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## Using Poisson processes to model lattice cellular networks

Venue: | in INFOCOM, 2013 Proceedings IEEE, 2013 |

Citations: | 24 - 11 self |

### Citations

3973 | Handbook of Mathematical Functions - Abramowitz, Stegun - 1970 |

793 | An Introduction to the Theory of Point Processes - Daley, Vere-Jones - 1988 |

250 | Stochastic Geometry and Wireless Networks, Volume I - Theory
- Baccelli, Blaszczyszyn
- 2009
(Show Context)
Citation Context ...pared in this context. Related work: It is beyond the scope of this short introduction to review all works with Poisson model of wireless networks. Some results and further references may be found in =-=[1, 2]-=-. More specifically, our results presented in this paper allow to extend to a general fading distribution the explicit expressions for the distribution function of the SINR derived in [3], where Rayle... |

238 | Stochastic geometry and random graphs for the analysis and design of wireless networks
- Haenggi, Andrews, et al.
- 2009
(Show Context)
Citation Context ...pared in this context. Related work: It is beyond the scope of this short introduction to review all works with Poisson model of wireless networks. Some results and further references may be found in =-=[1, 2]-=-. More specifically, our results presented in this paper allow to extend to a general fading distribution the explicit expressions for the distribution function of the SINR derived in [3], where Rayle... |

195 |
Numerical inversion of Laplace transforms of probability distributions
- ABATE, WHITT
- 1995
(Show Context)
Citation Context ...23) of the (conditional) CDF Fs is based on the Bromwich contour inversion integral of the Laplace transform LFs of 1−Fs. The expression (24) for this latter follows from (15). Remark 11: As shown in =-=[11]-=-, the integral in (23) can be numerically evaluated using the trapezoidal rule, with the parameter γ allowing control of the approximation error. The function Fs may be also retrieved from (15) using ... |

154 | Modeling and analysis of k-tier downlink heterogeneous cellular networks
- Dhillon, Ganti, et al.
- 2012
(Show Context)
Citation Context ... found in [1, 2]. More specifically, our results presented in this paper allow to extend to a general fading distribution the explicit expressions for the distribution function of the SINR derived in =-=[3]-=-, where Rayleigh fading is assumed. Our representation of the network via the process of propagation losses is similar tho this considered in [4] for other purposes, mostly to study the effect of shad... |

71 | Energy Efficiency Aspects of Base Station Deployment Strategies for Cellular Networks.
- Richter, Fehske, et al.
- 2009
(Show Context)
Citation Context ...smit some power P ≥ 0. In fact, in order for a base station to be able to transmit this power to the mobile, it needs to be powered (i.e., consumes energy per second) at the level P ′ > P . Following =-=[10]-=-, assume that these two quantities are related through a simple linear relation P ′ = cP+d for some positive constants c and d. The energy efficiency is defined by E := E(P ) = W log ( 1 + 1NL/P+f ) c... |

19 | A geometric interpretation of fading in wireless networks: Theory and applications. Information Theory,
- Haenggi
- 2008
(Show Context)
Citation Context ...s for the distribution function of the SINR derived in [3], where Rayleigh fading is assumed. Our representation of the network via the process of propagation losses is similar tho this considered in =-=[4]-=- for other purposes, mostly to study the effect of shadowing/fading on connectivity. Moreover, using the Laplace/Fourier analysis, we manage to characterize (no longer explicitly) the SINR over its en... |

12 | Linear-regression estimation of the propagationloss parameters using mobiles’ measurements in wireless cellular networ
- Błaszczyszyn, Karray
- 2012
(Show Context)
Citation Context ... SINR over its entire range, whereas the aforementioned explicit expressions are valid only for SINR ≥ 1. The result of Lemma 1 appeared in [5]. The infinite Poisson model was statistically fitted in =-=[6]-=- to some real data provided by an operator regarding propagation losses in order to estimate the parameters of the propagation loss using a simple linear regression model. The spectral and energy effi... |

8 |
Impact of the geometry, path-loss exponent and random shadowing on the mean interference factor in wireless cellular networks.
- laszczyszyn, Karray, et al.
- 2010
(Show Context)
Citation Context ...alysis, we manage to characterize (no longer explicitly) the SINR over its entire range, whereas the aforementioned explicit expressions are valid only for SINR ≥ 1. The result of Lemma 1 appeared in =-=[5]-=-. The infinite Poisson model was statistically fitted in [6] to some real data provided by an operator regarding propagation losses in order to estimate the parameters of the propagation loss using a ... |

6 |
Weighing The Odds: A Course
- Williams
- 2001
(Show Context)
Citation Context ...shows that such a modification is not significant in the Poisson approximation. To illustrate Theorem 3 and obtain some insight into the speed of convergence we used Kolmogorov-Smirnov (K-S) test, cf =-=[9]-=-, to compare the cumulative distribution functions (CDF) of the SIR of the typical user (see Section IV-A2) in the infinite Poisson model versus hexagonal one consisting of 30 × 30 = 900 stations on a... |

4 |
Spectral and energy efficiencies of OFDMA wireless cellular networks
- Karray
- 2010
(Show Context)
Citation Context ...on losses in order to estimate the parameters of the propagation loss using a simple linear regression model. The spectral and energy efficiency in hexagonal networks without shadowing was studied in =-=[7]-=-. Finally, the convergence result presented here is in the spirit of classical limit theorems of point processes, which are detailed in [8, Chapter 11]. In particular, these theorems show that under s... |