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.
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Description of point processes
Point process models
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asymptotically binomial point process bond percolation Boolean model Borel branching process Campbell measure connected counting measure coverage Cox process critical probability deﬁned deﬁnition denote disk graph edges event Example ﬁeld ﬁnd ﬁrst ﬁxed follows Gibbs process given Haenggi hard-core process Hence independent inequality inﬁnite component inﬁnite open cluster intensity function intensity measure Laplace transform Lebesgue measure LEMMA marked point process Matérn mean number moment-generating function non-negative number of nodes number of points obtain open path Palm distribution percolation model pgﬁ point pattern point process theory Poisson distribution Poisson point process Poisson process PPP of intensity PPP with intensity process on Rd Proof radius random geometric graphs random measure random set random variables Rayleigh fading realization result second moment measure shot noise site percolation space spatial stationary point process stochastic geometry success probability sufﬁcient transmitter tree uniform PPP vertex vertices wireless networks