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## Downlink capacity and base station density in cellular networks.” Available: http://arxiv.org/abs/1109.2992

Citations: | 22 - 3 self |

### Citations

1175 | Wireless Communications
- Goldsmith
- 2005
(Show Context)
Citation Context ... the question are not trivial, in particular when it comes to the case of multiple interfering base stations and mobile users. So far, the only attractable approach is to rely on simulations, where various models on radio channels and the spatial distribution of base stations and users are used. In this paper, we tackle the issue to derive closed form formulas for quickly answering the question. Many previous studies on cellular networks assumed that base stations are positioned regularly and tractable analysis was performed only for a fixed location user (e.g., cell center or edge user) [1], [4]. This regular model tends to overestimate the capacity of cellular networks owing to the perfect geometry of base stations and the neglect of weak interference from outer tier base stations. For this reason, we use the stochastic geometry approach, where base stations can be modeled as a homogeneous Poisson point process (PPP) [5]-[7]. The main advantage of this PPP model is that we can derive the signalto-interference-plus-noise ratio (SINR) distribution at an arbitrary location considering random channel effects such as fading and shadowing. Moreover, the PPP model reflects random location ... |

616 |
Spatial Tessellations: Concepts and Applications of Voronoi Diagrams
- Okabe, Boots, et al.
- 1992
(Show Context)
Citation Context ...to the spatial distribution of the BSs such as [5]-[7]. Besides, we consider the density of MUs, where the MUs are randomly distributed according to some independent homogeneous PPP with a different density. One can argue that the MU distribution may not be best modeled as the PPP. However, this is a tractable and reasonable approach as was also used in [15]. The spatial distribution of BSs follows PPP Φb with the density λb, over which MUs are positioned with PPP Φu with the density λu. Each MU is served by the nearest BS. This means that the cell area of each BS forms a Voronoi tessellation [16] as in Figure 1. We assume that the radio channel attenuation is dependent on pathloss and Rayleigh fading in our analysis (Section IV). Further, we consider lognormal shadowing as well in our simulations (Section V). We consider only one resource block at a given time and assume that only one MU is scheduled in the resource block. In other words, if there are multiple MUs in the Voronoi cell of a BS, then the BS can serve only one of them in the resource block. The resource block can be interpreted as a time slot (in time division multiple access systems), a sub-carrier (in frequency division... |

425 |
Femtocell networks: A survey
- Chandrasekhar, Andrews, et al.
- 2008
(Show Context)
Citation Context ...ans that the number of base stations installed should be more than n-times to increase the network capacity by a factor of n. Our results will provide a framework for performance analysis of the wireless infrastructure with a high density of access points, which will significantly reduce the burden of network-level simulations. I. INTRODUCTION The capacity of cellular networks has been a classical and important issue for efficient radio resource management [1]. The most improvement of the network capacity has come from reducing the cell size by installing more base stations such as femtocells [2], [3]. We may have a question, “How much does the network capacity increase as we install more base stations?” Unfortunately, answers to the question are not trivial, in particular when it comes to the case of multiple interfering base stations and mobile users. So far, the only attractable approach is to rely on simulations, where various models on radio channels and the spatial distribution of base stations and users are used. In this paper, we tackle the issue to derive closed form formulas for quickly answering the question. Many previous studies on cellular networks assumed that base stat... |

238 | Stochastic geometry and random graphs for the analysis and design of wireless networks
- Haenggi, Andrews, et al.
- 2009
(Show Context)
Citation Context ...ignalto-interference-plus-noise ratio (SINR) distribution at an arbitrary location considering random channel effects such as fading and shadowing. Moreover, the PPP model reflects random location characteristics of base stations. This randomly located base station scenario exists in heterogeneous networks where a large number of microcell and femtocell base stations are deployed. Particularly, user-deployed femtocells increase the randomness. The stochastic geometry approach has recently got much attention in particular for quantifying the co-channel interference in the wireless network (see [8] and literature therein). It has been applied to CDMA cellular networks [9], cellular networks with multi-cell cooperation [10], femtocells [11], cognitive radio networks [12] and CSMA/CA based wireless multihop networks [13], [14]. In this paper, we derive the downlink capacity of a cellular network, as closed form formulas, and evaluate its correctness by means of simulations. The most relevant research to our work is the one by Andrews et al. [5]. In that paper, the authors used a PPP modeling for the base station distribution but did not consider the user density. Therefore, their results ... |

