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A cellular network model with Ginibre configured base stations. (English) Zbl 1330.60066
Summary: Stochastic geometry models for wireless communication networks have recently attracted much attention. This is because the performance of such networks critically depends on the spatial configuration of wireless nodes and the irregularity of the node configuration in a real network can be captured by a spatial point process. However, most analysis of such stochastic geometry models for wireless networks assumes, owing to its tractability, that the wireless nodes are deployed according to homogeneous Poisson point processes. This means that the wireless nodes are located independently of each other and their spatial correlation is ignored. In this work we propose a stochastic geometry model of cellular networks such that the wireless base stations are deployed according to the Ginibre point process. The Ginibre point process is one of the determinantal point processes and accounts for the repulsion between the base stations. For the proposed model, we derive a computable representation for the coverage probability – the probability that the signal-to-interference-plus-noise ratio (SINR) for a mobile user achieves a target threshold. To capture its qualitative property, we further investigate the asymptotics of the coverage probability as the SINR threshold becomes large in a special case. We also present the results of some numerical experiments.

MSC:
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
90B18 Communication networks in operations research
60D05 Geometric probability and stochastic geometry
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[1] Andrews, J. G., Baccelli, F. and Ganti, R. K. (2011). A tractable approach to coverage and rate in cellular networks. IEEE Trans. Commun. 59, 3122-3134.
[2] Andrews et al. (2010). A primer on spatial modeling and analysis in wireless networks. IEEE Commun. Magazine 48, 156-163.
[3] Baccelli, F. and Błaszczyszyn, B. (2008). Stochastic geometry and wireless networks: Volume I Theory. Foundations Trends Networking 3, 249-449. · Zbl 1184.68015
[4] Baccelli, F. and Błaszczyszyn, B. (2009). Stochastic geometry and wireless networks: Volume II Applications. Foundations Trends Networking 4, 1-312. · Zbl 1184.68016
[5] Błaszczyszyn, B. and Yogeshwaran, D. (2010). Connectivity in sub-Poisson networks. In Proc. 48th Annual Allerton Conf. Commun. Control Comput. , IEEE, pp. 1466-1473.
[6] Decreusefond, L., Martins, P. and Vu, T.-T. (2010). An analytical model for evaluating outage and handover probability of cellular wireless networks. Preprint. Available at http://arxiv.org/abs/1009.0193v1.
[7] Dhillon, H. S., Ganti, R. K. and Andrews, J. G. (2012). Load-aware heterogeneous cellular networks: Modeling and SIR distribution. In Proc. 2012 IEEE Global Communications Conf. (GLOBECOM) , IEEE, pp. 4314-4319.
[8] Dhillon, H. S., Ganti, R. K., Baccelli, F. and Andrews, J. G. (2012). Modeling and analysis of \(K\)-tier downlink heterogeneous cellular networks. IEEE J. Sel. Areas Commun. 30, 550-560.
[9] Ganti, R. K., Baccelli, F. and Andrews, J. G. (2012). Series expansion for interference in wireless networks. IEEE Trans. Inf. Theory 58, 2194-2205. · Zbl 1365.60040
[10] Giacomelli, R., Ganti, R. K. and Haenggi, M. (2011). Outage probability of general ad hoc networks in the high-reliability regime. IEEE/ACM Trans. Networking 19, 1151-1163.
[11] Haenggi, M. (2013). Stochastic Geometry for Wireless Networks . Cambridge University Press. · Zbl 1272.60001
[12] Haenggi, M. et al. (2009). Stochastic geometry and random graphs for the analysis and design of wireless networks. IEEE J. Sel. Areas Commun. 27, 1029-1046.
[13] Hough, J. B., Krishnapur, M., Peres, Y. and Virág, B. (2009). Zeros of Gaussian Analytic Functions and Determinantal Point Processes . American Mathematical Society, Providence, RI. Also available at http://research.microsoft.com/en-us/um/people/peres/GAF_book.pdf. · Zbl 1190.60038
[14] Jo, H.-S., Sang, Y. J., Xia, P. and Andrews, J. G. (2012). Heterogeneous cellular networks with flexible cell association: a comprehensive downlink SINR analysis. IEEE Trans. Wireless Commun. 11, 3484-3495.
[15] Kostlan, E. (1992). On the spectra of Gaussian matrices. Directions in matrix theory (Auburn, AL, 1990). Linear Algebra Appl. 162/164, 385-388. · Zbl 0748.15024
[16] Madhusudhanan, P., Restrepo, J. G., Liu, Y. and Brown, T. X. (2012). Downlink coverage analysis in a heterogeneous cellular network. In Proc. 2012 IEEE Global Communications Conf. (GLOBECOM) , IEEE, pp. 4170-4175.
[17] Mukherjee, S. (2012). Distribution of downlink SINR in heterogeneous cellular networks. IEEE J. Sel. Areas Commun. 30, 575-585.
[18] Shirai, T. and Takahashi, Y. (2003). Random point fields associated with certain Fredholm determinants. I. Fermion, Poisson and boson point processes. J. Funct. Analysis 205, 414-463. · Zbl 1051.60052
[19] Soshnikov, A. (2000). Determinantal random point fields. Russian Math. Surveys 55, 923-975. · Zbl 0991.60038
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