citations
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Journal ArticleDOI
TL;DR: A general framework to evaluate the coverage and rate performance in mmWave cellular networks is proposed, and the results show that dense mmWave networks can achieve comparable coverage and much higher data rates than conventional UHF cellular systems, despite the presence of blockages.
Abstract: Millimeter wave (mmWave) holds promise as a carrier frequency for fifth generation cellular networks. Because mmWave signals are sensitive to blockage, prior models for cellular networks operated in the ultra high frequency (UHF) band do not apply to analyze mmWave cellular networks directly. Leveraging concepts from stochastic geometry, this paper proposes a general framework to evaluate the coverage and rate performance in mmWave cellular networks. Using a distance-dependent line-of-site (LOS) probability function, the locations of the LOS and non-LOS base stations are modeled as two independent non-homogeneous Poisson point processes, to which different path loss laws are applied. Based on the proposed framework, expressions for the signal-to-noise-and-interference ratio (SINR) and rate coverage probability are derived. The mmWave coverage and rate performance are examined as a function of the antenna geometry and base station density. The case of dense networks is further analyzed by applying a simplified system model, in which the LOS region of a user is approximated as a fixed LOS ball. The results show that dense mmWave networks can achieve comparable coverage and much higher data rates than conventional UHF cellular systems, despite the presence of blockages. The results suggest that the cell size to achieve the optimal SINR scales with the average size of the area that is LOS to a user.

1,342 citations


Cites background from "Modeling Heterogeneous Network Inte..."

  • ...There have been several extensions of the results in [16], such as analyzing a multi-tier network in [1 8] and predicting the site-specific performance in heterogene ous networks in [19]....

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Journal ArticleDOI
TL;DR: This article presents a comprehensive survey on the literature related to stochastic geometry models for single-tier as well as multi-tier and cognitive cellular wireless networks, and discusses the open research challenges and future research directions.
Abstract: For more than three decades, stochastic geometry has been used to model large-scale ad hoc wireless networks, and it has succeeded to develop tractable models to characterize and better understand the performance of these networks. Recently, stochastic geometry models have been shown to provide tractable yet accurate performance bounds for multi-tier and cognitive cellular wireless networks. Given the need for interference characterization in multi-tier cellular networks, stochastic geometry models provide high potential to simplify their modeling and provide insights into their design. Hence, a new research area dealing with the modeling and analysis of multi-tier and cognitive cellular wireless networks is increasingly attracting the attention of the research community. In this article, we present a comprehensive survey on the literature related to stochastic geometry models for single-tier as well as multi-tier and cognitive cellular wireless networks. A taxonomy based on the target network model, the point process used, and the performance evaluation technique is also presented. To conclude, we discuss the open research challenges and future research directions.

1,065 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a mathematical framework to model random blockages and analyze their impact on cellular network performance, and showed that the probability of a link not intersecting by any blockages decays exponentially with the link length.
Abstract: Large-scale blockages such as buildings affect the performance of urban cellular networks, especially at higher frequencies. Unfortunately, such blockage effects are either neglected or characterized by oversimplified models in the analysis of cellular networks. Leveraging concepts from random shape theory, this paper proposes a mathematical framework to model random blockages and analyze their impact on cellular network performance. Random buildings are modeled as a process of rectangles with random sizes and orientations whose centers form a Poisson point process on the plane. The distribution of the number of blockages in a link is proven to be a Poisson random variable with parameter dependent on the length of the link. Our analysis shows that the probability that a link is not intersected by any blockages decays exponentially with the link length. A path loss model that incorporates the blockage effects is also proposed, which matches experimental trends observed in prior work. The model is applied to analyze the performance of cellular networks in urban areas with the presence of buildings, in terms of connectivity, coverage probability, and average rate. Our results show that the base station density should scale superlinearly with the blockage density to maintain the network connectivity. Our analyses also show that while buildings may block the desired signal, they may still have a positive impact on the SIR coverage probability and achievable rate since they can block significantly more interference.

650 citations

Journal ArticleDOI
TL;DR: In this article, a tutorial on stochastic geometry-based analysis for cellular networks is presented, which is distinguished by its depth with respect to wireless communication details and its focus on cellular networks.
Abstract: This paper presents a tutorial on stochastic geometry (SG)-based analysis for cellular networks. This tutorial is distinguished by its depth with respect to wireless communication details and its focus on cellular networks. This paper starts by modeling and analyzing the baseband interference in a baseline single-tier downlink cellular network with single antenna base stations and universal frequency reuse. Then, it characterizes signal-to-interference-plus-noise-ratio and its related performance metrics. In particular, a unified approach to conduct error probability, outage probability, and transmission rate analysis is presented. Although the main focus of this paper is on cellular networks, the presented unified approach applies for other types of wireless networks that impose interference protection around receivers. This paper then extends the unified approach to capture cellular network characteristics (e.g., frequency reuse, multiple antenna, power control, etc.). It also presents numerical examples associated with demonstrations and discussions. To this end, this paper highlights the state-of-the-art research and points out future research directions.

397 citations

Posted Content
TL;DR: In this paper, a random network model based on stochastic geometry and distributed power control algorithms are proposed to ensure the cellular users have sufficient coverage probability by limiting the interference created by underlaid D2D users.
Abstract: This paper considers a device-to-device (D2D) underlaid cellular network where an uplink cellular user communicates with the base station while multiple direct D2D links share the uplink spectrum. This paper proposes a random network model based on stochastic geometry and develops centralized and distributed power control algorithms. The goal of the proposed power control algorithms is two-fold: ensure the cellular users have sufficient coverage probability by limiting the interference created by underlaid D2D users, while also attempting to support as many D2D links as possible. For the distributed power control method, expressions for the coverage probabilities of cellular and D2D links are derived and a lower bound on the sum rate of the D2D links is provided. The analysis reveals the impact of key system parameters on the network performance. For example, the bottleneck of D2D underlaid cellular networks is the cross-tier interference between D2D links and the cellular user, not the D2D intra-tier interference. Numerical results show the gains of the proposed power control algorithms and accuracy of the analysis.

