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  3. Stochastic Geometry for Wireless Networks
  • Cited by 1503
Publisher:
Cambridge University Press
Online publication date:
November 2012
Print publication year:
2012
Online ISBN:
9781139043816
DOI:
https://doi.org/10.1017/CBO9781139043816
Subjects:
Engineering, Wireless Communications
Information

Book description

Covering point process theory, random geometric graphs and coverage processes, this rigorous introduction to stochastic geometry will enable you to obtain powerful, general estimates and bounds of wireless network performance and make good design choices for future wireless architectures and protocols that efficiently manage interference effects. Practical engineering applications are integrated with mathematical theory, with an understanding of probability the only prerequisite. At the same time, stochastic geometry is connected to percolation theory and the theory of random geometric graphs and accompanied by a brief introduction to the R statistical computing language. Combining theory and hands-on analytical techniques with practical examples and exercises, this is a comprehensive guide to the spatial stochastic models essential for modelling and analysis of wireless network performance.

Reviews

'This book is a welcome addition to the rapidly developing area of applications of stochastic geometric models to telecommunications.'

Ilya S. Molchanov - American Mathematical Society

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Contents

Contents
References
References
References
Alon, N. & Spencer, J. (2008), The Probabilistic Method CrossRef | Google Scholar, 3rd edn., Wiley.
Andrews, J. G., Baccelli, F. & Ganti, R. K. (2011), A tractable approach to coverage and rate in cellular networks, IEEE Transactions on Communications 59 CrossRef | Google Scholar(11), 3122–3134.
Athreya, K. B. & Ney, P. E. (2004), Branching Processes Google Scholar, Dover Publications.
Baccelli, F. & Blaszczyszyn, B. (2009), Stochastic Geometry and Wireless Networks Google Scholar, NOW.
Baccelli, F., Blaszczyszyn, B. & Mirsadeghi, M. O. H. (2011), Optimal paths on the space–time SINR random graph, Advances in Applied Probability 43 CrossRef | Google Scholar(1), 131–150.
Baccelli, F., Blaszczyszyn, B. & Mühlethaler, P. (2006), An ALOHA protocol for multihop mobile wireless networks, IEEE Transactions on Information Theory 52 CrossRef | Google Scholar(2), 421–436.
Baddeley, A. J. & Silverman, B. W. (1984), A cautionary example on the use of second-order methods for analyzing point patterns, Biometrics 40 CrossRef | Google Scholar(4), 1089–1093.
Baddeley, A. & Turner, R. (2005), Spatstat: an R package for analyzing spatial point patterns, Journal of Statistical Software 12 CrossRef | Google Scholar(6), 1–42.
Baddeley, A. J. & van Lieshout, M. N. M. (1995), Area-interaction point processes, Annals of the Institute of Statistical Mathematics 47 CrossRef | Google Scholar(4), 601–619.
Baddeley, A., Bárány, I., Schneider, R. & Weil, W. (2007), Stochastic Geometry Google Scholar, Springer.
Balister, P., Bollobás, B., Sarkar, A. & Walters, M. (2005), Connectivity of random k-nearest-neighbor graphs, Advances in Applied Probability 37 CrossRef | Google Scholar, 1–24.
Balister, P., Bollobás, B., Sarkar, A. & Walters, M. (2010), Sentry selection in wireless networks, Advances in Applied Probability 42 CrossRef | Google Scholar(1), 1–25.
Balister, P., Bollobás, B. & Walters, M. (2004), Continuum percolation with steps in an annulus, Annals of Applied Probability 14 CrossRef | Google Scholar, 1869–1879.
Balister, P., Bollobás, B. & Walters, M. (2005), Continuum percolation with steps in the square or the disc, Random Structures and Algorithms 26 CrossRef | Google Scholar(4), 392–403.
Barbour, A. D. & Chen, L. H. Y. (2005), Stein's Method and Applications, Singapore CrossRef | Google ScholarUniversity Press.
Bedford, T. & van den Berg, J. (1997), A remark on the Van Lieshout and Baddeley J function for point processes, Advances in Applied Probability 29 CrossRef | Google Scholar(1), 19–25.
