Stochastic Geometry for Wireless Networks

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.

[1]  S. Musa,et al.  Co-Channel Interference of Spread Spectrum Systems in a Multiple User Environment , 1978, IEEE Trans. Commun..

[2]  T. Bedford,et al.  A Remark on the Van Lieshout and Baddeley J-Function for Point Processes , 1997, Advances in Applied Probability.

[3]  Leonard Kleinrock,et al.  Optimal Transmission Ranges for Randomly Distributed Packet Radio Terminals , 1984, IEEE Trans. Commun..

[4]  B. Ripley.  The Second-Order Analysis of Stationary Point Processes , 1976 .

[5]  John A. Silvester,et al.  Optimum Transmission Ranges in a Direct-Sequence Spread-Spectrum Multihop Packet Radio Network , 1990, IEEE J. Sel. Areas Commun..

[6]  Jehoshua Bruck,et al.  Continuum Percolation with Unreliable and Spread-Out Connections , 2005 .

[7]  Martin Haenggi,et al.  Spatial and temporal correlation of the interference in ALOHA ad hoc networks , 2009, IEEE Communications Letters.

[8]  Martin Haenggi,et al.  Outage Probability of General Ad Hoc Networks in the High-Reliability Regime , 2010, IEEE/ACM Transactions on Networking.

[9]  Béla Bollobás,et al.  Random Graphs , 1985 .

[10]  Martin Haenggi,et al.  Secrecy coverage , 2010, 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers.

[11]  M. Westcott.  The probability generating functional , 1972, Journal of the Australian Mathematical Society.

[12]  J. Neyman,et al.  Statistical Approach to Problems of Cosmology , 1958 .

[13]  P. Thiran,et al.  Percolation in the signal to interference ratio graph , 2006, Journal of Applied Probability.

[14]  Malvin Carl Teich,et al.  Power-law shot noise , 1990, IEEE Trans. Inf. Theory.

[15]  Mark Walters.  Small components in k-nearest neighbour graphs , 2012, Discret. Appl. Math..

[16]  S. Rice.  Mathematical analysis of random noise , 1944 .

[17]  Jeffrey G. Andrews,et al.  High-SIR Transmission Capacity of Wireless Networks With General Fading and Node Distribution , 2011, IEEE Transactions on Information Theory.

[18]  J. Hammersley,et al.  Percolation processes , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.

[19]  V. Schmidt,et al.  NORMAL CONVERGENCE OF MULTIDIMENSIONAL SHOT NOISE AND RATES OF THIS CONVERGENCE , 1985 .

[20]  M. Newman,et al.  Efficient Monte Carlo algorithm and high-precision results for percolation. , 2000, Physical review letters.

[21]  Jeffrey G. Andrews,et al.  Transmission Capacity of Wireless Networks , 2012, Found. Trends Netw..

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

[23]  Martin Haenggi,et al.  Outage, local throughput, and capacity of random wireless networks , 2008, IEEE Transactions on Wireless Communications.

[24]  Valerie Isham,et al.  Multitype Markov point processes: some approximations , 1984, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[25]  Massimo Franceschetti,et al.  Random networks for communication : from statistical physics to information systems , 2008 .

[26]  H. Kesten.  The critical probability of bond percolation on the square lattice equals 1/2 , 1980 .

[27]  Rudolf Mathar,et al.  On the distribution of cumulated interference power in Rayleigh fading channels , 1995, Wirel. Networks.

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

[29]  M. Haenggi,et al.  Dynamic Connectivity and Packet Propagation Delay in ALOHA Wireless Networks , 2007, 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers.

[30]  D. Newman,et al.  A new family of point processes which are characterized by their second moment properties , 1970, Journal of Applied Probability.

[31]  Martin Haenggi.  The secrecy graph and some of its properties , 2008, 2008 IEEE International Symposium on Information Theory.

[32]  M. Newman,et al.  Fast Monte Carlo algorithm for site or bond percolation. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[34]  Hans-Otto Georgii,et al.  Canonical and grand canonical Gibbs states for continuum systems , 1976 .

[35]  B. Bollobás,et al.  Continuum percolation with steps in the square or the disc , 2005, Random Struct. Algorithms.

[36]  F. Baccelli,et al.  Optimal paths on the space-time SINR random graph , 2009, Advances in Applied Probability.

[37]  M.N.M. van Lieshout,et al.  A J-function for inhomogeneous point processes , 2010, 1008.4504.