213 | A tractable approach to coverage and rate in cellular networks
- Andrews, Baccelli, et al.
(Show Context)
Citation Context ...o derive closed form formulas for quickly answering the question. Many previous studies on cellular networks assumed that base stations are positioned regularly and tractable analysis was performed only for a fixed location user (e.g., cell center or edge user) [1], [4]. This regular model tends to overestimate the capacity of cellular networks owing to the perfect geometry of base stations and the neglect of weak interference from outer tier base stations. For this reason, we use the stochastic geometry approach, where base stations can be modeled as a homogeneous Poisson point process (PPP) [5]-[7]. The main advantage of this PPP model is that we can derive the signalto-interference-plus-noise ratio (SINR) distribution at an arbitrary location considering random channel effects such as fading and shadowing. Moreover, the PPP model reflects random location characteristics of base stations. This randomly located base station scenario exists in heterogeneous networks where a large number of microcell and femtocell base stations are deployed. Particularly, user-deployed femtocells increase the randomness. The stochastic geometry approach has recently got much attention in particular for... |

154 | Modeling and analysis of k-tier downlink heterogeneous cellular networks - Dhillon, Ganti, et al. - 2012 |

115 |
Uplink capacity and interference avoidance for two-tier femtocell networks
- Chandrasekhar, Andrews
- 2009
(Show Context)
Citation Context ...ing. Moreover, the PPP model reflects random location characteristics of base stations. This randomly located base station scenario exists in heterogeneous networks where a large number of microcell and femtocell base stations are deployed. Particularly, user-deployed femtocells increase the randomness. The stochastic geometry approach has recently got much attention in particular for quantifying the co-channel interference in the wireless network (see [8] and literature therein). It has been applied to CDMA cellular networks [9], cellular networks with multi-cell cooperation [10], femtocells [11], cognitive radio networks [12] and CSMA/CA based wireless multihop networks [13], [14]. In this paper, we derive the downlink capacity of a cellular network, as closed form formulas, and evaluate its correctness by means of simulations. The most relevant research to our work is the one by Andrews et al. [5]. In that paper, the authors used a PPP modeling for the base station distribution but did not consider the user density. Therefore, their results are useful for calculating the area outage probability, i.e., the probability that an arbitrary location is under outage owing to the low SINR. ... |

109 |
Radio Resource Management for Wireless Networks. Artech House,
- Zander, Kim
- 2001
(Show Context)
Citation Context ...g observation is that the success transmission density increases with the base station density, but the increasing rate diminishes. This means that the number of base stations installed should be more than n-times to increase the network capacity by a factor of n. Our results will provide a framework for performance analysis of the wireless infrastructure with a high density of access points, which will significantly reduce the burden of network-level simulations. I. INTRODUCTION The capacity of cellular networks has been a classical and important issue for efficient radio resource management [1]. The most improvement of the network capacity has come from reducing the cell size by installing more base stations such as femtocells [2], [3]. We may have a question, “How much does the network capacity increase as we install more base stations?” Unfortunately, answers to the question are not trivial, in particular when it comes to the case of multiple interfering base stations and mobile users. So far, the only attractable approach is to rely on simulations, where various models on radio channels and the spatial distribution of base stations and users are used. In this paper, we tackle the... |

82 |
Stochastic Geometry and its Applications, 2nd ed.
- Stoyan, Kendall, et al.
- 1995
(Show Context)
Citation Context ... cells have more chance to cover a given fixed point (a randomly chosen MU), which is well explained in [18]. Using Lemma 2, we derive the user selection probability as follows: Proposition 2: The probability (pselection) that a randomly chosen MU is assigned a resource block at a given time and is served by the nearest BS is pselection = 1 λu/λb ( 1− ( 1 + 3.5−1λu/λb )−3.5 ) . Proof: The user selection probability given the number of the other MUs (i.e., N ′ = n) is equal to 1/ (n+ 1), and the location of the other MUs follows the reduced Palm distribution with the PPP Φu (Slivnyak’s theorem [19]). Therefore, using the law of total probability, pselection is given as pselection = ∞ ∑ n=0 1 n+ 1 · P [N ′ = n] = ∞ ∑ n=0 1 n+ 1 · ∫ ∞ 0 P [N ′ = n|Y = y] · fY (y) dy = ∫ ∞ 0 ∞ ∑ n=0 1 n+ 1 ( λu y λb )n n! e −λu y λb · fY (y) dy = ∫ ∞ 0 λb λu y−1 ∞ ∑ k=1 ( λu y λb )k k! e −λu y λb · fY (y) dy = ∫ ∞ 0 λb λu y−1 ( 1− e−λu y λb ) · fY (y) dy = 3.54.5 Γ (4.5) λb λu ∫ ∞ 0 y2.5e−3.5y − y2.5e− ( 3.5+λuλb ) y dy = 3.54.5 Γ (4.5) λb λu ( Ly2.5 (3.5)− Ly2.5 ( 3.5 + λu λb )) = 1 λu/λb ( 1− ( 1 + (3.5) −1 λu/λb )−3.5 ) . To verify our analysis, we conduct simulations with 105 independent samples of the... |