Bollobás, B. (2001), Random Graphs CrossRef | Google Scholar, 2nd edn., Cambridge University Press.
Bollobás, B. & Riordan, O. (2006), Percolation CrossRef | Google Scholar, Cambridge University Press.
Broadbent, S. & Hammersley, J. (1957), Percolation processes I. Crystals and mazes, Proceedings of the Cambridge Philosophical Society 53 CrossRef | Google Scholar, 629–641.
Campbell, N. (1909), The study of discontinuous phenomena, Mathematical Proceedings of the Cambridge Philosophical Society 15 Google Scholar, 117–136.
Cressie, N. (1993), Statistics for Spatial Data Google Scholar, revised edn., Wiley.
Daley, D. J. & Vere-Jones, D. (2003), An Introduction to the Theory of Point Processes, Volume I: Elementary Theory and Methods Google Scholar, 2nd edn., Springer.
Daley, D. J. & Vere-Jones, D. (2008), An Introduction to the Theory of Point Processes, Volume II: General Theory and Structure CrossRef | Google Scholar, 2nd edn., Springer.
Dhillon, H. S., Ganti, R. K., Baccelli, F. & Andrews, J. G. (2012), Modeling and analysis of K-tier downlink heterogeneous cellular networks, IEEE Journal on Selected Areas in Communications 30 CrossRef | Google Scholar(3), 550–560.
Dousse, O., Franceschetti, M., Macris, N., Meester, R. & Thiran, P. (2006), Percolation in the signal-to-interference ratio graph, Journal of Applied Probability 43 CrossRef | Google Scholar(2), 552–562.
Durrett, R. (1985), Some general results concerning the critical exponents of percolation, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 69 CrossRef | Google Scholar, 421–437.
Fekete, M. (1923), Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahigen Koeffizienten, Mathematische Zeitschrift 17 CrossRef | Google Scholar(1), 228–249.
Fortuin, C. M., Kasteleyn, P. W. & Ginibre, J. (1971), Correlation inequalities on some partially ordered sets, Communications in Mathematical Physics 22 CrossRef | Google Scholar(2), 89–103.
Franceschetti, M. & Meester, R. (2007), Random Networks for Communication: From Statistical Physics to Information Systems Google Scholar, Cambridge University Press.
Franceschetti, M., Booth, L., Cook, M., Bruck, J. & Meester, R. (2005), Continuum percolation with unreliable and spread out connections, Journal of Statistical Physics 118 CrossRef | Google Scholar(3/4), 721–734.
Ganti, R. K. & Haenggi, M. (2007), Dynamic connectivity and packet propagation delay in ALOHA wireless networks, in 41st Asilomar Conference on Signals, Systems, and Computers (Asilomar '07) Google Scholar, Pacific Grove, CA.
Ganti, R. K. & Haenggi, M. (2009a), Interference and outage in clustered wireless ad hoc networks, IEEE Transactions on Information Theory 55 CrossRef | Google Scholar(9), 4067–4086.
Ganti, R. K. & Haenggi, M. (2009b), Spatial and temporal correlation of the interference in ALOHA ad hoc networks, IEEE Communications Letters 13 CrossRef | Google Scholar(9), 631–633.
Ganti, R. K. & Haenggi, M. (2012), Dynamic connectivity and path formation time in Poisson networks, The Journal of Mobile Communication, Computation and Information Google Scholar, http://www.nd.edu/~mhaenggi/pubs/winet12.pdf.
Ganti, R. K., Andrews, J. G. & Haenggi, M. (2011), High-SIR transmission capacity of wireless networks with general fading and node distribution, IEEE Transactions on Information Theory 57 CrossRef | Google Scholar(5), 3100–3116.
Georgii, H.-O. (1976), Canonical and grand canonical Gibbs states for continuum systems, Communications in Mathematical Physics 48 CrossRef | Google Scholar(1), 31–51.
Giacomelli, R., Ganti, R. K. & Haenggi, M. (2011), Outage probability of general ad hoc networks in the high-reliability regime, IEEE/ACM Transactions on Networking 19 CrossRef | Google Scholar(4), 1151–1163.
Grandell, J. (1976), Doubly Stochastic Poisson Processes CrossRef | Google Scholar, Springer.
Grimmett, G. (1999), Percolation CrossRef | Google Scholar, 2nd edn., Springer.
