Spatial Stochastic Models and Metrics for the Structure of Base Stations in Cellular Networks

The spatial structure of base stations (BSs) in cellular networks plays a key role in evaluating the downlink performance. In this paper, different spatial stochastic models (the Poisson point process (PPP), the Poisson hard-core process (PHCP), the Strauss process (SP), and the perturbed triangular lattice) are used to model the structure by fitting them to the locations of BSs in real cellular networks obtained from a public database. We provide two general approaches for fitting. One is fitting by the method of maximum pseudolikelihood. As for the fitted models, it is not sufficient to distinguish them conclusively by some classical statistics. We propose the coverage probability as the criterion for the goodness-of-fit. In terms of coverage, the SP provides a better fit than the PPP and the PHCP. The other approach is fitting by the method of minimum contrast that minimizes the average squared error of the coverage probability. This way, fitted models are obtained whose coverage performance matches that of the given data set very accurately. Furthermore, we introduce a novel metric, the deployment gain, and we demonstrate how it can be used to estimate the coverage performance and average rate achieved by a data set.

[1]  Catherine Rosenberg,et al.  On fractional frequency reuse in imperfect cellular grids , 2012, 2012 IEEE Wireless Communications and Networking Conference (WCNC).

[2]  François Baccelli,et al.  A Stochastic Geometry Analysis of Dense IEEE 802.11 Networks , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[3]  Jeffrey G. Andrews,et al.  Modeling and Analysis of K-Tier Downlink Heterogeneous Cellular Networks , 2011, IEEE Journal on Selected Areas in Communications.

[4]  Jeffrey G. Andrews,et al.  Stochastic geometry and random graphs for the analysis and design of wireless networks , 2009, IEEE Journal on Selected Areas in Communications.

[5]  Sihai Zhang,et al.  A stochastic geometry approach to energy efficiency in relay-assisted cellular networks , 2012, 2012 IEEE Global Communications Conference (GLOBECOM).

[6]  Martin Haenggi,et al.  Stochastic Geometry for Wireless Networks , 2012 .

[7]  A. Baddeley,et al.  Practical Maximum Pseudolikelihood for Spatial Point Patterns , 1998, Advances in Applied Probability.

[8]  Jean-Marie Gorce,et al.  Interference Modeling in CSMA Multi-Hop Wireless Networks , 2008 .

[9]  Jeffrey G. Andrews,et al.  A Tractable Approach to Coverage and Rate in Cellular Networks , 2010, IEEE Transactions on Communications.

[10]  M. Tanemura.  Statistical Distributions of Poisson Voronoi Cells in Two and Three Dimensions , 2003 .

[11]  Adrian Baddeley,et al.  Practical maximum pseudolikelihood for spatial point patterns , 1998, Advances in Applied Probability.

[12]  Martin Haenggi,et al.  Toward Quasiregular Sensor Networks: Topology Control Algorithms for Improved Energy Efficiency , 2006, IEEE Transactions on Parallel and Distributed Systems.

[13]  Adrian Baddeley,et al.  Fast approximation of the intensity of Gibbs point processes , 2012 .

[14]  Ivan Stojmenovic,et al.  Addressing and Routing in Hexagonal Networks with Applications for Tracking Mobile Users and Connection Rerouting in Cellular Networks , 2002, IEEE Trans. Parallel Distributed Syst..

[15]  Zhisheng Niu,et al.  Optimal base station density for energy-efficient heterogeneous cellular networks , 2012, 2012 IEEE International Conference on Communications (ICC).

[16]  Philippe Martins,et al.  An Analytical Model for Evaluating Outage and Handover Probability of Cellular Wireless Networks , 2010, Wireless Personal Communications.

[17]  T. Mattfeldt.  Stochastic Geometry and Its Applications , 1996 .

[18]  Adrian Baddeley,et al.  spatstat: An R Package for Analyzing Spatial Point Patterns , 2005 .

[19]  Martin Haenggi,et al.  Interference and Outage in Poisson Cognitive Networks , 2012, IEEE Transactions on Wireless Communications.

[20]  P. Diggle,et al.  Monte Carlo Methods of Inference for Implicit Statistical Models , 1984 .

[21]  Shu Lin,et al.  Error Control Coding , 2004 .

[22]  Martin Haenggi,et al.  Mean Interference in Hard-Core Wireless Networks , 2011, IEEE Communications Letters.

[23]  Gaston H. Gonnet,et al.  On the LambertW function , 1996, Adv. Comput. Math..

[24]  Z. Néda,et al.  On the size-distribution of Poisson Voronoi cells , 2004, cond-mat/0406116.

[25]  D. Stoyan,et al.  Stochastic Geometry and Its Applications , 1989 .

[26]  D. Stoyan,et al.  Stochastic Geometry and Its Applications , 1989 .

[27]  C. Pipper,et al.  [''R"--project for statistical computing]. , 2008, Ugeskrift for laeger.

[28]  Janne Riihijärvi,et al.  A spatial statistics approach to characterizing and modeling the structure of cognitive wireless networks , 2012, Ad Hoc Networks.

[29]  K. K. Berthelsen,et al.  A primer on perfect simulation for spatial point processes , 2002 .

[30]  Charles J. Geyer,et al.  Likelihood inference for spatial point processes , 2019, Stochastic Geometry.

[31]  Tomoaki Ohtsuki,et al.  Codebook Based Interference Mitigation with Base Station Cooperation in Multi-Cell Cellular Network , 2011, 2011 IEEE Vehicular Technology Conference (VTC Fall).

[32]  Guillaume Chelius,et al.  Point processes for interference modeling in CSMA/CA ad-hoc networks , 2009, PE-WASUN '09.

[33]  François Baccelli,et al.  Stochastic geometry and wireless networks , 2009 .

[34]  Catherine Rosenberg,et al.  Impact of Network Load on Forward Link Inter-Cell Interference in Cellular Data Networks , 2006, IEEE Transactions on Wireless Communications.