50 |
Calculating the outage probability in a CDMA network with spatial Poisson traffic,”
- Chan, Hanly
- 2001
(Show Context)
Citation Context ...ocation considering random channel effects such as fading and shadowing. Moreover, the PPP model reflects random location characteristics of base stations. This randomly located base station scenario exists in heterogeneous networks where a large number of microcell and femtocell base stations are deployed. Particularly, user-deployed femtocells increase the randomness. The stochastic geometry approach has recently got much attention in particular for quantifying the co-channel interference in the wireless network (see [8] and literature therein). It has been applied to CDMA cellular networks [9], cellular networks with multi-cell cooperation [10], femtocells [11], cognitive radio networks [12] and CSMA/CA based wireless multihop networks [13], [14]. In this paper, we derive the downlink capacity of a cellular network, as closed form formulas, and evaluate its correctness by means of simulations. The most relevant research to our work is the one by Andrews et al. [5]. In that paper, the authors used a PPP modeling for the base station distribution but did not consider the user density. Therefore, their results are useful for calculating the area outage probability, i.e., the probabili... |

45 |
On the size distribution of Poisson Voronoi cells,” Physica A: Statistical Mechanics and its Applications,
- Ferenc, Neda
- 2007
(Show Context)
Citation Context ...ronoi cell. This probability will be used for calculating the aggregate inter-cell interference in Section IV. The user selection probability denotes the one that a randomly chosen MU is assigned a resource block at a given time and is served by the nearest BS. A. Inactive Base Station Probability At a given time, there can be some BSs that do not have any MU in their Voronoi cells. This happens when the BS density is high, e.g., femtocells. Those BSs are inactive. We start with the probability density function of the size of a typical Voronoi cell, which was derived by the Monte Carlo method [17]: fX (x) = 3.53.5 Γ (3.5) x2.5e−3.5x, (1) where X is a random variable that denotes the size of the typical Voronoi cell normalized by the value 1/λb. Using (1), we can derive the probability mass function of the number of MUs in a typical Voronoi cell: Lemma 1: Let the random variable N denote the number of MUs in the Voronoi cell of a randomly chosen BS. Then, the probability mass function of N is P [N = n] = 3.53.5Γ (n+ 3.5) (λu/λb) n Γ (3.5)n! (λu/λb + 3.5) n+3.5 . Proof: Using the law of total probability and the function (1), the probability mass function of N is given as P [N = n] = ∫ ∞... |

39 | Power control in cognitive radio networks: how to cross a multi-lane highway,”
- Ren, Zhao, et al.
- 2009
(Show Context)
Citation Context ...flects random location characteristics of base stations. This randomly located base station scenario exists in heterogeneous networks where a large number of microcell and femtocell base stations are deployed. Particularly, user-deployed femtocells increase the randomness. The stochastic geometry approach has recently got much attention in particular for quantifying the co-channel interference in the wireless network (see [8] and literature therein). It has been applied to CDMA cellular networks [9], cellular networks with multi-cell cooperation [10], femtocells [11], cognitive radio networks [12] and CSMA/CA based wireless multihop networks [13], [14]. In this paper, we derive the downlink capacity of a cellular network, as closed form formulas, and evaluate its correctness by means of simulations. The most relevant research to our work is the one by Andrews et al. [5]. In that paper, the authors used a PPP modeling for the base station distribution but did not consider the user density. Therefore, their results are useful for calculating the area outage probability, i.e., the probability that an arbitrary location is under outage owing to the low SINR. A key observation in [5] is tha... |

23 |
Is the PHY layer dead
- Dohler, Heath, et al.
- 2011
(Show Context)
Citation Context ...hat the number of base stations installed should be more than n-times to increase the network capacity by a factor of n. Our results will provide a framework for performance analysis of the wireless infrastructure with a high density of access points, which will significantly reduce the burden of network-level simulations. I. INTRODUCTION The capacity of cellular networks has been a classical and important issue for efficient radio resource management [1]. The most improvement of the network capacity has come from reducing the cell size by installing more base stations such as femtocells [2], [3]. We may have a question, “How much does the network capacity increase as we install more base stations?” Unfortunately, answers to the question are not trivial, in particular when it comes to the case of multiple interfering base stations and mobile users. So far, the only attractable approach is to rely on simulations, where various models on radio channels and the spatial distribution of base stations and users are used. In this paper, we tackle the issue to derive closed form formulas for quickly answering the question. Many previous studies on cellular networks assumed that base stations ... |