Haenggi, M. (2008a), A geometric interpretation of fading in wireless networks: theory and applications, IEEE Transactions on Information Theory 54 CrossRef | Google Scholar(12), 5500–5510.
Haenggi, M. (2008b), The secrecy graph and some of its properties, in 2008 IEEE International Symposium on Information Theory (ISIT '08), Toronto Google Scholar.
Haenggi, M. (2009), Outage, local throughput, and capacity of random wireless networks, IEEE Transactions on Wireless Communications 8 CrossRef | Google Scholar(8), 4350–4359.
Haenggi, M. (2011), Mean interference in hard-core wireless networks, IEEE Communications Letters 15 CrossRef | Google Scholar(8), 792–794.
Haenggi, M. & Ganti, R. K. (2008), Interference in Large Wireless Networks Google Scholar, NOW.
Hall, P. (1985), On the coverage of k-dimensional space by k-dimensional spheres, The Annals of Probability 13 CrossRef | Google Scholar(3), 991–1002.
Harris, T. E. (1960), A lower bound on the critical probability in a certain percolation process, Mathematical Proceedings of the Cambridge Philosophical Society 56 CrossRef | Google Scholar, 13–20.
Heinrich, L. & Schmidt, V. (1985), Normal convergence of multidimensional shot noise and rates of this convergence, Advances in Applied Probability 17 CrossRef | Google Scholar(4), 709–730.
Illian, J., Penttinen, A., Stoyan, H. & Stoyan, D. (2008), Statistical Analysis and Modeling of Spatial Point Patterns Google Scholar, Wiley.
Ilow, J. & Hatzinakos, D. (1998), Analytical alpha-stable noise modeling in a Poisson field of interferers or scatterers, IEEE Transactions on Signal Processing 46 CrossRef | Google Scholar(6), 1601–1611.
Isham, V. (1984), Multitype Markov point processes: some approximations, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 391 Google Scholar, 39–53.
Jacobsen, M. (2006), Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes Google Scholar, Birkhäuser.
Janson, S., Luczak, T. & Rucinski, A. (2000), Random Graphs CrossRef | Google Scholar, Wiley-Interscience.
Kesten, H. (1980), The critical probability of bond percolation on the square lattice equals 1/2, Communications in Mathematical Physics 74 CrossRef | Google Scholar(1), 41–59.
Kingman, J. F. C. (1978), Uses of exchangeability, The Annals of Probability 6 CrossRef | Google Scholar(2), 183–197.
Kingman, J. F. C. (1993), Poisson Processes Google Scholar, Oxford Science Publications.
Lee, C.-H. & Haenggi, M. (2012), Interference and outage in Poisson cognitive networks, IEEE Transactions on Wireless Communications 11 CrossRef | Google Scholar(4), 1392–1401.
Lindvall, T. (2002), Lectures on the Coupling Method Google Scholar, Dover Publications.
Linnartz, J.-P. M. G. (1992), Exact analysis of the outage probability in multiple-user radio, IEEE Transactions on Communications 40 CrossRef | Google Scholar(1), 20–23.
Lowen, S. B. & Teich, M. C. (1990), Power-law shot noise, IEEE Transactions on Information Theory 36 CrossRef | Google Scholar(6), 1302–1318.
Matérn, B. (1986), Spatial Variation CrossRef | Google Scholar, 2nd edn., Springer.
Mathai, A. M. (1999), An Introduction to Geometrical Probability Google Scholar, Gordon and Breach Science Publishers.
Mathar, R. & Mattfeldt, J. (1995), On the distribution of cumulated interference power in Rayleigh fading channels, Wireless Networks 1 CrossRef | Google Scholar(1), 31–36.
Matthes, K., Kerstan, J. & Mecke, J. (1978), Infinitely Divisible Point Processes Google Scholar, John Wiley & Sons.
Meester, R. & Roy, R. (1996), Continuum Percolation CrossRef | Google Scholar, Cambridge University Press.
Musa, S. & Wasylkiwskyj, W. (1978), Co-channel interference of spread spectrum systems in a multiple user environment, IEEE Transactions on Communications 26 CrossRef | Google Scholar(10), 1405–1413.
Newman, D. S. (1970), A new family of point processes which are characterized by their second moment properties, Journal of Applied Probability 7 CrossRef | Google Scholar(2), 338–358.
