Stochastic geometry and random graphs for the analysis and design of wireless networks

Haenggi, Martin; Andrews, Jeffrey G.; Baccelli, François; Dousse, Olivier; Franceschetti, Massimo

doi:10.1109/jsac.2009.090902

Cited by 1,576 publications

(1,150 citation statements)

References 98 publications

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“…However, up to now, most theoretical studies on SCNs only consider simple path loss models that do not differentiate Line-of-Sight (LoS) and Non-Line-of-Sight (NLoS) transmissions [2][3][4][5]. The major conclusion [2][3][4][5] is that neither the number of small cells nor the number of cell tiers changes the coverage probability in interference-limited fully-loaded cellular networks. Such conclusion implies that the area spectral efficiency (ASE) will monotonically grow as small cells go dense.…”

Section: Introductionmentioning

confidence: 99%

Will the Area Spectral Efficiency Monotonically Grow as Small Cells Go Dense?

Ding

Liu²,

Mao

et al. 2014

2015 IEEE Global Communications Conference (GLOBECOM)

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Abstract-In this paper, we introduce a sophisticated path loss model into the stochastic geometry analysis incorporating both line-of-sight (LoS) and non-line-of-sight (NLoS) transmissions to study their performance impact in small cell networks (SCNs). Analytical results are obtained on the coverage probability and the area spectral efficiency (ASE) assuming both a general path loss model and a special case of path loss model recommended by the 3rd Generation Partnership Project (3GPP) standards. The performance impact of LoS and NLoS transmissions in SCNs in terms of the coverage probability and the ASE is shown to be significant both quantitatively and qualitatively, compared with previous work that does not differentiate LoS and NLoS transmissions. Particularly, our analysis demonstrates that when the density of small cells is larger than a threshold, the network coverage probability will decrease as small cells become denser, which in turn makes the ASE suffer from a slow growth or even a notable decrease. For practical regime of small cell density, the performance results derived from our analysis are distinctively different from previous results, and shed new insights on the design and deployment of future dense/ultra-dense SCNs.

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Section: Introductionmentioning

confidence: 99%

Will the Area Spectral Efficiency Monotonically Grow as Small Cells Go Dense?

Ding

Liu²,

Mao

et al. 2014

2015 IEEE Global Communications Conference (GLOBECOM)

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“…They appear in numerous complex systems including in nanoscience [3], epidemiology [4,5], forest fires [6], social networks [7,8], and wireless communications [9][10][11]. Such networks exhibit a general phenomenon called percolation [12,13], where at a critical connection probability (controlled by the node density), the largest connected component (cluster) of the network jumps abruptly from being independent of system size (microscopic) to being proportional to system size (macroscopic).…”

Section: Introductionmentioning

confidence: 99%

Impact of boundaries on fully connected random geometric networks

2012

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Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the transition to full connectivity is strongly influenced by details of the boundary, but observe an alternative form of universality. Our approach correctly distinguishes connectivity properties of networks in domains with equal bulk contributions. It also facilitates system design to promote or avoid full connectivity for diverse geometries in arbitrary dimension.

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“…As shown in (17)λ is monotonically decreasing with M and with all the terms of the power consumption model. Furthermore, if the ratio M/K is kept fixed, thenλ is also monotonically decreasing with K. Therefore, if no AR constraint is imposed and practical values of M and K are considered, the optimal density can be very small (see for example the results illustrated in Fig.…”

Section: B Optimal Ap Densitymentioning

confidence: 83%

“…In a wireless network the spatial distribution of APs is highly irregular and the cell geometry plays a key role when determining the performance. Stochastic geometry is a promising tool to derive tractable analytical results and to model the random properties of practical network deployments [17]. Therefore, we consider the downlink of a network with zero-forcing (ZF) precoding in which the locations of APs are distributed according to a homogeneous Poisson point process (PPP).…”

Section: Introductionmentioning

confidence: 99%

Optimal design of wireless networks for broadband access with minimum power consumption

Verenzuela

Björnson

Sanguinetti

2016

2016 IEEE International Conference on Communications (ICC)

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Abstract-The continuous rise in wireless data traffic brings forth an increase in power consumption and static users constitute a large fraction of these traffic demands. This work focuses on designing cellular networks to deliver a given data rate per area and user, while minimizing the power consumption. In particular we are interested in optimizing the transmission power, density of access points (APs), number of AP antennas and number of users served in each cell. To this end, we consider a network model based on stochastic geometry and a detailed power consumption model to derive closed form expressions and obtain insights on the interplay of the aforementioned design parameters. The results show that, in contrast with previous works on optimal network design for energy efficiency, having exceedingly high AP density does not bring the most benefits in terms of power savings. Instead the AP density should be chosen according to the area data rate that we want to deliver. In addition numerical results show that the minimum power consumption is obtained in the Massive MIMO regime with many antennas and users per AP.

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Stochastic geometry and random graphs for the analysis and design of wireless networks

Cited by 1,576 publications

References 98 publications

Will the Area Spectral Efficiency Monotonically Grow as Small Cells Go Dense?

Will the Area Spectral Efficiency Monotonically Grow as Small Cells Go Dense?

Impact of boundaries on fully connected random geometric networks

Optimal design of wireless networks for broadband access with minimum power consumption

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