21 |
Using Poisson processes to model lattice cellular networks,” to appear in
- Blaszczyszyn, Karray, et al.
- 2013
(Show Context)
Citation Context ...rive closed form formulas for quickly answering the question. Many previous studies on cellular networks assumed that base stations are positioned regularly and tractable analysis was performed only for a fixed location user (e.g., cell center or edge user) [1], [4]. This regular model tends to overestimate the capacity of cellular networks owing to the perfect geometry of base stations and the neglect of weak interference from outer tier base stations. For this reason, we use the stochastic geometry approach, where base stations can be modeled as a homogeneous Poisson point process (PPP) [5]-[7]. The main advantage of this PPP model is that we can derive the signalto-interference-plus-noise ratio (SINR) distribution at an arbitrary location considering random channel effects such as fading and shadowing. Moreover, the PPP model reflects random location characteristics of base stations. This randomly located base station scenario exists in heterogeneous networks where a large number of microcell and femtocell base stations are deployed. Particularly, user-deployed femtocells increase the randomness. The stochastic geometry approach has recently got much attention in particular for qua... |

10 | A stochastic-geometry approach to coverage in cellular networks with multi-cell cooperation,”
- Huang, Andrews
- 2011
(Show Context)
Citation Context ...fading and shadowing. Moreover, the PPP model reflects random location characteristics of base stations. This randomly located base station scenario exists in heterogeneous networks where a large number of microcell and femtocell base stations are deployed. Particularly, user-deployed femtocells increase the randomness. The stochastic geometry approach has recently got much attention in particular for quantifying the co-channel interference in the wireless network (see [8] and literature therein). It has been applied to CDMA cellular networks [9], cellular networks with multi-cell cooperation [10], femtocells [11], cognitive radio networks [12] and CSMA/CA based wireless multihop networks [13], [14]. In this paper, we derive the downlink capacity of a cellular network, as closed form formulas, and evaluate its correctness by means of simulations. The most relevant research to our work is the one by Andrews et al. [5]. In that paper, the authors used a PPP modeling for the base station distribution but did not consider the user density. Therefore, their results are useful for calculating the area outage probability, i.e., the probability that an arbitrary location is under outage owing ... |

5 |
Cross-layer optimization and network coding in CSMA/CA based wireless multihop networks,”
- Hwang, Kim
- 2011
(Show Context)
Citation Context ...tions. This randomly located base station scenario exists in heterogeneous networks where a large number of microcell and femtocell base stations are deployed. Particularly, user-deployed femtocells increase the randomness. The stochastic geometry approach has recently got much attention in particular for quantifying the co-channel interference in the wireless network (see [8] and literature therein). It has been applied to CDMA cellular networks [9], cellular networks with multi-cell cooperation [10], femtocells [11], cognitive radio networks [12] and CSMA/CA based wireless multihop networks [13], [14]. In this paper, we derive the downlink capacity of a cellular network, as closed form formulas, and evaluate its correctness by means of simulations. The most relevant research to our work is the one by Andrews et al. [5]. In that paper, the authors used a PPP modeling for the base station distribution but did not consider the user density. Therefore, their results are useful for calculating the area outage probability, i.e., the probability that an arbitrary location is under outage owing to the low SINR. A key observation in [5] is that the area outage probability is independent of th... |

2 |
A cross-layer optimization of IEEE 802.11 MAC for wireless multihop networks,”
- Hwang, Kim
- 2006
(Show Context)
Citation Context ...m level simulations. Figure 4 contains our results where the pathloss component varies between 2 and 4. In the figure, we see that the capacity of networks 0 10 20 30 40 50 60 70 80 90 100 0 5 10 15 20 25 λ b C s e rv ic e α=4 α=3.5 α=3 α=2.5 α=2 Fig. 4. The service capacity Cservice for various pathloss exponents α (the mobile user density is λu = 30, the target signal to interference-noise ratio is γ = 0dB, and interference limited system). increases as the pathloss exponent becomes higher. This is due to the fact that the higher pathloss will filter co-channel interference among the cells [20]. On the other hand, we see that the behavior of diminishing the marginal capacity remains the same as in Figure 3-(b). C. Asymptotic Cases To get simpler closed form formulas, we consider two asymptotic cases. The first is the one that the density of BSs is much higher than that of MUs (i.e., λb ≫ λu) like femtocells. In this case, the user selection probability can be approximated to one (i.e., pselection ≈ 1) and the density of the transmitting BSs can be approximated to that of the MUs (i.e., λi ≈ λu). Therefore, service success probability and service capacity are given as follows: pservi... |

1 | Computation of aggregate interference from multiple secondary transmitters,” - Ruttik, Koufos, et al. - 2011 |