Newman, M. E. J. & Ziff, R. M. (2000), Fast Monte Carlo algorithm for site or bond percolation, Physical Review Letters 85 Google Scholar(19), 4104–4107.
Neyman, J. & Scott, E. L. (1952), A theory of the spatial distribution of galaxies, Astrophysical Journal 116 CrossRef | Google Scholar, 144–163.
Neyman, J. & Scott, E. L. (1958), Statistical approach to problems of cosmology, Journal of the Royal Statistical Society, SeriesB 20 Google Scholar(1), 1–43.
Nguyen, X. X. & Zessin, H. (1979), Integral and differential characterization of the Gibbs process, Mathematische Nachrichten 88 Google Scholar, 105–115.
Peierls, R. (1936), On Ising's model of ferromagnetism, Mathematical Proceedings of the Cambridge Philosophical Society 32 CrossRef | Google Scholar, 477–481.
Penrose, M. (2003), Random Geometric Graphs CrossRef | Google Scholar, Oxford University Press.
Rényi, A. (1967), Remarks on the Poisson process, Studia Scientifica Mathematica Hungarica 2 Google Scholar, 119–123.
Rice, S. O. (1944), Mathematical analysis of random noise, Bell System Technical Journal 23 CrossRef | Google Scholar, 282–332.
Ripley, B. D. (1976), The second-order analysis of stationary point processes, Journal of Applied Probability 13 CrossRef | Google Scholar, 255–266.
Samorodnitsky, G. & Taqqu, M. S. (1994), Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance Google Scholar, Chapman & Hall.
Sarkar, A. & Haenggi, M. (2011 Google Scholar), Percolation in the secrecy graph. ArXiv, http://arxiv.org/abs/1107.4613.
Sarkar, A. & Haenggi, M. (2012), Secrecy coverage, Internet Mathematics Google Scholar. Available at http://www.nd.edu/~mhaenggi/pubs/im12.pdf.
Schottky, W. (1918), Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern, Annalen der Physik 57 Google Scholar, 541–567.
Sousa, E. S. (1990), Interference modeling in a direct-sequence spread-spectrum packet radio network, IEEE Transactions on Communications 38 CrossRef | Google Scholar(9), 1475–1482.
Sousa, E. S. & Silvester, J. A. (1990), Optimum transmission ranges in a direct-sequence spread-spectrum multihop packet radio network, IEEE Journal on Selected Areas in Communications 8 CrossRef | Google Scholar(5), 762–771.
Spencer, J. (2001), The Strange Logic of Random Graphs CrossRef | Google Scholar, Springer.
Srinivasa, S. & Haenggi, M. (2010), Distance distributions in finite uniformly random networks: theory and applications, IEEE Transactions on Vehicular Technology 59 CrossRef | Google Scholar(2), 940–949.
Stoyan, D., Kendall, W. S. & Mecke, J. (1995), Stochastic Geometry and its Applications Google Scholar, 2nd edn., John Wiley & Sons.
Takagi, H. & Kleinrock, L. (1984), Optimal transmission ranges for randomly distributed packet radio terminals, IEEE Transactions on Communications 32 CrossRef | Google Scholar(3), 246–257.
van Lieshout, M. N. M. (2000), Markov Point Processes and their Applications CrossRef | Google Scholar, Imperial College Press.
van Lieshout, M. N. M. (2011), A J-function for inhomogeneous point processes, Statistica Neerlandica 65 CrossRef | Google Scholar(2), 183–201.
van Lieshout, M. N. M. & Baddeley, A. J. (1996), A nonparametric measure of spatial interaction in point patterns, Statistica Neerlandica 50 Google Scholar(3), 344–361.
Walters, M. (2012), Small components in k-nearest neighbour graphs, Discrete Applied Mathematics Google Scholar.
Weber, S. & Andrews, J. G. (2012), Transmission Capacity of Wireless Networks Google Scholar, NOW.
Weber, S., Yang, X., Andrews, J. G. & de Veciana, G. (2005), Transmission capacity of wireless ad hoc networks with outage constraints, IEEE Transactions on Information Theory 51 CrossRef | Google Scholar(12), 4091–4102.
Westcott, M. (1972), The probability generating functional, Journal of the Australian Mathematical Society 14 CrossRef | Google Scholar, 448–466.
Zorzi, M. & Pupolin, S. (1995), Optimum transmission ranges in multihop packet radio networks in the presence of fading, IEEE Transactions on Communications 43 CrossRef | Google Scholar(7), 2201–2205.

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