379 citations

References
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Reference BookDOI
TL;DR: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool as discussed by the authors, and it can be found in many libraries.
Abstract: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool.

4,083 citations


"Modeling Heterogeneous Network Inte..." refers methods in this paper

  • ...convenient to compute it using the truncated series definition [46], [47] while for larger values of the asymptotic expression can be employed [48]....

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Book
18 Jul 1996
TL;DR: Random Closed Sets I--The Boolean Model. Random Closed Sets II--The General Case.
Abstract: Mathematical Foundation. Point Processes I--The Poisson Point Process. Random Closed Sets I--The Boolean Model. Point Processes II--General Theory. Point Processes III--Construction of Models. Random Closed Sets II--The General Case. Random Measures. Random Processes of Geometrical Objects. Fibre and Surface Processes. Random Tessellations. Stereology. References. Indexes.

4,079 citations

Journal ArticleDOI
TL;DR: The proposed model is pessimistic (a lower bound on coverage) whereas the grid model is optimistic, and that both are about equally accurate, and the proposed model may better capture the increasingly opportunistic and dense placement of base stations in future networks.
Abstract: Cellular networks are usually modeled by placing the base stations on a grid, with mobile users either randomly scattered or placed deterministically. These models have been used extensively but suffer from being both highly idealized and not very tractable, so complex system-level simulations are used to evaluate coverage/outage probability and rate. More tractable models have long been desirable. We develop new general models for the multi-cell signal-to-interference-plus-noise ratio (SINR) using stochastic geometry. Under very general assumptions, the resulting expressions for the downlink SINR CCDF (equivalent to the coverage probability) involve quickly computable integrals, and in some practical special cases can be simplified to common integrals (e.g., the Q-function) or even to simple closed-form expressions. We also derive the mean rate, and then the coverage gain (and mean rate loss) from static frequency reuse. We compare our coverage predictions to the grid model and an actual base station deployment, and observe that the proposed model is pessimistic (a lower bound on coverage) whereas the grid model is optimistic, and that both are about equally accurate. In addition to being more tractable, the proposed model may better capture the increasingly opportunistic and dense placement of base stations in future networks.

3,309 citations


"Modeling Heterogeneous Network Inte..." refers background or methods in this paper

  • ...In [10] PPPs are used to model various components of a telecommunications network including subscriber locations, base station locations, as well as network infrastructure leveraging results on Voronoi tessellation....

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  • ...We also demonstrate how to employ the proposed fixed cell analysis in a heterogeneous network consisting of mixtures of the different kinds of infrastructure....

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  • ...Further, as urban areas are built out, even macro and micro base station infrastructure is becoming less like points on a hexagonal lattice and more random [5]....

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  • ...Alternatively, if it is desired to analyze a “typical” fixed cell, the radius could be chosen to be a function of the density....

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Journal ArticleDOI
TL;DR: The technical and business arguments for femtocells are overview and the state of the art on each front is described and the technical challenges facing femtocell networks are described and some preliminary ideas for how to overcome them are given.
Abstract: The surest way to increase the system capacity of a wireless link is by getting the transmitter and receiver closer to each other, which creates the dual benefits of higher-quality links and more spatial reuse. In a network with nomadic users, this inevitably involves deploying more infrastructure, typically in the form of microcells, hot spots, distributed antennas, or relays. A less expensive alternative is the recent concept of femtocells - also called home base stations - which are data access points installed by home users to get better indoor voice and data coverage. In this article we overview the technical and business arguments for femtocells and describe the state of the art on each front. We also describe the technical challenges facing femtocell networks and give some preliminary ideas for how to overcome them.

3,298 citations


"Modeling Heterogeneous Network Inte..." refers background in this paper

  • ...I. INTRODUCTION Cellular network deployment is taking on a massively heterogeneous character as a variety of infrastructure is being deployed including macro, pico, and femto base stations [1], as well as fixed relay stations [2] and distributed antennas [3]....

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Book ChapterDOI
Minoru Nakagami1
01 Jan 1960
TL;DR: In this article, the authors summarized the principal results of a series of statistical studies in the last seven years on the intensity distributions due to rapid fading, and presented an extremely simplified method for estimating the improvement available from various systems of diversity reception.
Abstract: This paper summarizes the principal results of a series of statistical studies in the last seven years on the intensity distributions due to rapid fading The method of derivation and the principal characteristics of the m-distribution, originally found in our hf experiments and described by the author, are outlined Its applicability to both ionospheric and tropospheric modes of propagation is fairly well confirmed by some observations Its theoretical background is also discussed in detail A theoretical interpretation of the log-normal distribution is given on the basis of this formula An extremely simplified method is presented for estimating the improvement available from various systems of diversity reception The mutual dependences between the m-formula and other basic distributions are fully discussed Some generalized forms of the basic distributions are also investigated in relation to the m-formula Two methods of approximating a given function with the m-distribution are shown The joint distribution of two variables, each of which follows the m-distribution, is derived in two different ways Based on this, some useful associated distributions are also discussed

2,441 citations


Additional excerpts

  • ...If X is Nakagami distributed [30] with parameters µ and ω then Y = X2 has a Γ[k, θ] distribution with k = µ and θ = ω/µ....

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