[38]  R. Peierls.  On Ising's model of ferromagnetism , 1936, Mathematical Proceedings of the Cambridge Philosophical Society.

[39]  Dimitrios Hatzinakos,et al.  Analytic alpha-stable noise modeling in a Poisson field of interferers or scatterers , 1998, IEEE Trans. Signal Process..

[40]  A. Baddeley,et al.  A cautionary example on the use of second-order methods for analyzing point patterns , 1984 .

[41]  J. Neyman,et al.  A theory of the spatial distribution of galaxies , 1952 .

[42]  Daryl J. Daley,et al.  An Introduction to the Theory of Point Processes , 2013 .

[43]  François Baccelli,et al.  An Aloha protocol for multihop mobile wireless networks , 2006, IEEE Transactions on Information Theory.

[44]  Martin Haenggi,et al.  Distance Distributions in Finite Uniformly Random Networks: Theory and Applications , 2008, IEEE Transactions on Vehicular Technology.

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

[46]  J. Kingman.  Uses of Exchangeability , 1978 .

[47]  Mathew D. Penrose,et al.  Random Geometric Graphs , 2003 .

[48]  Peter Hall.  On the Coverage of $k$-Dimensional Space by $k$-Dimensional Spheres , 1985 .

[49]  Martin Haenggi.  A Geometric Interpretation of Fading in Wireless Networks: Theory and Applications , 2008, IEEE Transactions on Information Theory.

[50]  Martin Haenggi,et al.  Interference and Outage in Clustered Wireless Ad Hoc Networks , 2007, IEEE Transactions on Information Theory.

[51]  Jean-Paul M. G. Linnartz,et al.  Exact analysis of the outage probability in multiple-user mobile radio , 1992, IEEE Trans. Commun..

[52]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[53]  Michele Zorzi,et al.  Optimum transmission ranges in multihop packet radio networks in the presence of fading , 1995, IEEE Trans. Commun..

[54]  van Marie-Colette Lieshout,et al.  Markov Point Processes and Their Applications , 2000 .

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

[56]  J. Grandell.  Doubly stochastic Poisson processes , 1976 .

[57]  A. Baddeley,et al.  A non-parametric measure of spatial interaction in point patterns , 1996, Advances in Applied Probability.

[58]  B. Bollobás,et al.  Connectivity of random k-nearest-neighbour graphs , 2005, Advances in Applied Probability.

[59]  T. Lindvall.  Lectures on the Coupling Method , 1992 .

[60]  M. Haenggi,et al.  Interference in Large Wireless Networks , 2009, Found. Trends Netw..

[61]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[62]  M. Jacobsen.  Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes , 2005 .

[63]  A. Baddeley,et al.  Area-interaction point processes , 1993 .

[64]  Svante Janson,et al.  Random graphs , 2000, ZOR Methods Model. Oper. Res..

[65]  T. E. Harris.  A lower bound for the critical probability in a certain percolation process , 1960, Mathematical Proceedings of the Cambridge Philosophical Society.

[66]  C. Fortuin,et al.  Correlation inequalities on some partially ordered sets , 1971 .

[67]  Martin Haenggi,et al.  Dynamic connectivity and path formation time in Poisson networks , 2013, Wireless Networks.

[68]  Béla Bollobás,et al.  Sentry Selection in Wireless Networks , 2010, Advances in Applied Probability.

[69]  W. Schottky.  Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern , 1918 .

[70]  M. Taqqu,et al.  Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance , 1995 .

[71]  R. Durrett.  Some general results concerning the critical exponents of percolation processes , 1985 .

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

[73]  J. Spencer.  The Strange Logic of Random Graphs , 2001 .

[74]  M. Fekete.  Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten , 1918 .

[75]  E. CastroPeter,et al.  Infinitely Divisible Point Processes , 1982 .

[76]  Andrew D. Barbour,et al.  Stein's Method And Applications , 2005 .

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

[78]  B. Bollobás,et al.  Continuum percolation with steps in an annulus , 2004, math/0503544.

[79]  Jeffrey G. Andrews,et al.  Transmission capacity of wireless ad hoc networks with outage constraints , 2005, IEEE Transactions on Information Theory.

[80]  A. Rényi.  Remarks on the Poisson process , 1967 .

[81]  Hans Zessin,et al.  Integral and Differential Characterizations of the GIBBS Process , 1979 .

[82]  Elvino S. Sousa,et al.  Interference modeling in a direct-sequence spread-spectrum packet radio network , 1990, IEEE Trans. Commun..